Atomic Energy of Canada Limited
A PROGRAM FOR NUCLEAR PHYSICS IN THE SEVENTIES AND BEYOND
Edited by
J.C. HARDY, A.B. McDONALD and J.C.D. MILTON
Chalk River Nuclear Laboratories Chalk River, Ontario September 1973 v AECL-4596 Atomic Energy of Canada Limited
A PROGRAM FOR NUCLEAR PHYSICS Us' THE SEVENTIES AND BEYOND*
edited by
J.C. Hardy A.B. McDonald and J.C.D. Milton
ABSTRACT
This report discusses a possible research program for the Nuclear Physics tsror>ch in the second half of this decade and beyondA- a program which,if followed, would undoubtedly expand the boundaries of our knowledge "several fold, but more than that, a program that seems likely to lead to fundamentally new and exciting discoveries. The core of the discussion is contained in Chapter II. which reviews the prospects in nine major areas: li nuclei far from the region of beta stability, 2) superheavy nuclei. 3) fission. 4) in-beam studies of electromagnetic properties, 5| heavy ion scattering. 6| transfer reactions with heavy ions. 7) studies with light ion beams. Hi ranges and stopping powers of heavy ions, ard atomic collisions, and 9| fundamental interactions and symmetries The material from thir. chapter leads to the view that the future looks very bright in fields which could he studied with higher energy beams, particularly of heavy ions, in Chapter III the types of beams, and the energy and resolution required to carry out all aspects of the proposed programs are specified and l^ad to the conclusions that a desirable accelerator would be able to produce beams of all ions from hydrogen to uranium with energies variable up to 300 MeY for hydrogen and 10 MeV/nucleon for uranium, with a resolution of 0.01';. A brief discussion is given in Chapter IV of three possible additions to the MP Tandem that would meet all these requirements. The final Chapter. Chapter V. reviews the experimental equipment and data handling facilities that would be necessary to cany out the proposed program in an efficient manner. Much of this aneilliary equipment already exists at the MP Tandem installation.
Chalk River Nuclear Laboratories Chalk River, Ontario September 1973
AECL-4596
* This report is based on the Atomic Energy of Canada Limited unpublished internal report CRNL-714, manuscript prepared February 1972, printed October 1972. Programme de physique nucléaire pour les années 1970 et au-delà*
édité par
J.C. Hardy A.B. McDonald et J.C.D. Milton
Résume
On envisage un programme de recherches possibles pour le Département de physique nucléaire dans la deuxième partie de la présente décennie et au-delà, programme qui pourrait certainement enrichir nos connaissances et qui semble susceptible de conduirp à des découvertes passionnantes. L'essentiel de la proposition figure dans le Chapitre II qui passe en revue les possibilités offertes dans neuf domaines principaux: 1) noyaux éloignés de la région de stabilité béta, 2) noyaux extrêmement lourds, 3) fission, 4) étude sous faisceaux des propriétés électromagnétiques, 5) diffusion des ions lourds, 6) réactions de transfert avec des ions lourds, 7) études effectuées avec des faisceaux d'ions légers, 8) gammes et puissances d'arrêt des ions lourds et collisions atomiques et 9) interactions fondamentales et symétries. Les données de ce chapitre permettent de conclure que l'avenir se présente sous un jour très favorable dans les domaines qui pourraient être étudiés avec des faisceaux d'énergie supérieure, particulièrement ceux d'ions lourds. Dans le Chapitre III, les espèces de faisceaux, l'énergie et la résolution requises pour réaliser tous les aspects des programmes proposés sont spécifiées et laissent à penser que l'accélérateur souhaitable devrait pouvoir produire des faisceaux de tous les ions depuis l'hydrogène jusqu'à l'uranium avec des énergies variables allant jusqu'à 300 MeV pour l'hydrogène et 10 MeV/ nucléon pour l'uranium, avec une résolution de 0.01%. On commente brièvement au Chapitre IV les trois additions possibles au Tandem MP qui répondraient à toutes ces exigences. Le dernier chapitre, le Chapitre V, passe en revue le matériel expérimental et les dispositifs de traitement des données qui seraient nécessaires pour réaliser le programme proposé de façon efficace. Une grande partie de cet équipement auxiliaire existe déjà dans l'accélérateur Tandem MP.
L'Energie Atomique du Canada, Limitée Laboratoires Nucléaires de Chalk River Chalk River, Ontario
Septembre 1973 AECL-4596
* Rapport découlant du document CRNL-714, rapport interne de l'EACL dont le manuscrit a eie préparé en février 1972 et imprimé en octobre 1972 INTRODUCTION
SOME AREAS IN WHICH NEW AND EXCITING DEVELOPMENTS ARE LIKELY
0. Summary 9 1. The Study of Nuclei Far from the Region of Beta Stability : Z < Q0 A. Introduction 13 B. Specific Problems of Future Interest 14 a) Beta-delayed Particle Emission 14 b) Beta-delayed Nuclear Fission 14 c) New Radioactivities 15 d) Nuclear Masses and the Boundary of Stability 15 e) Nucleosynthesis, Exolic Nuclei and Other Astrophysical Considerations 16 0 Double Beta-decay 1(> g) Beta-decay at High Energies 16 h) Mirror Nuclei 1 ft i) Nuclear Structure 17 C. Production Techniques and Requirements 17 a) Compound Nuclear Reactions 17 b) Transfer Reactions i1) c) Heavy-Ion Induced Fission 21 d) Summary' 27 References 22
2. Superheavy Nuclei A. Introduction 27 B. Properties 27 C. Production -'1 D. Detection 53 E. Summary 34 References 34
3. Fission A. Introduction and Survey 3° B. Coulomb Fission 40 C. Intermediate Structure 41 D. Fission Isomers 43 References 43 4 In-beam Studies of Electromagnetic Properties of Nuclei 47 A. Introduction B. Pertinent Problems in Nuclear Structure 47_ a) Vibrational Nuclei ' b) Rotational Nuclei (Even A) 4^ c) Closed Shell Nuclei 48 C. Reaction Mechanisms a) Compound-Nucleus Reactions 48 b) Transfer Reactions 49 D. Experimental Techniques '" a) Nuclear-Lifetime Measurement Using the Recoil-Distance Method (RDM) 50 b) Nuclear-Lifetime Measurement Using the Doppler-Shift-Attenuation Method (DSAM) 51 c) Angluar-Distribution Studies Following Heavy-Ion Reactions 52 d) g-Factors of Excited Nuclear Levels 53 E. Beam Requirements 53 References 53 5. Heavy-Ion Elastic and Inelastic Scattering A. Introduction 57 B. Optical Model Analysis 57 C. Microscopic Theories 58 D. Experimental Requirements 60 References (,3
6. Transfer Reactions with Heavy Ions A. Introduction 67 B. Nucleon Exchange in Heavy-Ion Scattering 67 C. Few-Nucleon Transfer Reactions 68 D. Multi-Nucleon Transfer Reactions 69 E. The Nuclear "Josephson" Effect -ji
References 7?
7. Studies with Light-Ion Beams A. Introduction -,-, B. Nudeon-Nucleon Scattering 77 C. Many-Body Final States gO D. Quasi-Free Scattering on Nuclei gi E. Meson Production in Nuclei g-j F. Summary References 84 8. Ranges, Stopping Powers and Atomic Collisions
Part 1: Ranges and Stopping Powers of Heavy Ions A. Introduction 89 B. Applications and Inadequacies 89 a) Coulomb Excitation 89 b) Doppler-Shift Measurements 90 C. Future Development 91 Part 2: Properties of United Atoms 92 References 92
9. Fundamental Interactions and Symmetries A. Introduction 95 B. Strong Interactions 95 a) Nucleon-Nucleon Scattering 95 b) Symmetries in Nuclei and Nuclear Reactions 96 C. Nuclear Gamma Decay 99 a) Time-Reversal Invariance 99 b) Parity Violation 100 c) E.M. Studies oflsospin Symmetries 100 d) Exchange Currents 101 D. Nuclear Beta Decay 101 a) Weak Interactions 102 b) Induced Interactions 102 c) Fundamental Nuclear Properties 104
References 105
HI. SUMMARY OF OPTIMUM ACCELERATOR PROPERTIES
1. Introduction 111 2. Mass and Energy Range of Projectiles 111 3. Energy Resolution 111 4. Current and Emittance 113 References "3 IV. SOME HEAVY ION ACCELERATORS 1. Introduction H7 2. The MD Tandem Van de Graaff as a Preaccelerator 117 3. A Helix Linear Accelerator for Heavy Ions 118 4. A Heavy-Ion Cyclotron 118 5. A Heavy-Ion Synchrotron 120 References ! -3 V. EXPERIMENTAL FACILITIES AND TECHNIQUES
1. Introduction '^' 2. Computing Facilities A. Introduction '^8 B. Detailed Description I28 3. Target-Making Facilities <29 A. Solid Targets '29 B. Differentially Pumped Gas Target 130 4. Gamma-Ray Detection 130 5. Beta-Ray Detection 130 6. Charged Particle Detectiun and Identification 13 i A. Introduction 131 B. Solid State Detectors 131 C. QD1 Magnetic Spectrometer 132 D. Particle Identification 133 a) Solid-State Counter Telescopes 133 b) QD3 Magnetic Spectrometer 134 7. Beam-Pulsing Facility ]35 8. Isotope Separator 136 9. Polarized Beams and Targets 136 References j^g A PROGRAM FOR NUCLEAR PHYSICS IN THE SEVENTIES AND BEYOND
PREFACE
This report is an attempt to answer the question, "What are the most interesting, important and valuable thUigs tha1 could be done by the nuclear Physics Branch in the seventies?" The answer is based soundly on th.> knowledge and interests of the members of the Branch. No attempt has been made to survey fields in nuclear physics outside the existing areas of competence of the Branch. However no further restrictions were placed on the authors. A program following the suggestions in this report would thtrefore be a logical and natural extension of the present program and would be securely based on tht existing expertise and equipment The relevance of such a program to the objectives of AECL and ,he means of implementing it have not been discussed at this time; such things will come later. Nevertheless, to indicate that the program is a realistic one, a brief discussion is given of three possible additions to the MP Tandem, any one of which might satisfy the requirements, which are' the ability to provide beams of all ions from protons to uranium (or heavier) with energies up to 300 MeV for protons, greater than 10 MeV/nucleon for uranium and with intensities greater than ~ 1012 particles per second. A facility with these capabilities would be unique in the world. Furthermore, the existing MP Tandem with high-gradient tubes provides an ideal first-stage accelerator, o le which would likely be selected wherever such a facility were planned. This presents an enormous local advantage. AUTHORS
The following members of the Nuclear Physics Branch bore major responsibilities for specific sections:
H.R. Andrews (II-2, V-9) G.C. Ball (III, V-6) W.G. Davies (II-7) A.J. Ferguson (II-5) J.S. Forster (IJ-6) J.S. Geiger (II-4, II-8, V-5) R.L. Graham (II-4, II-8, V-5) J.C. Hardy (I, H-l, HI, V-8) O. Hausser (II-9) A.B. McDonald (II-2, V) J.C.D. Milton (II-3) D. Ward (II-4)
In addition, contributions were made by people from other branches. These included:
J.A. Davies (II-8-D) J.S. Fraser (IV) M. Harvey (II-5) F.C. Khanna (II-7,11-9) H.C. Lee (II-7) H.R. Schneider (IV) I.S. Towner (II-9-D) Chapter I. INTRODUCTION In nuclear physics, both our understanding of the cost; each would provide a facility which in its physical phenomena and tht techniques available for versatility and energy range was unique in the world. probing them have developed with amazing speed. It The study of nuclear phenomena plays a pivotal is only seventy-five years since the first observation of role in man's attempt to understand the physical radioactivity, sixty years since the discovery of the world. It is an essential link between physical nucleus, and twenty years since the first mode! was observables and the fundamental laws and symmetries proposed which could explain its gross properties. which we require to explain them. While elementary- And now we are on the threshold of relating the particle physics is concerned primarily with the properties of nuclei to the "fundamental" inter- properties of individual particles, and solid-state actions between nucleons. It is only forty years since physics, for example, deals with the collective the first particle accelerators were invented and built, behaviour of enormous numbers, it is nuclear physics and a mere fifteen years since there have been usable which explores the interactions among moderate but accelerated beams of ions heavier than helium. And precisely known numbers of individual particles. Here now it is technically feasible to accelerate all ions the effects of fundamental principles can still be seen including uranium up to energies which are sufficient but they are beginning to submerge into collective or to surmount the Coulomb barrier of any stable target. statistical behavour. It is the nature of this transition Now at last it is possible for nuclear physicists — and between the fundamental and the collective which is scientists in related fields — to ask themselves what problems are intrinsically most interesting and the central concern of nuclear physicists. Its impor- relevant, not just within the limitations of existing tance cannot be overemphasized since it is not only accelerators but bounded only by the extent of their necessary for the true understanding of observed own ingenuity. phenomena but it also provides the means by which physical principles can be used to the benefit of What are the fundamental questions in Nuclear mankind. Nuclear power is a proven and particularly Physics? Where are future breakthroughs likely to relevant example; furthermore, it will be shown in occur1? Of course, no one can answer these ques- section H-3 of this report that it is not impossible to tions with certainty, but in the following chapters we hope for improvement in use of the fission process advance some suggestions. This is not a proposal in the following the observation and study of superheavy usual sense: we are not proposing the construction of nuclei. a specific accelerator. Instead, we have attempted to One of the chief strengths that nuclear physics has examine the field of nuclear physics and indi- in the study of many-body phenomena is the fact cate in chapter II those areas which appear most that the number of particles, or nucleons, in nuclei likely to be fruitful in the future. Based on this exami- being studied can be readily varied from two to nation, we determine those characteristics which an several hundred. This parameter variability is a very ideal accelerator must have to make it capable of important asset in isolating the properties attributable meeting all foreseeable needs. Significantly, these to either individual or collective effects. An equally characteristics, which are summarized In chapter III, important parameter to be able to vary is the relative need not be compromised but they can in fact be numbers of charged and uncharged nucleons — pro- completely realized by current technology. We des- cribe in chapter IV several different types of accele- tons and neutrons. In the past we have been largely rators which could meet our criteria at very modest restricted in our freedom to vary this parameter: we could only study properly those nuelei which were
-1- quite close in N and Z to stable isotopes'. Clearly this section II-8, they are closely related to it — one as a is an unsatisfactory situation. The variation of N and measurement technique and the other as a parti- Z must be understood individually before the signifi- cularly exciting means of studying the atomic cance of changing A can be comprehended, structure which corresponds to exotic nuclei. The particularly since for stable nuclei the ratio N/Z is not authors' primary concern in this report has been to constant as A increases. In sections II-l and II-2 we examine the fruitful advance of nuclear physics. explore in more detail the significance of producing However, any facilities built in the future as a result nuclei in new regions of A, Z or N. In addition to the of subgestions made here would certainly not be increased flexibility for systematic studies, quite new confined to applications in nuclear physics, any more phenomena are expected to >x:cur, many with far- than such facilities have been so confined in the past. reaching results in testing current theories and We do believe, though, that the most convincing producing new ones. Some of the more important arguments for applications in fields such as Solid tests are explained fully in section II-9. State Physics, Chemistry, Material Science, Biology and Medicine are made by those now active in such As an aid to understanding the many-body fields. properties of nuclei, models are created which in their simplest form merely systematize observed data, but A strong spirit of cooperation with scientists in as they become more sophisticated these models other fields and from other institutions has been built embody all we know of the relation between nuclear at Chalk River. V,e interaction that accompanies properties and fundamental interactions. As a result, sharing the MP tandem and other CRNL2 facilities much of the effort today in nuclear physics is with scientists from universities in the neighbouring expended either in refining the theoretical picture of geographical region is particularly valued for its effect such models or in experimentally testing their pre- in enriching and broadening the scientific life and dictions. Often, though, several conceptually capabilities of the laboratory. It is anticipated that different models may coincide very closely in their these regional ties would be maintained and strength- predictions for certain observable properties. Thus, in ened if upgraded facilities for advanced Nuclear addition to extending ouf investigations to the new Physics research were installed here, and this report regimes already described we must ensure the ability has been written with such relationships very much in to make very precise measurements in all regions mind. Expertise in the design, construction and use of including the ones with which we are now partially an accelerator exists at Chalk River, together with familiar. The questions involved in the testing of much sophisticated experimental equipment Thus, nuclear models are discussed in sections II-4, II-5 and the establishment of upgraded facilities for a new II-6 where it is shown that many benefits would generation of research could, we feel, be done most follow from the production of heavy-ion beams with easily here; the reasons for this belief should become higher energy and greater mass than are available clear in the reading of Chapters IV and V. However, now. the advance of nuclear physics will be best served by involving the largest number of university scientists in Of course, our understanding of the relationship the conceptual planning and use of such new between the nucleus as a whole and the basic facilities interactions among its constituent nucleons depends not only upon an accurate model but upon a detailed It is the future of nuclear physics that is the knowledge of those interactions themselves. Such a subject of this report. But it is the present from knowledge can best be gained by examining systems which we must derive our perspectives. We have tried which involve a very few nucleons. The conditions to extrapolate from current knowledge to future which best suit this purpose are discussed in section discoveries, and from current experience to future 11-7 where a number of possible directions for study interests knowing that, while these are important are suggested. links which are essential to sound development, they Although several topics which are not, strictly are not sufficient in themselves. They must be speaking, part of nuclear physics are discussed in accompanied by a genuine expansion into unknown fields, for if opportunities do not exist to make new ana surprising discoveries then the thrill which The number of protons is denoted by Z, neutrons by N and total nucleons by A = N + Z. CRNL — Chalk River Nuclear Laboratories
-2- inspires research will be lost This aspect of our study of nuclei as yet unknown — in principle, the number is the most difficult to convey succinctly to the of observed nuclei could be increased at least by a reader since it amounts to saying that despite a factor of five over the present! That fundamentally detailed study of future possibilities, the most different phenomena are expected nan ly seems exciting developments will probably be unforeseen. necessary to state. But with such an expansion of the An accelerator capable of producing all projectiles up field of study, what of the unexpected? It is with the to uranium at energies well above the Coulomb excitement of that question that this report has been barrier would be a fantastically powerful machine. It written. could be used, for example, to obtain a vast number
-3- Chapter II. SOME AREAS IN WHICH NEW AND EXCITING DEVELOPMENTS ARE LIKELY
0. SUMMARY 1. THE STUDY OF NUCLEI FAR FROM THE REGION OF BETA STABILITY: Z « 92 2. SUPERHEAVY NUCLEI 3. FISSION 4. IN-BEAM STUDIES OF ELECTROMAGNETIC PROPERTIES OF NUCLEI 5. HEAVY ION ELASTIC AND INELASTIC SCATTERING 3. TRANSFER REACTIONS WITH HEAVY IONS 7. STUDIES WITH LIGHT ION BEAMS 8. RANGES, STOPPING POWERS AND ATOMIC COLLISIONS 9. FUNDAMENTAL INTERACTIONS AND SYMMETRIES 0. SUMMARY This chapter discusses in detail nine significant and Fission: Heavy ions as projectiles can be used to important areas in which new and exciting develop- prepare fissioning states of specific character in order ments in nuclear physics, or intimately related to examine the properties of the fission process. subjects, are likely. Brief summaries of these discus- Heavy ions provide the ideal way of exciting collec- sions are given below. From them it is clear that the tive modes and in addition can transfer large amounts areas selected cover a very large part of nuclear of angular momentum, thus controlling two valuable physics and that a program of study, even in only a parameters. The phenomenon of Coulomb fission, few of them, could make major contributions to our which as yet has not been observed, could provide knowledge. high specificity through a well-understood reaction mechanism. Also, the new-found ability to enlarge Study of Nuclei Far from the Region of Beta the region of nuclear study could dramatically Stability: Of the more than 7000 nuclei predicted to increase the number of known fissioning nuclei to exist with identifiable ground states only 7% have include superheavy nuclei as well as those which been studied adequately. With high-energy heavy-ion undergo 0-delayed fission. All these advances would beams any nucleus could in principle be produced by lead to improvements in the understanding and bombardment, thus giving freedom to study whatever possibly the harnessing of the fission process. nuclei best illustrate specific problems. Fields of particular interest include: /3-delayed particle Electromagnetic Properties of Nuclei: Since the emission; ^-delayed fission, protor, double-proton nature of electromagnetic forces is well understood, and double-neutron radioactivity; extended nuclear studying nuclear electromagnetic properties is one of mass measurements; double (3-decay; tests of weak- the best ways to probe the accuracy of nuclear interaction theory involving high-energy (3-decays; models. Such studies have been an important part of examination of nuclear symmetries by comparisons the Chalk River experimental progra.i for many of mirror nuclei; and systematic studies of nuclear- years. Improvements in scope and accuracy would model predictions for wide variations in N and Z, follow from making available a wide selection of including new regions of deformed nuclei. It is of heavy projectiles at higher energies. These would equal significance that the production of nuclei far include: selective production of new nuclei; Coulomb from ^-stability would open for study a funda- excitation of high-spin states; the study of multiple mentally new nuclear regime with all the potential for and higher-order processes in Coulomb excitation; the discovery which accompanies the breaking of new study of Coulomb distortion; measurement of pre- ground. viously inaccessible nuclear lifetimes; alignment of high-spin states: and the measurement of g-factors for Production and Study of Superheavy Elements: short lived nuclear levels. Nuclear theories predict a new region of nearly stable elements near atomic number 114 and suggest that Heavy-Ion Elastic and Inelastic Scattering: Studies these elements may be most easily produced by of these mosl basic reaction processes may be nuclear reactions with high-energy heavy ions. Studies expected to lead to a better understanding of the in this completely new region of the periodic table interactions between large but finite numbers of may be expected to enrich greatly our knowledge of nucleons. Such interactions are fundamentally impor- nuclear and atomic physics. The chemical properties tant to the fission process, the structure of heavy of these elements are difficult to predict and their nuclei and heavy-ion reactions in general. atomic structure is expected to reflect the effects of non-linear electrodynamics induced by their large Transfer Reactions with Heavy Ions: Higher nuclear charge. The nuclear properties observed in energy beams of a wide variety of ions would readily this region will test present theories of nuclear permit the study of reactions transferring one, two or structure, fission and heavy-ion reaction mechanisms. many nucleons, and in most cases the same transfer The unusual fission properties expected for these could be studied from the same target with many nuclei, involving twice the energy released in fission different projectiles. This could be used to eliminate of the actinides and five times the number of projectile-dependent effects and illuminate more neutrons per fission, suggest far-reaching applications clearly the reaction mechanism. Once established, the if they can be produced in significant quantity. process could be used to examine nuclear model
-9 - understanding the physical phenomena involved. predictions, particularly those involving nucleon Extended and more accurate measurements could be clustering within the nucleus. In addition, the purity made. High energy heavy-ion beams could also be of the isospin quantum number could be investigated used to investigate the emission of X rays from the over a wide range of nuclei. Finally, heavy-ion transient combination of two ions — the projectile transfer reactions could be used to observe and probe and the target. If successful for "united atoms" the enh. .iced transfer of nucleon pairs which occurs considerably heavier than the known elements, the as a nuclear counterpart of the Josephson effect. technique could provide a test of atomic structure theory in a completely new atomic-number regime. Studies with Light-Ion Beams: Experiments with beams of light ions at energies up to 300 MeV would provide vital information about nuclear forces, which Fundamental Interactions and Symmetries: is a fundamental requirement for all calculations of Studies of the fundamental symmetries of the strong, nuclear structure. The study of reactions involving electromagnetic and weak interactions are in the only a few nucleons would elucidate the properties of forefront of current experimental effort directed the basic nucleon-nucleon interaction, whereas reac- towards an understanding of the basic laws of tions such as (p,2p) on heavier nuclei would reflect physics. Experiments involving nuclear reactions and the interactions between many nucleons by probing decays show promise for a variety of tests of the nuclear shell structure. It is intended that such time-reversal invariance and parity conservation. studies of basic interactions may be combined with Higher incident energies are expected to enhance the information on collective behaviour derived from sensitivity in many such tests, and the vast extension heavy ion reactions tu provide a complete picture of of accessible nuclei possible with high-energy heavy the structure of the nucleus. ions should provide new decay schemes favourable to the observation of these minute effects. Detailed Ranges, Stopping Powers and Atomic Collisions: quantitative knowledge of the form of the strong Remarkably little is known about the range and rale interactions will result from experiments with high- of energy loss for energetic heavy ions passing energy light-ion beams, and similar information for through matter. Such knowledge is of value for the electromagnetic and weak interactions can be Nuclear Physics techniques such as Coulomb excita- expected from studies of the gamma and beta decay tion and Doppler shift measurements, as well as for properties of new nuclear species.
- 10- 1. THE STUDY OF NUCLEI FAR FROM THE REGION
OF BETA STABILITY: Z < 92
A. Introduction
B. Specific Problems of Future Interest
C. Production Techniques and Requirements
References A. INTRODUCTION
It has been predicted (My65, Ga66, Ke66, Ga69) in the nucleus. The effects of this include a very that there are more than 4000 nuclei with Z =S 92 different binding energy for the two types of which should have half-lives longer than a milli- nucleons and the concomitant difference between the second; and there are perhaps 3000 more which have radii of neutron and proton distributions. The extent shorter half-lives but still possess an identifiable to which these radii differ reflects directly on our ground state. Of these 7000 nuclei, there are fewer understanding of the nuclear symmetry energy and is than 1500 about which we know any single fact, and manifested in observable nuclear properties such as to say that we have a variety of good data on 500 electromagnetic moments and energy spectra. Simi- nuclei — or T'c of the total — would almost certainly larly, the relative effects of Coulomb and nuclear be an overestimate. Furthermore, this T/'c sample has forces are quite different particularly for the lighter not been chosen so as best to examine nuclear nuclei; cne possible application of this fact could properties under diverse conditions. In fact, it has not involve study of nuclear charge-dependent forces been chosen at all, but has grown helter-skelter within which would be exposed more clearly in highly boundaries set by the limitations of existing accele- proton-deficient nuclei. Finally, very high-energy rators and detection techniques. The nuclei which (3-decays occur which can lead not only to unusual have been studied well all lie in a narrow band around subsequent decay modes but can also yield new the naturally occurring stable nuclei. information on nuclear matrix-elements and even test The nuclei which exist beyond this band differ in the fundamental theories of weak interactions. many essential features from those known, and a These properties are illustrated in Table II-1-I study of their properties can yield new and quite where some relevant energies are listed for three different information. On the simplest level, they representative elements; three isotopes are shown for differ in the relative numbers of neutrons and protons each element: one which is neutron deficient, one
TABLE II-l-I: Energetics of representative nuclei; for each element, neutron-deficient, "normal", and proton deficient isotopes are showna'.
Element Z N BE(p)b> BE(n)b> BE (total)b) Coulombc % (MeV) (MeV) (MeV) (MeV) (MeV)
Calcium 20 15 1.0 16.9 15 8 262 21 8.9 8.3 0.4 350 -• 70 40 22.9 3.0 15.2 458
Tin 50 50 2.1 16.2 8.3 820 63 7.6 7.7 1.0 961 ~300 90 16.6 4.3 8.0 1130
Mercury 80 100 1.1 11.8 8.0 1400 117 6.5 6.6 0.8 1560 ~650 140 13.2 3.6 7.8 1680
a) Mass predictions from (My65, Ga66, Ke66, Ga69). b) BE = Binding energy of the last proton (p), the last neutron (n) and the total. ] 1 3 c) Coulomb energy calculated from Ec = 3/5 x Z /(Nt Z) ' .
- 13- which is in the region of ^-stability, and one which is large enough that decay branches can proceed to proton deficient. Where these elements, and others, slates in the daughter which are unstable to particle lie in relation to the boundaries of iiucleon stability emission, then each such branch will be characterized can be deduced from Figure II-1-1. There the stable by the emission of panicles exhibiting the half-life of nuclei are shown, together wiih the region of the f}-decay but having a discrete energy or energies. "known" nuclei and the limits of nuckon stability. A sample decay scheme is shown in Figure II-1-2.
Figure U-l-2 — Decay scheme for delayed-proton or 3 He decay where Z > N.
Figure II-l-l — Chart of identifiable nuclei. The solid Delayed neutron deray lRo39i and delayed-proton blocks represent the stable nuclei and the thin lines decay (Ba63. Kab3| are by now familiar phenomena delineate the "known" nuclei. The heavy solid lines and their value in determining nuclear properties has define the neutron and proton drip lines, i.e. the been established. For example, a recent study point at which these nucleons become energeticaUy (Ha? la) of the /3-delayed proton decay of 35Ar unbound. The dashed line at the left indicates yielded precise information (energies and absolute approximately where the last proton is unbound by transition strengths) on 26 individual (3-decay SOH of the Coulomb barrier. branches to 33CI. 2nd provided a convincing demon stration of isospin mixing in the lowest T = 3 2 state in 3 3 CL Since delayed protons and neutrons will ly B. SPECIFIC PROBLEMS OF FUTURE INTEREST the predominant mode of decay for more than a thousand neutron- and proton-deficient nuclei, the A list of the physics problems associated with the sophisticatici: of existing detection techniques would investigation of nuclei far from ^-stability has been provide a ready means of studying these nuclei if an made by Berlovich (Be/Oa) and with several additions accelerator were available to produce them. In it is reproduced in me subsequent discussion. Before addition. Berlovich and Novikov (Be69a) have pre- beginning, however, it should he understood that one dicted the occurrence of ,J-delayed ' H and 3 He decay, of the principle attractions of studying these nuclei is and for the former, at least, hundreds of examples are that we should be embarking for an unknown and anticipated. Their predictions are shown graphically fundamentally different region. Although predictions in Figure 11-1-3. The observation of either process can be made from what is already known, in all would initially be interesting as a new mode of decay likelihood the most fruitful results will be in areas but with the use of high-resolution detectors and quite unforeseen. It can he understood now that paitide identification these decay products could be there are many areas which will be important; what is used to "tag" and study nuclei on the fringes of more exciting is that there are many others which will stability. be unexpected. The following is a list of the subjects which are anticipated to be of greatest interest: b) Beta-delayed Nuclear Fission
a) Beta-delayed Particle Emission Figure II-1—4 shows the region of nuclei which are predicted
d) Nuclear Masses and the Boundary of Stability It has been said that "studying nuclear masses means studying in the most direct way the nuclear m m m at vt Hamiltonian which is the core of everything" (Sw67); certainly there is great current interest in mass Figure II-1-4 — Regions of 0-delayed fission. The calculations. These are, at present, semi-empirical in areas marked are (1) known nuclei (2) neutron-rich nature but are based upon a variety of models from delayed fission precursors predicted from My6S. the liquid drop (My65) to the shell model (Ze67) as Those nuclei marked (o or D) are proton rich well as certain symmetrical mass relationships (Ga66, candidates for the same decay mode (from Be69b). Ga69. Ke66). In the region of (3-stability most contemporary calculations agree fairly well with one another and with experimental data. To dis- tinguish among them accurate experimental masses c) New Radioactivities are needed for nuclei beyond this region and, perhaps more importantly, the boundaries of nucleon Proton and double-proton radioactivity (Go66) as stability need to be determined. Only then will it be well as double-neutron radioactivity (8e70a, Be70c) possible to gain realistic insight into the forces which have been predicted to occur in many cases. The govern the binding of multinucleon systems. The nuclei responsible will delineate the limits of nucleon experimental means for determining masses and stability and as such will be doubly significant. stability limits would include i) multinucleon transfer However, since their lifetime is determined by pene- trability of the Coulomb barrier (for protons) and the reactions (Ce71), ii) /3-delayed and self-delayed centrifugal barrier, a long and thereby experimentally particle emission (for example Ha70), iii) 0-decay accessible half-life will usually be accompanied by end-point measurements (Ru70) and iv) on-line and off-line mass-spectroscopy (Jo70) to name a few.
- 15- e) Nucleosynthesis, Exotic Nuclei and Other Another example is that of higher-order contributions + + Astrophysical Considerations to 0 ->0 isospin-forbidden ^-transitions. Here the Fermi matrix element <1> contributes only by virtue A knowledge of nuclei which, in our environment, of isospin mixing in one of the nuclear states are far from stability becomes of vital importance in involved, and it is expected to be suppressed by at understanding astrophysical phenomena. A number least two orders of magnitude (B166). The signifi- of examples occur in supernova explosions. There, cance of higher order matrix elements
-16- in heavier nuclei may be provided by branching ratios The subjects which can be studied in nuclei far from from double-proton decay as well as other methods the region of Instability are undoubtedly more nume- previously described. rous than those discussed here. Hopefully, though, the preceding outline has made clear that this field i) Nuclear Structure provides a remarkable opportunity for combining an extension of existing techniques and research inter- In the preceding discussion, special emphasis has ests with an area of fundamentally new and significant been placed upon those aspects of nuclei far from material. Where this is possible, surely many of the ^-stability which are novel or unique to that region. most exciting development cannot be foreseen. One should not lose sight of the fad, though, that many of the problems of nuclear structure now under study may be extended quite naturally and with C. PRODUCTION TECHNIQUES AND REQUIRE- valuable consequences to nuclei farther from stabi- MENTS lity. Level-structure, spins, parities, lifetimes, etc. can all be examined with fixed Z (or N) over a very large Since a completely versatile heavy-ion accelerator range of N (or Z) and could thus be scanned from does not yet exist, it is impossible to be certain which closed shell through deformation to closed shell again. techniques will prove optimum for the production of The significance of such a scan is best illustrated by any given /3-unstable nucleus. However, by extrapo- Figure 11-1-5 where it becomes obvious what a small lating present knowledge and using mass-predictions fraction of any region of deformation we have so far (My65, Ga66, Ga69, Ke66) it is possible to arrive at examined (Ma63); in fact there are evidently two certain energy requirements which must be met by an regions about which we know nothing. The study of accelerator if it is to be useful in this respect. analogue states extended well beyond the stable I ' i ' I" ' • r- ~i- :- — . .._ nuclei will reveal information on Coulomb energies — 6.'"c*oss SECTtCJJS and Coulomb (or isospin) mixing under conditions
where the relative importance of the Coulomb force S is altered. Finally, on a different tack, the properties / of highly excited states can be examined when they i -
occur as the final states in 0-decay, and where particle •/. / emission follows, the statistical features of the p'-decay strength function itself can also be extracted.
Figure H-l-6 — Measured (p,xn) cross sections on 209Bi(fromBe56). a) Compound Nuclear Reactions
The present method of producing neutron- deficient nuclei involves the evaporation of neutrons following compound-nucleus formation. Excitation functions for (p,xn) and (160,xn) are shown in Neutron number Figures 11-1-6 (Be56) and II-1-7 (Ne69). For both projectiles the reaction selectivity becomes progres- Figure H-l-5 — Chart of nuclides showing regions of sively less with increasing x; for the heavy-ion case, deformation. The thin banana-shaped curve approxi- maximum selectivity is achieved just above the mately encloses nuclei that have been experimentally Coulomb barrier — where, in this instance, x = 4. studied (from Ma63). Thus, it is evident that to achieve selectivity in the production of any given nucleus, a wide variety of projectiles must be available so that the compound nucleus initially formed can be varied at will. This is
-17- TABLE IM-It: Compound nuclei produced by various target-projectile combinations.
projectile target compound projectile target compound nucleus nucleus
139 t4 11 130Ce P La "Ca "•o "Sn : 12s a 134 Ba 1J8Ce "•o " Sn Ce
30 ll>6 l26 a l32Ba 13 6 Ce No Cd Ce
a l30Ba 134 Ce "s ":Mo l24Ce "6Sn 133Ce
particularly important if in-beam spectroscopy is nuclei by the eventual predominance of proton being attempted but even with on- or off-line evaporation; the latter becomes significant when the mass-separation techniques the benefits of production neutron separation energy exceeds ihe effective selectivity cannot be ignored. The variety of com- Coulomb barrier for protons. Figure H-l-8 is taken pound nuclei available in principle is illustrated in from St71 and summarizes their results: the stable Table Il-l-II for isotopes of Ce. Note that in general nuclei are shown, together with solid lines labelled by the compound nucleus can be made more neutron the expected yield (Y) relative to the probability of deficient by increasing the mass of the projectile (and compound-nucleus formation, and a dashed line reducing that of the target). This does not mean marked LCN which refers to the lightest compound though that product nuclei can be selected quite so nuclei that can be made from naturally occurring easily. targets and projectiles. For orientation, the proton drip-line illustrated in Figure II-l-l can be thought of as lying between the LCN and Y < 10"' curves. Since the most sensitive off-line techniques require yields greater than ~ 10~12, we are thus presented with an "ultimate" limit which is dependent upon the pro- duction mechanism rather than the energy of the projectiles initiating a reaction.
Figure II-1-7 — Excitation functions calculated fo* i8iTa(i6Oxnji97-xT, reactions (fro
It can also be seen from Figures 11-1-6 and 11-1-7 that the cross sections do not exhibit any appreciable decrease as x increases, but this is very much Figure II-1-8 - Chart of nuclides showing yield (Y) dependent upon the nuclei involved. It has been limits and the lightest compound nucleus (LCN) that shown recently (St71) that the neutron evaporation can be formed from stable projectile-target combina- process is limited in producing neutron-deficient tions (St71).
-18- These ideas have been translated into required b) Transfer Reactions projectile laboratory energies per amu (where amu - atomic mass unit) in Figure II-1-9. Here are displayed Until recently it was believed that the only way to the energies required to produce with any projectile reach very proton-deficient nuclei was through the all neutron-deficient nuclei (Z < 92) as far as the fission process. The results of Volkov's group at proton drip-line, and as far as the yield limit (Y < Dubna (Ar70) have now shown that such nuclei can 10"'2). Also shown is a less flexible but still adequate be produced by the direct pick-up of neutrons from a condition whose requirements are set by the thres- neutron-rich target. The types of reactions they have hold for eight-neutron evaporation reactions with observed by bombarding a 2 3 2 Th target are listed in each projectile. The significance of this energy Table II-1-1II, and a beautiful example of their condition is that it still allows production of nuclei at experimental data is shown in Figure 111-10. Perhaps the yield limit but only with a selected projectile- surprisingly, the cross sections observed for even the target combination; the flexibility of many possible most exotic reactions are far from small and appear combinations is lost. Finally, the Coulomb barrier is to bear a simple relationship to the Q-value for the indicated for projectiles on targets with the same reaction; this point is illustrated for the 'fl O + 2 3 - Th charge (Z, - Z2) or with A = 20, 50 or 92 (uranium); reaction in Figure II-l-ll. As an approximate rule-of- the former provides an approximate lower limit to thumb the cross section can be considered to decrease the projectile energy which c. i be usefully employed an order of magnitude for every five MeV increase in in this context. Presumably, th> ideal machine would Q-value if Z is kept constant. provide continuous and convenient energy variation Although detailed results have appeared for only from this lower limit up to the energy set by the relatively light projectiles, the method has already "yield limit threshold energy". been extended to 40Ar (Ar71) and there is every reason to believe it can be successfully applied to still 25 heavier projectiles. Consider, for example, the reaction "8Ca + 232Th. The ground-state to ground- state Q-value (Qgg) for 8-neutron pickup to 56Ca is PROTON DRIP-LINE only * -16 MeV; so if the single-neutron pickup /THRESHOLD ENERGY process is assumed to have a differential cross section of ~ 1 mb/sr — as suggested by Figure 11-1-11 — then for 56Ca production it is likely that do/dfi ~ 1 /nb/sr. Since differential cross sections as low as 10 nb/sr are YIELD LIMIT experimentally accessible (Ce71), such a value is not L^-'I'HRESHOLD ENERGY at all unreasonable and the possibility of producing even heavier isotopes of calcium by this technique could be contemplated. 8n EVAPORATION THRESHOLD ENERGY " 10* 'F"
45° CRITICAL -f ''. !- u -ANGLE ENERGY* "F • "0'o"" ' " "'"n- "^""c" ••' '' ' e Ne ^ * .OMB e* r ^J „„..• >•„•>' ••'.", "c" "c" 1^ r ' f -o-'i • / .. f
CHANHEL NIJHBER (f-fiE)
80 160 240 PROJECTILE MASS Figure 11-1-10 — Experimental yields of neon, fluo- rine, oxygen, nitrogen and carbon isotopes from the Figure H-l-9 — Projectile energy necessary to meet "Ne + 232Th reaction at 174 MeV (7.9 MeV/ certain criteria which are described in the text. Note, nucleon) (from Ar70), energy is expressed in MeV/amu.
-19- TABLE II-l-IU- Types of reactions observed (Ar70) following bombardment of 2 2 Th
Type of reaction projectile transferred nucleus projectile transferred nucleus nucleons produced nucleons producec
22 23 1) neutron 180 + ln "O Ne + ln Ne pick-up "O +2n "Ne +2n "Ne
21 25 i.o +3n 0 "Ne +3n Ne
26 "0 +4n "0 "Ne +4n Ne
12 2) proton "B -3p »He I5N •3p Be stripping 15N -4p "Li I6Q -4p 12 Be
3) nucleon 15N -2p, *2n "B "Ne •3p, +2n 21N exchange '"0 -3p,+2n 15B "Ne -2p,+3n 23O
"o •2p, +2n >»C "Ne -2p, +4n 24 0
•lp,+3n 20Ne "Ne -Jp, +4n
Figure 11-1-11-Dif- ferential cross sections measured at 40 for production of various isotopes from the ' 0 + 2 3 2 Th reaction (Ar70).
(MeV)
-20- Figure H-l-12 — Angular distri- butions for various bombarding energies in the '"Aul"1^ 13 l9s N) Au reaction; 0C, the critical grazing angle, is shown for each. All quantities, E, 8 and do/dO are in the centre-of- mass frame (Ne69).
30 30
In order to determine what bombarding energy is 135 ) where the elastic scattering will be considerably necessary to initiate multi-neutron pickup reactions, reduced; the required beam energy would be very it is important to realize that they take place entirely nearly the Coulomb-barrier value and, of course, at the nuclear surface. The differential cross sections would also result in considerable reduction of back- are observed to peak very strongly at the classical ground activity. Thus, once again, the necessity for grazing angle — that angle at which the bombarding easily variable beam energies down to at least the and target nuclei barely touch one another. This Coulomb barrier is evident. effect is clearly seen in Figure H-l-12 which shows data from the reaction "7Au (I4N, I3N) l98Au. It may not be desirable in an experiment of this type to have a critical angle of greater than 45° in the laboratory frame since that could result in excessive energy loss (and spread) in the target. This criterion can then be used to set the minimum possible bombarding energy for any target-projectile combi- nation. The required energy has been calculated in this manner for all projectiles on a 3 3 2 Th target and the resultant curve appears in Figure II-1-9 where it is labelled "45° critical-angle energy". Curves corres- ponding to bombardment of lighter targets would lie at lower energies.
It should be emphasized that the criterion chosen Lo (25 ISO 175 MAS5 NUMBER here to determine projectile-energy requirements is only intended as an indication. Depending upon the Figure II-1-13 — Mass distribution of Fission frag- technique used to detect the scattered particles, the ments produced by heavy-ion induced fission of the energy which produces a 45° critical angle may be indicated targets (Ka68). insufficient to ensure sufficient resolution to identify them. On the other hand, if the energy of the c) Heavy-Ion Induced Fission particles is not important but their decay is to be studied, then the critical angle requirement could be Recent results from Dubna (Ka68) show that relaxed and a lower bombarding energy would heavy-ion induced fission can be used as a valuable become acceptable. Finally, there are many experi- tool for producing proton-deficient nuclei. It's advan- mental situations where it would be desirable to tage over thermal-neutron induced fission is demon- observe the scattered particles at backward angles (~ strated in Figure H-l-13. Not only can the peak
-21- position and width of the mass distribution be varied d) Summary by an appropriate choice of projectile and target, bi-1 In the preceding sections approximate criteria ha\c by increasing the projectile energy the width of the been set which should be met by an accelerator if it is distribution in Z for a fixed value of A can also be to be useful in the production of nuclei far from the increased without altering the most probable value. In region of beta stability. Most of these are summarized addition the cross sections are not particularly small. in Figure 11-1-9. Presumably the ultimate machine fur In this case, it is more difficult to set upper limits this purpose alone would accelerate projectiles of all on the desirable energies for an accelerator. Certainly masses; H would provide variable energy from a the energy for each projectile mass must exceed the minimum of the "Z, - Z;" Coulomb barrier up to a Coulomb barrier for a uranium target (see Figure maximum set by the "yield-limit threshold energy" H-l-9) but beyond that it is very likely that as the or by 10 MeV nucleon. whichever is higher. A slightly energy increases the production of nuclei very far less versatile, but still adequate, machine could have from stability will also increase. It is impossible to say as its upper energy the higher of the "proton drip-line where is the onset of diminishing returns hut 8-10 threshold energy" or the "-15J critical-angle energy". MeV nueleon would definitely nnl be excessive (Pr69).
REFERENCES
Ar70 A.G. Artukh, V.V. Avdeichikov. J. Ero. G.F. B169 R.J. Blin-Stoyle, in Isospin in Nuclear Physics, Gridnev, V.L. Nikheev, V.V. Volkov and J. edited by D.H. Wilkinson (North-Holland Wilczynski, International Conference on Uie Publishing Company, Amsterdam 1969) 115. Properties of Nuclei Far from the Region of BI71 R.J. Blin-Stoyle, J.A. Evans and A.M. Khan. Beta-Stability, CERN 70-30 (19701 47. Phys. Lett. 36B (1971) 202. Ar71 A.G. Artukh, V.V. Avdeichikov. G.F. Bu57 E.M. Burbidge. G.R. Burbidge, W.A. Fowler Gridnev, V.L. Mikheev, V.V. Volkov, J. and F. Hoyle. Rev. Mod. Phys. 29 (19571 Wilczynski, Dubna 119711 preprint E7-5917. 547. Ba63 R. Barton. R. McPherson, R.E. Bell. W.R. Ce71 J. Cerny. Fourth International Conference on Frisken, W.T, Link and R.B. Moore, Can. J. Atomic Masses and Fundamental Constants Phys. 41 (1963) 2007. (19711, Lawrence Radiation Laboratory pre- Beo6 R.E. Bell and H.M. Skarsgard, Can. J. Fhys. print LBL-234. 34(1956) 745. Ga66 G.T. Garvey and I. Kelson, Phys. Rev. Lett. Be69a E.E. Berlovich and Yu. N. Novikov, Bulletin 16(1966) 197. of the Academy of Sciences of the L'.S.S.R. 33(1968)626. Ga69 G.T. Garvey, W.J. Gerace, R.L. Jaffe, I. Talmi Be69b E.E. Berlovich and Yu. N. Novikov, Soviet and 1. Kelson, Rev. Mod. Phys. 41 (1969) SI. Physics Doklady 14 (1969) 349. Go65 V.I. Goldanskii, Phys. Lett. 14 (1965) 233. Be70a E.E. Berlovich, International Conference on Go66 V.I. Goldanskii, Ann. Rev. Nucl. Sci. 16 the Properties of Nuclei Far from the Region (1966)1. of Beta-Stability, CERN 70-30 (1970) 497. Ha70 P.G. Hansen, H.L. Nielsen, K. Wilsky, M. 3e70b E.E. Berlovich and Yu. N. Novikov, Soviet Alpsten, M. Finger, A. Lindahl, R.A. Physics Doklady 14 (1970) 986. Naumann and O.B. Nielsen, Nucl. Phys. A148 (1970) 249. Be70c E.E. Berlovich, O.M. Golubev, Yu. N. Novikov, JETP Letters 12 (1970) 195. Ha71a J.C. Hardy, J.E. Esterl, R.G. Sextro and J. Cerny, Phys. Rev. C3 (1971) 700. B166 S.D. Bloom, in Isobaric Spin in Nuclear Physics edited by J.D. Fox and D. Robson Ha71b J.C. Hardy, J.S. Geiget, R.L. Graham and W.J. (Academic Press, New York, 1966) 123. Chase, Atomic Energy of Canada Limited Report AECL-3996 (1971) 12.
22- Ja70 K.P. Jackson, C.li. Cardinal, H.C. Evans, N.A. Pr69 Proposal for a Regional Accelerator Facility: Jelley and J. Cerny, Phys. Lett. 3.ÎB (1970) Midwest Tandem Cyclotron, Argonne 281. National Laboratory Report ANL-7582 Jo7U W.H. Johnson, Jr., International Conference (1969)250. on the Properties of Nuclei Far From the Ro39 R.B. Roberts, R.C. Meyer and P. Wang, Phys. Region of Beta-Stability, CERN 70-30 ( 1970) Rev. 55(1939)510. 307. Ru70 G. Rudstam, E. Lund, L. Westgaard and G. Ka63 V.A. Karnaukhov, G.M. Ter-Akopian, V.G. Grapengiesser, International Conference on Subbotin, Report JINR (Dubna) P1072, the Properties of Nuclei Far From the Region translation UCRL-Trans-919 (1963). of Beta-Stability, CERN 70-30 (1970) 341. Ka68 S.A. Karamyan, F. Normuratov, Yu. Ts. So70 R.A. Sorensen, International Conference on Oganesyan, Yu. E. Penionzhkevich, B.T. the Properties of Nuclei Far from the Region Pustylnik and G.N. Flerov, Joint Institute for of Beta-Stability, CERN 70-30 (1970) 1. Nuclear Research, Dubna (1968) preprint St71 F.S. Stephens, J.R. Leigh and R.M. Diamond, P7-3732 (ANL translation 747). Nucl. Phys. A170 (1971) 321. Ke66 1. Kelson and G.T. Garvey, Phys. Lett. 23 Sw67 W.J. SwiMecki, Arkiv fur Fysik 36 (1967) (1966)689. 325. Ma63 E. Marchalek, L.W. Person and R.K. Sheline, To72 I.S. Towner and J.C. Hardy, Nucl. Phys. Rev. Mod. Phys. 35 ( 1963) 108. A179 (1972) 489. My65 W.D. Myers and W.J. Swiatecki, Lawrence Wi70 D.H. Wilkinson, Phys. Lett. 31B (1970) 447. Radiation Laboratory report—UCRL-11980 (1965, unpublished). Ze67 N. Zeldes, A. Grill and A. Simievic, Dan. Mat. Fys.Skr. 3 no. 5 (1967) 163. Ne69 J.O. Newton, Progress in Nuclear Physics 11 (1969)53.
-23- 2. SUPERHEAVY NUCLEI
A. Introduction B. Properties
C. Production
D. Detection
E. Summary
References A. INTRODUCTION The possible existence of a region of stable now be predicted. "super-heavy" nuclei near Z = 114 has been the subject of considerable recent interest in the field of B. PROPERTIES nuclear physics. Extrapolations of nuclear shell struc- ture have predicted that the next closed proton shell Termination of the sequence of stable elements at will occur at Z - 114 or possibly Z - 126 and the proton number Z = 83 is a direct consequence of the next closed neutron shell at N - 184. Calculated ever increasing importance of the Coulomb energy decay properties suggest that some of the nuclei in with increasing proton number. For elements lying the region of these closed shells may be sufficiently above lead in the periodic table the probabilities for long-lived to exist in nature and that many will alpha decay and spontaneous fission tend to increase with atomic number .such that the longest lived certainly live long enough to be detected if they are isotope of the heaviest element presently known, produced in nuclear reactions. Hahnium (Z = 105), has a half life of 1.6 seconds. To date, the search for superheavy nuclei in nature This trend to ever shorter half lives would continue has produced inconclusive results. It has been sug- monotonically but for the additional nuclear binding gested that the most fruitful method for the produc- associated with the closure of proton and/or neutron tion and detection of superheavy nuclei will be shells. Myers and Swiatecki (My66) were the first to nuclear reactions using high-energy heavy-ion beams. demonstrate that the influence of these shell closure The search for superheavy nuclei and the subse- effects could prove sufficient to give rise to a group quent determination of their properties will result in of relatively long-lived nuclei in the region of the next a number of fundamental tests of current nuclear and closed proton shell which was then expected to be atomic theories. Since these theories have been found at Z = 126. Subsequently, shell model calcula- developed to explain the chemical and physical tions by Meldner (Me67) based on a non-local potential properties of known elements, their extrapolation to which had been adjusted to reproduce nuclear binding the region of superheavy elements will provide a energies and single particle energies as deduced from demanding test of their validity. Furthermore, some (e.e'p) scattering on tightly bound protons indicated of the predicted properties are unique to this very that an energy gap of some 4 to 6 MeV exists in the high mass region. For example, the increased size and proton level sequence at Z = 114 which could give rise charge of the nucleus is expected to introduce to long-lived isotopes of this element. Subsequent significant perturbations in atomic structure, and the shell model calculations by Wong (Wo66|, extremely large electric fields existing near a super- Sobiczewski et al.(So66) and Rost (Ro68) based on heavy nucleus may make it possible to observe local Woods-Saxon potentials all confirmed Meldner's non-linear effects in quantum electrodynamics. In finding of an energy gap at proton number 114. The addition, the predominance of fission as a mode of single- particle states as deduced in these calculations decay and the differences in fission barrier shapes will are shown in Figure II-2-1. make this region a particularly fruitful one for fission studies. Finally, the structure of nuclei near the The experimental search for these superheavy doubly magic nucleus 398 114 are very important as elements is regarded by many nuclear physicists as tests of microscopic nuclear theories. the most exciting challenge of our day. The concur- rent theoretical problem of accurately predicting the These topics are discussed in detail in the fol- nuclear and atomic properties, and in particular the lowing sections and methods are proposed for the nuclear half lives, is receiving major attention both in production and detection of superheavy nuclei in its own right and in recognition of the major high-energy heavy-ion reactions. expenditure on accelerators which will be necessary The properties of superheavy nuclei are expected to permit artificial production of these nuclei. Major to provide new and useful tests of current theories. It theoretical investigations of the superheavy nuclei are should also be emphasized that a significant reason underway in S.G. Nilsson's group at Lund and in for extending experiments into these new and drama- Nix's group at Los Alamos. The nuclear model used tically different areas is the expectation that in these studies is based on the original Myers and phenomena may be encountered which will contri- Swiatecki work in which the gross binding is deduced bute to physical knowledge in ways which cannot from a liquid drop description of the nuclei and to
-27- —hll/2 0- p3/2 H9/2 i 15/2 — P3/2 -113/2 113/2 — 99/2 _ i||/2 -E- (7/2 -2- H5/2 ^Sl 184) k!7/2 ill/2 — PI/2 PI/2 p 1/2 P3/2 (5/2 |l3/2 kl7/2 p3/2 PI/2 —h3/2 sl/2 hll/2 = i 13/2 (5/E _. hll/2 (5/2 — P3/2 — —(7/E d3/2 —krr/2 (5/2 (JI4) S -6- d3/2 d3/3 W -6- (7/2 — H3/2 sl/2 = s I/-; (7/2 f7/2 i 13/2 — hll/2 ,j5/2 [13/2 -8- ,_ 97/2 —(7/2 — » 9/z -8- h9/2 — U3/2 /T\ JI5/2 i=iil5/2 -10- —"/I —115/2 g 9/2 -10- h9/2 ftl -,9/2 -Ml/2 —111/2 (126) -12 )5/2 WONG MELDNER GAREEV ROST WONG MELDNER GAREEV ROST
PROTON STATES NEUTRON STATES
Figure H-2-1 — Single-particle states deduced in calculations by Wo66, Me67, So66 and Ro68. this is added a correction term evaluated from shell- completely stable against beta decay. The partial half model calculations for the particular nucleus in lives fora decay and spontaneous fission, obtained by question. The importance of shell effects in the Nilsson and co-workers (Ts70) are given in Figure creation of a fission barrier is shown in Figure 11-2-2 11-2-5. It will be noted that the isotope ;94110 is due to Nix (Ni70) which shows the relative contri- butions of shell and liquid-drop effects. A shortcoming of the original Myers and Swiatecki study arose from the fact that it was applicable only to small deformations. Strutinski (St66) introduced the computational techniques necessary to permit one to include the dependence of the shell correction term on the nuclear distortion in calculation of the Fission barrier. The various approaches used in the calculations are described in the recent review paper by Nix (Ni70). Figure 11-2-3 shows the single particle level energies obtained by Bolsterli et al (Bo71) using a Yukawa type potential adjusted to fit the single particle energies for '6 O, 4 ° Ca, * 8 Ca and 3 ° 8 Pb and the corresponding level energies obtained by the group at Lund using a potential whose parameters were obtained by a "brave and linear" extrapolation of the potential parameters appropriate to the rare earth and actinide regions (Gu70). The agreement between these two approaches is very good and both show shell closures at Z = 114 and N = 184. The location of the "island of stability" sur- rounding Z = 114 on the chart of nuclides is shown in 298 Figure II-2-4. The island straddles the line of beta Figure 11-2-2 - Fission barriers for 114 for th<- liquid-drop model (dashed) and liquid-drop model stability and several of the nuclei are predicted to be plus shell effects (solid).
-28- predicted to have a lifetime of about 108 years. factor of 106 has been assigned to these half-life Because of the stabilizing influence of the unpaired predictions corresponding to an uncertainty in a- nucleon in odd mass nuclei one may reasonably decay energy of 1 MeV and an inertial mass para- expect some odd A nuclei to have even longer meter uncertainty of 30 percent. The predicted half lifetimes (Me69). The half-life estimates exhibit lives are sufficiently long thai even a pessimistic extreme sensitivity to the detailed nature of the alpha evaluation of the uncertainty does not render the particle and fission barriers and an uncertainty of a nuclei unobservable due to short half lives.
NEUTRONS PROTONS
- (Bolsterlietal.) (Gustafsson et al.) . (Bolsteri et al.) (Gustafsson et al.)
Figure II-i-3 — Single-particle states obtained by Bolsterli et al. (Bo71) and Gustafsson (Gu70). (See text,)
ITS ITB 180 IBZ I6« 166 IBB 190 I3Z 194 196 199 aoo ZOB go* gO6
Bo NumnnmtvN
Figure II-2-4 — Location of possible island of super- heavy nuclei relative to peninsula of known nuclei. Figure II-2-5 — Decay properties of superheavy nuclei as calculated by Tsang and Nilsson (Ts70).
-29- non-linear effects in electrodynamics such as predicted by the theory of Born and Infeld (Bo34). However, recent comparisons (Fr72a, Ft72b) with measure- ments of electron binding energies for'ooFm indicate that non-linear effects are less than 1% of the magnitude predicted by Rafelski et a). Non-linear effects, if they exist, increase greatly at higher Z, which would complicate the use of X-ray analysis for superheavy element identification but at the same time offer the possibility of a valuable test of quantum electrodynamics.
1 TABLE II-2-1: Some Predicted Properties of Elements 113 and 114
t fil Element 113 (eka-Uiallium)
Chemical group HI IV Atomic weight 297 298 Atomic volume, rro3/mole 18 21 Density, g/cm1 16
i iiiii Most stable oxidation state +1 1 ' I 1 I I I il Oxidation potential, volts M-*M I I i \ I I I U>: -0.6 -0.9 I ! I ; I I I I First ionization potential, eV 7.4 8.5 I I I I M Second ionization potential, eV 16.8 J J
Ionic radius. Angstroms 1.48 1.31 Figure II-2-6 — Extrapolated periodic table of the Metallic radius, Angstroms 1.75 1.85 elements showing predicted electronic shell structure Melting point, °C J30 10 (from Se70). Boilinn point, °C 1100 150
Heat of vaporization, kcal/mole 31 Chemical techniques are certain to be important in Heat of =u blimp lion, kcal/mole 34 10 the separation and identification of superheavy ele- Debye temperature, aK "0 J6 ments. An extrapolated version of the Periodic Table Entropy, eu/motc (25&C) 17 20 (Se70) is shown in Figure II-2-6. It is expected that the elements from Z = 104 to Z = 120 will be closely To summarize this section, from the point of view related chemically to the corresponding known of nuclear physics, there are three important rea- elements. The predicted chemical properties of eka- sons to produce and study superheavy elements. thallium and eka-lead (Z = 113, 114) are given in Their stability and other properties will provide Table II-2-I (Ke70). Careful relativistic self-consistent sensitive tests of the nuclear structure theories which field calculations by Mann and Waber (Ma70) suggest have been extrapolated to predict their existence. The that relativistic effects will cause the Sp shell to begin properties of a new doubly magic nucleus and the filling at Z = 121 so that the chemical and physical surrounding nuclides are very important for the properties of elements 121 to 168 may differ refinement of microscopic theories of the nucleus. appreciably from the rare earths and actinides. The Finally, many of these nuclei will decay by sponta- study of atomic, chemical and physical properties of neous fission so that fission studies will have a greatly superheavies will be rewarding because of the greatly enlarged scope and a much richer store of experi- increased importance of relativistic and nuclear size mental data. A detailed study of fission phenomena effects. It has also been pointed out by Rafelski et aL is of practical importance and is a necessity for the (Ra71) that the extremely large electric fields near a complete understanding of nuclear deformation in superheavy nucleus may make it possible to detect non-fissioning nuclei.
-30- C. PRODUCTION projectiles may have to be used in order to come closer to the centre of the island of stability. There are two methods by which superheavy Three main types of reaction have been proposed nuclei may be produced: multiple neutron capture for the production of superheavy nuclei: compound and heavy ion reactions. The former method is the nucleus formation, direct transfer and fission. basis for the so-called r-process (Bu57) believed to occur in supernovae, in which nuclei successively The first method involves the (HI,xn) reaction, capture neutrons until photoneutron reactions which suffers the problem previo < ly discussed that become competitive and then increase their proton for either heavy target and light projectile, or medium number by beta decay until neutron capture is weight target and projecuie, it is not possible to possible again. In nuclear explosions (Be67a), there is achieve the proper neutron-proton ratio to come no time for the beta decays to occur so that in order close to the centre of the island of stability at to produce superheavy nuclei a very neutron-rich Z = 114. On the other hand the region of Z = 124 nucleus must be formed which will subsequently beta may be more accessible, through reactions such as decay to the "island of stability". In both cases the 8 process may be terminated by competing fission other suggestions (Le70) for producing compound decays before producing superheavy nuclei (Ni70). nuclei with low excitation energy in the region of There are conflicting views concerning the possibility Z - 126, which might then decay by the emission of of production by multiple neutron capture (see Ni70, one or more alphas to form possible stable nuclei Vi69, Se68). As yet no production of superheavy between Z - 126 and Z - 114. One example is !*, Kr T nuclei in nuclear explosions has been reported and 2i2,Th->316126-»fasta->fast a -» 3U" 122. the evidence for natural occurrence is uncertain. Spontaneous fission in lead samples has been reported Direct transfer reactions provide the possibility of by Flerov and co-workers (F169) at Dubna, which producing nuclei which have a more favourable ratio they suggest might be due to eka-lead (element 114) of neutrons to protons. For example with a half life of 5 x 1020 years, but Cheifetz et al. ^Pu + SgZr- (Ch70) obtain a lower limit of 4 X 1022 years for eka-lead in various lead samples using a neutron multiplicity detector.
Much work is being done in the search for superheavy nuclei in nature (see Pr71), but it is The nuclei produced in such reactions may be stable generally felt that heavy-ion reactions are the main enough for detection, or may decay to detectable hope for studying the island of stability Heavy-ion nuclei. reactions have already been used for the production of elements 102 to 105 by groups at Berkeley and Dubna. It was found that within the capabilities of the present heavy-ion accelerators, it was best to use the heaviest target and lightest projectile combination possible (Se68). The main production reaction is (HI, xn) such as 2S?Cf + 12C ->• 2S7104 + 4n. However, difficulties increase for the production of higher atomic numbers by this method, because the number of available targets decreases, the cross section for heavier-ion beams decreases, and the half lives of the resulting isotopes decrease. Attempts have been made to produce element 114 by this type of reaction at Berkeley (24.lCm + ??Ar-- 284114 + 4n) and Dubna 2S4 ("2U + |?Ti - 114 + 4n) but without success, 125 150 175 2S4 probably because 114, being far from the centre MASS NUMBER of the island of stability at N = 184, has been Figure 11-2-7 —Mass distribution of fission fragments predicted to have a spontaneous fission lifetime less produced by heavy-ion-induced fission of targets than a nanosecond. It appears that much heavier listed in the figure (from Ka68).
-31- The F.nal reaction mechanism is based on the idea elements. For example, a beam of 100 particle- 29H of producing a very massive compound nucleus which nanoamps of uranium would produce twelve 114 2 would undergo fission, in which one of the products nuclei per second in a 0.5 milligram/cm uranium is a superheavy nucleus. Calculations have been target. performed by Karamian and Oganesyan (Ka69) of the Additional processes may modify these results. If yield of elements 100 and 114 produced by the the fission yield curves are modified by shell struc- reaction of Xe and U on uranium. The calculations ture, rather than being smooth functions as shown in are an extrapolation of measurements (Ka68) of the Figure H-2-7, then the yield of the doubly magic mass and charge distributions of fission fragments nucleus 298114 could be enhanced. However, super- produced by heavy ion bombardment of gold and heavy nuclei are relatively "brittle"; that is, it does uranium by lighter ions as shown in Figure H-2-7. The not take much deformation to produce fission. This is calculations assume that the effective Pf/rn of nuclei illustrated in Figure 11-2-8 (from Ni70) which near Z - 114 is small, as Sikkeland (Si67) has contrasts the double fission barrier for 242Pu with calculated, so that secondary fission is small. The the much thinner barrier for 21)8114. Thus, to results are presented in Table II-2-II and they indicate produce a superheavy nucleus, the system must relatively large cross sections for the production of rearrange itself from its initial configuration in such a nuclei with Z = 114. In fact, cross sections of the manner that the superheavy nucleus is left in nearly- order of magnitude shown in Table H-2-II would spherical shape. This may limit production cross produce readily observable quantities of superheavy sections in fission reactions, and has led Swiaticki
TABLE II-21I. Parameters and results from the calculation of proriuction cross sections of the nuclei!'" 110 and 2 *" 114 in the reactions U(U,f) and U(Xe,f) (from Ka69).
"U(136Xe,f) 8U(;38U,f)
Total excitation energy of the compound nucleus (MeV)
Parameter of the width 3500 3800 4500 of the mass distribution11'
Charge dispersion 2.5 2.7 3.7 v Number of neutrons evaporated from the reaction product
Most probable mass of 2=11 288 288 284 the reaction product after the evaporation Z = 1 ] 299 296 300 296 of neutrons
z 3 Production cross ' * 11 0.7 x 10" ° 0.3 x lO"'0 6x10-" 0.4 x 10"10 section (cm2) 2981] 3x lO'10 sxiir" 1.5 x 10-"
The standard deviation of the fission-product distribution is oA/\/2 and is - 43 for a Xe projectile and "- 46 for a U projectile. Since the fission yield drops only to 13% of the peak value at ± 2 standard deviations, the fission products within a range about 180 mu wide have comparable yields.
-32- (SwB9) to suggest that a "pinch off" reaction, as to study the variation in the yield of superheavy illustrated in Figure 11-2-9 may be more suitable. nuclei as a function of incident energy, and to Observations on liquid drops indicate by analogy that optimize their production. Thus a machine with a when two heavy nuclei collide, the inner portion may variable energy ranging up to 11 MeV/nucleon for fuse to form a relatively spherical core with the uranium ions and a capability Cor producing beams of emission of two lighter nuclei. the order of 100 particle nanoamps of a wide range of elements v.ould be very suitable for the production of superheavy elements by the reaction processes Deformed qroundstt described here.
242:,Pu D. DETECTION \7 -5- Saddle point The detection and confirmation of the properties Spherical of new elements will require a wide variety of .9 ground_ state c physical and chemical techniques. Many very sensitive 0-- 298, methods have been developed by the groups at Berkeley and Dubna for the detection and identifi- cation of elements 102-105 which will be useful in -10 0 part for the heavier elements. These techniques have Deformation — involved a knowledge of the predicted chemical properties of these elements, and studies of mother- Figure II-2-8 — Fission barriers and equilibrium daughter relationships wherein new elements are shapes. identified by the recognition of the subsequent decay properties of their alpha-decay products.
The chemical properties of elements with 104 < Z < 121 may be predicted with reasonable confidence to be similar to those of elements 72 < Z < 89 and chemical techniques may be devised on this basis, providing that sufficient quantities, with sufficiently long half lives, are produced. Relatively efficient chemical separation procedures can be developed based on the predicted volatilities, oxidation states («6I7 ) O and formation of gaseous compounds (Zv66). Ele- ment 118 should be distinctive as it is expected to be a noble gas. As discussed above, the chemistry of elements with Z > 121 is in greater doubt because of the close spacing of the 8p, 5g, 6f and 7d orbitals so that identification here may have to be based solely on nuclear properties of these elements. An additional piece of atomic information which Figure H-2-9 — Pinch-off direct transfer reaction lor may be useful in the identification of superheavy producing superheavy nuclei. elements is the energies of X-rays emitted in the pro- cess of internal conversion or by transitions to inner Incident energies required for any of the above shell vacancies. These X-rays have been observed for processes must exceed the Coulomb barrier, which is elements up to Z - 102 (Be71) and calculations have increased for these heavy ion reactions by the effects extrapolated energies to higher Z values (Ca69). This of distortion of the target and projectile (Be67b, technique may eventually be limited by calculational Wo68). This results in a Coulomb barrier of about 8.2 difficulties presented by the very high electric fields at MeV/nucleon for uranium on uranium. An additional high Z; at this point the physics of atomic X-rays is 2 to 3 MeV/nucleon would be very desirable in order interesting in itself, providing that other identifi- cation methods are devised to determine Z.
-33- The identification of the charge and mass of (Ha71) to isolate and study the decay of lighter superheavy nuclei by means of their nuclear proper- nuclei off the line of /J stability would also be very ties will depend on the establishment of genetic useful in removing product nuclei to low back- relationships between them which can be related ground areas, with the possibility of fast chemistry eventually to known nuclei. The region of nuclei being employed in the process. The on-line mass between Z = 105 and Z « 114 which are predicted to spectrometer proposed in chapter V would be an have very short half lives for spontaneous fission will extremely useful experimental tool, particularly for complicate this task considerably, but the comparison the examination of isotopes produced in fission-type of observed properties with the results of the many reactions, where a very large spectrum of masses may calculations which have been performed may provide be produced. Internal conversion will be a dominant sufficiently distinctive signatures of superheavy mode of de-excitation of low-lying states of super- elements. For example, the neutron multiplicity heavy nuclei. To study these processes facilities such following fission of element :'"114 is expected as the on-line orange (3 - spectrometer facility and iNi69i to be 10.5 compared with 2.8 for :40Pu. The off-line "v'2 iron-free high-resolution (3 spectrometer alpha, neutron and proton binding energies of nuclei described in chapter V would be very valuable. Such in the vicinity of 'he island of stability have been electron spectroscopy could also be used to identify calculated ITSTOI and some distinctive properties are the Z of the decaying atoms and permit precision evident such as the very high alpha-decay energies of measurement of electron binding energies. elements with Z ~ 124 i ^ 14 MeVi. The combination of observations of decay energies and production E,SUMMARY cross sections from cross bombardments should provide a systematic picture of the nuclear properties There is considerable theoretical evidence for the of the superheavy nuclei. This points out again the existence of a region of nuclear stability near Z = 114 necessity of having an accelerator with variable or 126, X = 184. The atomic and nuclear properties incident energy and a wide range of projectile masses of nuclei in this region are of considerable interest in to perform these studies. extending our knowledge of nuclear models, the fission process, chemical properties of new elements The large recoil velocities resulting from heavy ion and possibly tests of non-linear electrodynamics in reactions will be of significant use in removing the high electric fields. Heavy-ion reactions, at energies product nuclei from the target and permitting their much higher than presently available, show promise of detection for half lives as short as a nanosecond. producing these superheavy nuclei in measurable Longer lived nuclei could be captured on moving quantities thus opening a large region of previously belts, wheels or plungers and removed from the target inaccessible nuclei and presenting the possibility of area for study of their decay properties. Gas sweeping answering a number of very interesting questions in techniques, such as those being employed in the Physics and Chemistry. Chalk River Nuclear Laboratories by Hardy et al REFEREXCES
Be67a G.I. Bell. Rev. Mod. Phys. 39 119671 59. Buoi E.M. Burbidge. G.R. Burbidge. W.A. Fowler Be67b R. Beringer. Phys. Rev. Lett. 18 119671 1006. and F. Hoyle. Rev. Mod. Phys. 29 11957) 547. Be71 C.E. Bemis, Jr., P.F. Dittoer, 0.C. Hensley, CD. Goodman and R.I. Silva, PTOC. of the Ca69 T.A. Carlson, C.W. Nestor. Jr.. F.B. Malik and Inter. Conf. on Heavy Ion Physics, Dubna T.C. Tucker, Nucl. Phys. A135 (1969) 57. (1971) 175. Ch70 E. Cheifetz, E.R. Gatti, H.R. Bowman, Ft.C. Bo34 M. Born and L. Infeld, Proc. Roy. Soc. Ser. Jared, J.B. Hunter and S.G. Thompson, Inter. A144 (1934) 425. Conf. on Properties of Nuclei Far from the Region of Beta Stability, Leysin, CERN 70-30 Bo71 M. Bolsterli, E.O. Fiset and J.R. Nix, cited in (1970)709. Gu70.
-34- FI69 G. Flerov, Proc. Inter. Conf. on Properties of Ni69 J.R. Nix, Phys. Lett. 30B (1969) 1. Nuclear States, Montreal (1969) 175. Ni70 J.R. Nix, Inter. Conf. on the Properties of Fr72a M.S. Freedman, F.T. Porter and J.B. Mann, Nuclei Far from the Region of Beta-Stability, Phys. Rev. Lett. 28 (1972)711. Leysin, CERN 70-30 (1970) 605. Fr72b B. Fricke, J.P. Desclaux and J.T. Waber, Pr71 Proc. of the Inter. Conf. on Heavy Ion Phys. Rev. Lett. 28 (1972)714. Physics, Dubna Report D7-5769, Dubna (1971). Gu70 C. Gustafsson, Inter. Conf. on the Properties Ra71 J. Rafelski, L.P. Fulcher and W. Greiner, of Nuclei Far from the Region of Beta Phys. Rev. Lett. 27 (1971) 958. Stability, Leysin, CERN 70-30 (1970) 654. Ro68 E. Rost, Phys. Lett. 26B (1968) 184. Ha71 J.C. Hardy, J.S. Geiger, R.L. Graham, W.J. Chase and H. Schmeing, Atomic Energy of Se68 G.T. Seaborg, Ann. Rev. Nucl. Sci. 18 (1968) Canada Limited Report AECL-3996 (1971) 53. 14. Se70 G.T. Seaborg, Isotop. Radiat. Technol. 7 Ka68 S.A. Karamyan, F. Normuratov, Yu. Ts. Oga- (1970)251. nesyan, Yu. E. Penionzhkevich, B.I. Pustylnik andG.N. Flerov, JINR, Dubna (1968) preprint Si67 T. Sikkeland, Arkiv Fysik 36 (1967) 539. P7-3732 (Argonne National Laboratory ANL So66 A. Sobiczewski, F.A. Gareev and B.N. translation 747). Kalinkin, Phys. Lett. 22 (1966) 500. Ka69 S.A. Karamian and Yu. Ts. Oganesyan, JINR, ftfifi V'.M. Strutinsky, Sov. J. Nucl. Phys. 3 (1966) Dubna (1969) preprint P7-4339 (Argonne 449 and Arkiv Fysik 36 (1967) 629. National Laboratory ANL translation 745). Sw69 W.J. Swiatecki, Proc. of the Inter. Conf. on Ke70 O.L. Keller, Jr., J.L. Burnett, T.A. Carlson and C.W. Nestor, Jr., J. Phys. Chem. 74 Nuclear Reactions Induced by Heavy Ions, (1970) 1127. Heidelberg, 1969 (North-Holland Publishing Company, Amsterdam, 1970) 729. Le70 M. Lefort, M. Riou, Inter. Conf. on the Ts70 C.F. Tsang and S.G. Nilsson, Nucl. Phys. A140 Properties of Nuclei Far from the Region of (1970) 275, 289 and appropriate references Beta-Stability, Leysin, CERN 70-30 (1970) therein. 723. Vi69 V.E. Viola, Jr., Nucl. Phys. A139 (1969) 188. Ma70 J.B. Mann and J.T. Waber, J. Chem. Phys. 53 (1970)2397. Wo66 C.Y. Wong, Phys. Lett. 21 (1966) 688. Me67 H. Meldner, Arkiv for Fysik 36 (1967) 593. Wo68 C.Y. Wong, Phys. Lett. 26B (1968) 120. Me69 H. Meldner and G. Herrmann, Z. Naturforsch. Zv66 I. Zvara, Yu. T. Chuburkov, R. Tsaletka, T.S. 24a (1969) 1429. Zvarova, M.R. Shalaevskii and B.V. Shilov, Soviet At. En. 21 (1966) 709. My66 W.D. Myers and W.J. Swiatecki, Nucl. Phys. 81 (1966) 1.
-35- 3. FISSION
A. Introduction and Survey
B. Coulomb Fission
C. Intermediate Structure
D. Fission Isomers
References A- INTRODUCTION AND SURVEY The possibility of a high-energy heavy-ion facility The narrowness of our view has resulted from the reveals several exciting prospects in the field of very restricted range of nuclei that are available for nuclear fission. First, fission is a collective readily interpretable experiments: essentially those phenomenon and heavy ions provide the ideal way nuclei for which 88^Zi 98. One aspect of this of exciting collective modes. Second, the rol'j of restriction can be stated more clearly in terms of the angular momentum in fission is not at all well fissility parameter, x (« Z2/(50A)). Its value can be understood and heavy ions are unique in their ability between 0 and 1 but for nuclei in the region to bring in large amounts of angular momentum. extending from 2 •"' Ra to ""Cf it is severely limited Third, fission data are ofttn difficult to interpret to 0.69 < x < 0.76. The availability of interpretable because several initial states of the system are data at x * 0.87 (="IK114) or x - 1 (3'2126) would involved; their properties are either not well known, thus nearly treble or even quadruple the range of x. or the experimenter has no control over their The fissioning nuclei which have been traditionally selection, or both. In the past, the light projectile studied may represent a special case in another transfer reactions (d,p), (t,d| and (t,p) have been very respect as well. It may be that many things we think useful in overcoming these difficulties, so heavy ion of as characteristic of fission are in fact characteristic transfer reactions (cf. section 11-6) would of the double-humped barrier that dominates the supplement existing data and offer in addition the process in this region. Although the structure intro- new prospect of observing fission of the projectile. duced by shell effects in the potential energy of a Fourth, the as yet unobserved phenomenon of nucleus as a function of its deformation is completely Coulomb-induced fission has intrinsic interest and, if general and applicable to all nuclei (e.g. St68), it is it exists, provides a tool for selective preparation of likely to be important for the fission process only in a fissioning states rivalled only by photofission in few areas of the periodic table and then only for a specificity and in our fundamental understanding of very small range of neutron numbers (Bj69, BJ70). the reaction mechanism (cf, section II-4), but far One of these narrow regions (N = 140-150) centres outdistancing that rival in versatility. Only a high- around Pu and U, and encompasses all the nuclei energy heavy-ion facility can make use of this about which detailed fission properties are known. mechanism. The influence of this second barrier is expected to be negligible in the region of the superheavies (Ni69) and Finally, for the study of nuclear fission, by far the the ^-delayed fission isotopes. On the other hand a greatest application of high-energy heavy-ion beams new and unexplored region characterized by double- — and it is a unique one — is in producing a humped barriers is expected to exist for proton-rich vastly increased range of nuclear species to be nuclei around 203At (St68). It is extremely impor- studied. These newly available nuclei fall into two tant to verify these "long distance" shell effects. groups: the superheavies (see section 11-2) and the They probably exist and may have influence in all neutron rich fi-delayed fission precursors (see section nuclei but it is fission which provides one of the best 11-1, particularly Fig. 11-1-4). In both cases fission is ways of studying them. Conversely, their study has expected to be the dominant mode of decay. The radically altered the whole approach to fission (see latter group alone doubles the number of nuclei for example the Proceedings of the Second IAEA available for studying fission at low excitation ener- Symposium on the Physics and Chemistry of Fission, gies; but it is the increase in variety, not in number, Vienna 1969) and given the subject new vigor. that is important. Fission does not suffer from a dearth of data, but rather perhaps from a surfeit since The predicted fission properties of the superheavy we are blinded in our understanding by the extreme narrowness of the window through which we must nuclei are rather different from those of the actinides, look. Thus, it is no exaggeration to say that although the most striking difference being in the total energy the amount of information garnered in 35 years of released: 300-40(1 MeV as opposed to 200 MeV research in fission is tremendous, its accumulation has (Ni69, Sc71). Although the fragment kinetic energy is not resulted in a commensurate amount of under- somewhat increased as a result, the most noticeable standing and, at least until the last few years, has had difference is that the total number of neutrons is 10 almost no effect at all on nuclear physics as a whole. or 11 ins 'ad of ~ 2.5. Some of the superheavies are
-39- predicted to be thermally fissile, e.g. ""126, while on the distribution of K-states. It would also be of others such as"94 110 should be fissionable with neu- particular interest lo look for fissioning isomeric trons well below the average energy of those emitted states with r i 1 ns and, if they are found, to lNi69). Thus from a reactor-physics point of view measure the intensity of competing gamma-decay they have appealing properties and might, if they branches. could he produced cheaply enough, have far reaching applications. It should be clear from the preceding discussion 10 that our fundamental understanding of ihe fission process is not good but great strides have recently been made and hopes are bright. A heavy - ion accelerator could make several unique contributions towards a fuller understanding. What such an under- standing will bring with it is, of course, unknown and therein lies the beauty of research into any field where ignorance surpasses knowledge. It is fanciful to 3 io speculate on the possibility of manipulating the / fission process to the benefit of power reactors. The to' / chances are not high, for nuclear processes are not 5 A easily modified by external influences, but they are 1/ not zero either and the rewards of success could be 10' enormous.
10* - 1 0 B. COULOMB FISSION I 10 . 1 0 The distortion of a heavy fissionable nucleus from to its equilibrium deformation through interaction with the Coulomb field of a heavy projectile may provide an important way of gaining experimental infor- 10" 1 1 1 1 1 . 1 i 1 1 » mation on the fission barrier. Early classical calcu- 30 50 70 90 lations (Gu66. Wi67) showed that the fission Figure II-3-1 — Coublomb-excitation cross sections cross sections for the process depend sensitively on for the highest 0-vibrational states (N = 5,6) for the saddle-point deformation and on the curvature of 234 the barrier. More recently, quantum mechanical backwards scattering from U of projectiles of calculations have been used to yield order-of- various charges Z near their respective Coulomb magnitude estimates of cross sections for sub- barriers (from Be69). threshold fission (Be69. Be70). Typically the excitation process involves at least 6 separate steps High-energy heavy-ion beams would produce large and therefore the backward scattering cross sections recoil velocities and could allow the use of Doppler- increase enormously with the Z of the projectile. The shift techniques to measure fission lifetimes in the predictions (Be69) are shown in Figure II-3-1 where it range 10"'2 - 10"'4 s. This would require determining can be seen that the difference in cross section changes in the forward-backward asymmetries of the between oxygen and uranium ions as projectiles is neutron yield or changes in the opening angle for the roughly a factor 107 in favour of the heavier. fission products when a slowing-down medium is introduced. Even lower limits on the fission lifetime In this process, reasonably detailed experimental (~ 10"'6 s) could be obtained by establishing whether information can also be obtained for the fissioning K X-rays of the fissioning nuclei are in coincidence states. The excitation region in the target nucleus can with the fission fragments. If coincidences are be determined by measuring the energy of the observed, the fission lifetime must be longer than * inelastically backscattered ions and it can be varied 10"16s, the time required to fill electron vacancies in by varying the bombarding energy. Angular- the K-shell which were produced by the preceding distribution measurements might provide information heavy-ion collision.
-40- Coulomb-induced fission has never been observed. There is every reason to believe, though, that this is only because of the unavailability of ions which are heavy enough and energetic enough to induce its occurrence. If so, an accelerator capable of producing such ions would be unique as a tool for controlled and versatile studies of fission.
T, a FISSION \ C. INTERMEDIATE STRUCTURE The discovery of fission isomers in 1962 at Dubna (Po62) led directly but somewhat slowly to realistic 7 ^^^v FISSION V f Y.n ' ^^. ISBMER calculations of shell effects in highly deformed nuclei. \ Although large effects had been predicted by Hill and '^/ \ V^ X Wheeler (Hi53) nearly ten years before, and consi- SPONTANEOUS dered by Myers and Swiatecki (My66), it was not FISSION until 1968 that Strutinski (St68) published the first quantitative calculations indicating a second minimum in the fission barrier of the actinides. The DEFORMATION essence of his results (St69) is illustrated in Figure II-3-2. With a well-defined second minimum in the deformation energy, a whole spectrum is introduced of Figure II-3-2 — Two-humped barrier in the defor- mation energy of a heavy nucleus. Transitions so-called Class II states which are completely analo- between the two families of stationary states are gous to the "normal" Class I states. indicated (from St69). This explanation of the fission isomers as shape isomers immediately received impressive confirmation from the observation of strongly grouped sub-barrier fission resonances (Mi68) as shown in Figure II-3-3. It is believed that the narrow closely spaced resonances shown in the figure are Class I states, while the
Figure II-3-3 — The fission cross section of 24uPu is com- pared with the total cross section to demonstrate grouping of the fission reso- nances.
I 5 i i 5 I S S I 1 I ? S
-41- • 1 1
-
Figure II-3-4 —Class II vibra- tional levels are shown together with the transmission reso- CK4CT • WKB nances which Lhey cause.
,/
DEFORMATION c ENERGY CMcV) broader, widely spaced resonances correspond to mation such as spins can also be obtained by single-particle states in the second well which contain analyzing the angular distributions of protons a portion of the strength of one of the p-vibrational produced in the direct reaction, and an attempt at levels. The discovery of these phenomena radically such an analysis has also been made (Sp69). altered the approach to fission, the activity in the field, and its relationship to the rest of nuclear physics. In addition, it paved the way to sensible predictions for superheavy nuclei. Although the effects have so far been most dramatic in the fission of the actinide nuclei, long-distance shell effects are not confined just to fission or to the actinides but exist in all nuclei and may be important for some purposes even in light nuclei. l tfiPftitfS- The spectroscopy of Class II levels can in principle be studied in a manner similar to "classical" nuclear spectroscopy. Vibrational states are particularly important in the second well as they give rise to .\ '••• •-.,*• transmission resonances, or spikes in the barrier penetrability at energies corresponding to vibrational excitation; this is indicated in Figure II-3-4. The theory of these vibrational states, including their coupling with the Class I states, has been outlined by Figure 11-3-5 — Direct experimental results showing Lynn (Ly69) and he has predicted the expected form single and coincidence proton spectra obtained during that experimental results should take. deuteron bombardment of 2 3 9Pu (from Sp69). In work done at CRNL, Specht et al. (Sp69| 30 observed fine structure in - Pu by means of the It is of very considerable interest to continue 239 Pu (d,pf) reaction. Their spectra, shown in Figure experiments of this type, but they are hard, requiring II-3-5, exhibit an energy resolution of 17 keV which high energy-resolution and detectors capable of with- is insufficient to resolve the electron-volt spacing of standing severe radiation damage from heavy-ion Class I levels; however they suggest that the observed bombardment An instrument such as a QD3 spectro- structure corresponds to individual Class II states. meter is essential. There is another more fundamental The broad structure or bump in this region results problem. It is necessary to search carefully to find from the coupling of the 0-vibrational level respon- other examples as favourable as that of 340Pu, and, sible for the transmission resonance into the neigh- in fact, it may be extremely difficult to get more such bouring single-particle levels. Spectroscopic infor- information from any of the other actinides. By
-42- Figure II-3-4 — Class II vibra- tional levels are shown together with the transmission reso- nances which they cause.
0.2 0.4 4.0 DEFORMATION « ENERGY (MlV) broader, widely spaced resonances correspond to mation such as spins can also be obtained by single-particle states in the second well which contain analyzing the angular distributions of protons a portion of the strength of one of the (3-vibtational produced in the direct reaction, and an attempt at levela The discovery of these phenomena radically such an analysis has also been made (Sp69). altered the approach to fission, the activity in the field, and its relationship to the rest of nuclear physics. In addition, it paved the way to sensible predictions for superheavy nuclei. Although the effects have so far been most dramatic in the fission of the actinide nuclei, long-distance shell effects are not confined just to fission or to the actinides but exist in all' nuclei and may be important for some purposes even in light nuclei. The spectroscopy of Class II levels can in principle be studied in a manner similar to "classical" nuclear spectroscopy. Vibrational states are particularly important in the second well as they give rise to transmission resonances, or spikes in the barrier penetrability at energies corresponding to vibrational excitation; this is indicated in Figure II-3-4. The theory of these vibrational states, including their coupling with the Class I states, has been outlined by Figure II-3-5 — Direct experimental results showing Lynn (Ly69) and he has predicted the expected form single and coincidence proton spectra obtained during that experimental results should take. deuteron bombardment of 239Pu (from Sp69). In work done at CRNL, Specht et al. (Sp69) observed fine structure in 24oPu by means of the It is of very considerable interest to continue 2J9Pu (d,pf) reaction. Their spectra, shown in Figure experiments of this type, but they are hard, requiring II-3-5, exhibit an energy resolution of 17 keV which high energy-resolution and detectors capable of with- is insufficient to resolve the electron-volt spacing of standing severe radiation damage from heavy-ion Class I levels; however they suggest that the observed bombardment. An instrument such as a QD3 spectro- structure corresponds to individual Class II states. meter is essential. There is another more fundamental The broad structure or bump in this region results problem. It is necessary to search carefully to find from the coupling of the j0-vibrational level respon- other examples as favourable as that of 240Pu, and, sible for the transmission resonance into the neigh- in fact, it may be extremely difficult to get more such bouring single-particle levels. Spectroscopic infor- information from any of the other actinides. By
-42 - increasing the number of nuclei which are accessible three elements: uranium, plutonium and americium. to study, a high-energy heavy-ion accelerate/ could Many unanswered questions remain; for example, make many other experiments feasible, and would why are there none in neptunium? A well-defined provide in addition the potentialities of Coulomb second minimum is predicted (St68) in the region of induced fission for spectroscopic study. 203 At but a recent search (Bj70) failed to find any fission isomers. Furthermore, in most cases little is D. FISSION ISOMERS known about the observed isomers except their half life. There is thus a greal deal to be done in looking Apart from sparking an interest in long-range shell for new regions of isomerism and in learning more effects, the study of fission isomers has yielded much about the old. A heavy-ion accelerator could be most interest of its own. About 30 fission isomers are now useful in providing new species and for introducing known (Bj69) and these have provided valuable large amounts of angular momentum. In this way one information on barrier parameters. However, all of might even find a spin isomer in the second well. these isomers occur in 5 elements and 90% are in
REFERENCES
Be69 K. Beyer and A. Winther, Phys. Lett. 30B My66 W.D. Myers and W.J. Swiatecki, Nuc!. Phys. (1969) 296. 81 (1966) 1. Be7G K. Beyer, A. Winther and U. Smilansky, in Ni69 R. Nix, Los Alamos report LA-DC10530, Nuclear Reactions Induced by Heavy Ions, 1969. edited by R. Bock and W.R. Hering (North- Po62 S.M. Polikanov, V.A. Druin, V.A. Karnauk- Holland Publishing Company, Amsterdam, hov, V.L. Mikheev, A.A. Pleve, N.K. 1970) 804. Skobelev, V.G. Subbotin, G.M. Ter-Akop'yan Bj69 S. Bj0mhoim, Proceedings of the Robert A. and V.A. Fomichev, Sov. Phys. JETP 15 Welch Foundation Conference on the Tran- (1962) 1016. suranium Elements, Houston (1969) 447. Sc71 H.W. Schmitt and U. Mosel, Bu!l. Am. Phys. Bj70 S. Bj0rnholm, J. Borggreen and E.K. Hyde, Soc. II, 16(1971) 1149. Nucl. Phys. A156 (1970) 561. Sp69 H.J. Specht, J.S. Fraser, J.C.D. Milton and Gu66 E. Guth and L. Wilets, Phys. Rev. Lett. 16 W.G. Davies in Physics and Chemistry of (1966) 30. Fission IAEA-SM-122/128 (International Atomic Energy Agency, Vienna, 1969) 363. Hi53 D.L. Hill and J.A. Wheeler, Phys. Rev. 89 (1953) 1102. St68 V.M. Strutinski, Nucl. Phys. A122 (1968) 1. Ly69 J.E. Lynn in Physics and Chemistry of St69 V.M. Strutinski and H.C. Pauli in Physics and Fission, IAEA SM-122/204 (International Chemistry of Fission, IAEA-SM-122/203 Atomic Energy Agency, Vienna, 1969) 249. (International Atomic Energy Agency, Vienna, 1969) 165. Mi68 E. Migneco and J.P. Theobald, Nucl. Phys. AU2 (1968) 603. Wi67 L. Wilets, E. Guth and J.S. Tenn, Phys. Rev. 156 (1967) 1349.
-43- 4. IN-BEAM STUDIES OF ELECTROMAGNETIC PROPERTIES OF NUCLEI
A. Introduction
B. Pertinent Problems in Nuclear Science
C. Reaction Mechanisms
D. Experimental Techniques
E. Beam Requirements References A. INTRODUCTION
The study of electromagnetic properties of nuclear Many benefits to the theory of nuclear models states provides a reliable means of testing the predic- can be expected to follow from such a wide range of tions of model calculations since the nature of improvement in experimental data. electromagnetic forces is well understood. Any discrepancies between calculation and experiment can B. PERTINENT PROBLEMS IN NUCLEAR STRUC- only reflect on limitations in the assumed nuclear TURE wave functions and not on the interactions between them. Recognition of this fact has led to a great a) Vibrational Nuclei number and variety of experiments to measure At the present time detailed knowledge of the transition strengths between levels as well as static properties of levels in the even-mass vibrational nuclei properties such as g-factors and moments of the levels is limited to those involving one- and two-phonon themselves. Many experiments of this type have been excitations. The one-phonon level in a number of performed at Chalk River and, in fact, some of the these nuclei has been found to have a large static relevant techniques now widely used elsewhere were quadrupole moment in contradiction to the simple pioneered here (lifetime measurements by Dopplei- vibrational picture (De68); also the matrix elements shift attentuation — E148; angular correlation techni- for transitions between two-phonon and one-phonon ques— Li61; Ge(Li) detectors — Ew64; and lifetime states are in general somewhat smaller than those measurements by the recoil-distance method —A170). predicted on the basis of M(E2; 2+ -> 0) for the However, as in an'1 *ich field our present knowledge 1 de-excitation of one-phonon states. Empirical mixing points the direct » in which still more fruitful gains of the one-and two-phonon states (Ro69) does not can be anticipat . prove sufficient to account for the observed In this sectio i will be briefly outlined those areas deviations. of nuclear-structure study where major improvements A detailed study of the properties of the three- in knowledge can be expected, and the particular phonon vibrational states in these nuclei would be significance of a high-energy heavy-ion beam in possible using higher-energy heavy-ion beams to facilitating them will be emphasized. It will then be increase the cross sections for multiple processes. shown how the use of heavy ions improves and With this added knowledge it may prove possible to extends the applicability of the most advanced decide whether the deviations from the simple vibra- experimental techniques currently used for in-beam tional picture can be adequately described by a gamma-ray spectroscopy. perturbation treatment or whether some completely The improvements will be seen to follow from different approach is required. making available a wide selection of heavy projectiles In the case of the odd-mass vibrational nuclei, the at energies variable up to or slightly above the available experimental data relate largely to the Coulomb barrier for the heaviest target. This will multiple! of levels arising from the coupling of the permit: one-phonon vibration of the core to the ground i) the selective production of nuclei off the stabi- intrinsic state. Intermediate-coupling models have lity line by direct or compound-nucleus reac- proven quite successful in describing the properties of tions; this class of states (see e.g. Ru68j. More stringent tests of this model require detailed knowledge of the ii) Coulomb excitation to high-spin states; properties of the levels arising from the coupling of iii) the study of multiple processes and higher-order multiple-phonon oscillations to both the intrinsic effects in Coulomb excitation; ground state and to low-lying intrinsic states other iv) the study of Coulomb-distortion effects; than the ground state. Higher-energy heavy-ion beams would also make it possible to populate these states v) measurement of many previously inaccessible with adequate intensities by multiple-step excitations. nuclear lifetimes; Briefly, the use of higher-energy heavy-ion beams vi) alignment of high-spin states, and for iii-beam 7-ray spectroscopy studies on the vibra- vii) the measurement of g-factors for short-lived tiona. nuclei would permit: nuclear levels.
-47 - i) the identification and study of 3-phonon levels factors. A knowledge of these properties is essential in vibrational nuclei; in making a detailed comparison with the shell model. ii) more reliable measurements of the static quadru- In what follows, techniques will be described that ple moments of the Iowesl>energy 2+ states in depend upon high-energy heavy-ion beams, and could even vibrational nuclei; be employed in the measurement of: iii) the measurement of static properties, in parti- i) transition strengths (E2, Ml, etc.) between cular g-factors. of 1- and 2-phonon levels; and single-particle levels; iv) the investigation of intermediate couplings in ii) the static properties of single-particle levels (g- odd-mass nuclei in the vibrational region. factors); and iii) the properties of high-spin levels whose descrip- b) Rotational Nuclei (Even A) tion is given by 2- and 3-particle configurations near the shell closures. The central problem in the rotational regions is understanding how the intrinsic state responds to C. REACTION MECHANISMS rotation. The instrinsie state properties are observed to change with increasing rotational angular momen- a) Compound-Nucleus Reactions tum. Present thinking is to attribute this to a centrifugal stretching of the nucleus and a weakening In on-line studies of reaction products produced of the pairing-force interactions (see e.g. Di71). If the through the compound-nucleus mechanism, it is usual rotation angular momentum becomes higher than a to choose a bombarding energy close to the Coulomb critical value — the Mottelson-Valatin limit barrier so that the excitation energy of the compound (M06O) — this interaction can become negative and nucleus will be as low as possible. This condition such states will have an intrinsic structure that is results in maximum product specificity and mini- practically orthogonal to the ground state, with a mizes the generation of unwanted background moment of inertia equal to the rigid-rotor value. The radiations. The systematics of the Coulomb barriers currently available data are not sufficiently accurate and reaction Q-values are such that under this or extensive to permit quantitative assessments of this bombardment condition the excitation energy in the interpretation. With higher-energy heavy-ion beams it compound state never exceeds ~ 60 MeV • for any would be possible to carry out some experiments stable target-projectile combination producing com- which could shed further light on the subject: pound nuclei of A < 240. An excitation of 60 MeV in the compound state will result typically in the i) measurements of the static properties of rota- evaporation of 3 or 4 particles prior to the emission tional states beyond the 2+ level (Q2, Q4 and g of gamma rays from the residual final nucleus. The factors); evaporated particles will be neutrons if the system is ii) measurements of transition moments (E2 and not very neutron deficient, or combinations of n, p E4) at spins up to and beyond the Mottelson- and a if it is. Even in cases where the yield is Valatin limit (M06O) which occurs at spins of 14 fragmented, it may still be possible to interpret the to 18 in the rare earths; and in-beam gamma spectrum, and deduce level schemes. For example, ' 26Ce (14 neutrons removed from the iii) the determination of the pairing strength in the l40 different rotational members of the ground-state most abundant stable isotope Ce) was recently band using transfer reactions (Di70). (See studied this way (St71). section H-4-C-b which follows.) A very wide range of neutron-deficient nuclei can be studied with (HI, particles) reactions (where c) Closed Shell Nuclei "particles" can consist of n, p and a). There are a vast number of possible projectile-target combinations The techniques of charged-particle spectroscopy which make it possible to study the systematics of have been successful in identifying a large number of collective levels of isotopes ( r isotones) over large the single-particle states around closed-shell nuclei. variations in N (or Z); these regions may be suffi- With few exceptions, however, little is known concer- ning E2 and Ml strengths for the decays of these levels. In cases where tha levels are at high energies, Possible flattening of very heavy nuclei might raise and hence short lived, there are no measurements of g- this figure by as much as 20 MeV.
-48- ciently wide to range from closed-shell through for excitation can result in excitation probabilities via vibrational to rotational behaviour for a given N (or higher-order processes comparable with those from Z). (See section II-1.) single E\ excitations. For example, several existing accelerators provide beams of sufficient energy to b) Transfer Reactions excite, by successive E2 steps, levels of up to spin 12+ with measurable cross sections. The interference Because of the classical behaviour of heavy- between direct excitation (including multiple excita- projectile heavy-target scattering phenomena, the tion) and excitation via interaction with the static general complexity of the mechanics of transfer electric moments of the levels makes it feasible to reactions reduces to the simple idea of surface-grazing measure the static moments. Since these processes exchange. The angular distribution and excitation involve only the Coulomb interaction along a semi- functions for scattering with transfer are adequately classical orbit, the excitation cross section can Sje given by the Frahn-Ventner model (Fr64) although calculated quite simply and very accurately in terms this model contains no spectroscopic information at of the static and transition EX moments for the all. The present experimental knowledge of heavy-ion nucleus. Background radiations in such experiments transfer reactions is very limited. The measurement are exceedingly low if elementary precautions are and quantitative interpretation of the transfer- taken. reaction cross section to specific states in the final nucleus are important current problems in low-energy 22 nuclear physics and are discussed in section II-6. As JSm the projectile charge increases these cross sections will 20 GROUND STATE BAND be affected by the high probability for Coulomb IB excitations in the incoming and outgoing channels. This offers the chance of studying particle transfers 16 from excited states of the target, and the possibility of measuring E2 strengths from excited states of the 14 residual nucleus which might otherwise be inacces- sible (Wa69). Despite the present limited under- 12 standing of the transfer-reaction process, if the 10 bombarding energy is high enough it can be used to produce excited residual nuclei which are in 8 collimated beams, have high recoil velocities, and are ideally suited to study with the techniquesto be 6 described in part D of this section. 4 The transfer reaction provides the only method of producing neutron-rich nuclei for study in-beam (see section II-l). By choosing the bombarding energy appropriately one can study transfer reactions at a 10 20 30 40 50 60 70 80 90 scattering angle of 180°; it is then possible to do spectroscopy by delecting gamma rays in coincidence with the "residual" projectile since the background Figure II-4-1 —Plot showing the highest-spin rota- radiation is relatively small. tional levels that could be Coulomb excited in " Sm with 1% probability as a function of the charge of the c) Coulomb Excitation projectile, Zp. The projectile energy is assumed to be at 80% of the Coulomb barrier height (Go69). The high Z of a heavy-ion projectile makes electromagnetic interactions much more probable The energy requirement in Coulomb excitation is than they are for particles of unit Z. For instance that the bombarding energy should he slightly lower with 4 ° Ar ions, at energies near 4 MeV per nucleon than the Coulomb barrier. Therefore for this purpose (below the barrier), the probability for excitation of a the ideal machine should provide beams of ~ 6 rare-earth nucleus summed over the levels below 2 MeV/ nucleon throughout the periodic table. The MeV can be greater than 90%. The high probability greater the charge, Zp, of the projectUe, the greater
-49- will be the cross section for multiple processes and With these heavy projectiles the reliability and higher order effects; Figure II-4-1 shows how the accuracy with which static electric moments could be cross section for populating high-spin states depends measured through the reorientation effect would be on Zp (Go69). The importance of bombarding at considerably improved. A number of measurements energies close to the barrier height is demonstrated in of this type have been made at Chalk River in the 14 Figure II-4-2. The excitation probabilities shown there past The size of the reorientation effect for ' Cd are applicable to the measurement of B( E2) values up to (for example) is about a factor of five larger with a 208 16 the Mottelson-Valatin spin cut-off in the ground-state Pb projectile than with 0, the beam used in the band of 160Dy (Jo71). With Pb ions as projectiles, majority of previous studies. More important, the however, the probabilities for exciting the 16+ and larger cross sections would allow measurements to be 18+ states would be more than an order of magnitude made at a number of scattering angles and incident larger for the same separation between the surfaces. energies for each of several projectiles. The increased In fact, since excitations of the projectile should be cross sections would likely make it possible to isolate kept small, 208Pb appears to offer most advantages, the reorientation effect from other second-order but considerable flexibility should be made available processes. For example, it should be possible to in order to isolate the many different effects by identify the contribution of El polarizabilitias, and working up through successively heavier projectiles. the static deformation of octupole-vihrational states would also become measurable. There is at present FERMIS virtually no experimental information on these 3 2 0 DISTANCE BETWEEN SURFACES «V 1.48) quantities. 6+ 8+ Energetic beams of very heavy ions would also be
10+ EXCITATION required to study experimentally Coulomb-distortion PROBABILITY effects. The distortion depends on the stiffness of the AT 170° FOR colliding nuclei against quadrupole and octupole deformation (Je70), and gives rise to a change of Coulomb-barrier height. Measurement of Coulomb- K+ excitation cross sections near the barrier, and threshold behaviour for particle emission should be promising ways of attacking this phenomenon.
D. EXPERIMENTAL TECHNIQUES
a) Nuclear-Lifetime Measurement Using the Recoil- Distance Method (RDM)
In applying the recoil-distance method (e.g. A170) it is necessary to choose the target-projectile combi- nation that will result in the largest possible recoil r velocity vr for the excited target nuclei. The range of 160 C£ ENERGY (MeV) recoil angles is restricted either by kinematic considerations or by imposition of a coincidence requirement. Gamma rays emitted by these recoiling Figure II-4-2 — Plot of the probability for Coulomb nuclei are detected in a high-resolution Ge(Li) exciting a ground state rotational level, J , in 160Dy detector viewing the target at an angle 8 relative to vs 3 5 Cl ion energy. The calculations are for a specific the mean direction of recoil. A stopper at a distance d ion trajectory, at 6 = 170 . On the top scale, zero dis- from the target brings atoms reaching it very quickly tance between the surfaces corresponds to the Cou- to rest (< 1 ps). Gamma rays emitted from the nuclei lomb barrier; in most Coulomb-excitation studies a as they recoil through vacuum have their energy minimum separation of 2 to 3 fermis is necessary for Doppler shifted by an amount quantitative interpretation of the cross section.
-50- so that the observed 7-ray spectrum shows a peak of LINE SHAPE FOR 2+-0* (871 keV) in MMo area M at energy E + AE arising from 7 decays BACKSCATTER COINCIDENCE WITH MC< (ICOMeV) occurring during flight and a peak of area S at energy E resulting from the decays taking place after the nuclei reach the stopper. The lifetime is determined from a plot of S(S + MJT1 versus d. The two features which limit the range of applicability of this method are i) the requirement that the peaks S and M be resolved m the Ge(Li) 7-ray spectrum, i.e. AE > FWHM - 2 to 3 keV. ii) the requirement that a significant fraction of the nuclei in the excited state of interest survive the transit period across the smallest gap which can be realized between target and stopper; i.e. there must be a measurable stopped peak S in the 7-ray spectrum.
For the first requirement, a recoil velocity of 4% of the velocity of light results in a separation of the stopped and moving peaks at 0 = 0° of 4 keV for a 100-keV 7 ray and proportionately more for higher energy 7's. These separations are sufficient to com- pletely resolve the peaks in good Ge(Li) detectors. In many cases it is useful to be able to position a 7-ray counter at backward angles; because the beam itself excludes the region near 180°, the full shift will not v/c % be visible and still higher recoil velocities would be E MeV useful. RECOIL< > Figure II-4-3 — DSAM gamma-ray line shape of the Concerning the second requirement, the best 871 keV (2+ -»• 0+) transition in 94Mo as observed in performance routinely achievable in recoil-distance coincidence with backscattered 35CI ions. The high- experiments is a controlled separation of 0.5 mils. If energy shoulder results from 7-rays emitted before the we somewhat arbitrarily select ti^ = 1 ps as the recoiling 94Mo atoms s>t,op in the target material. shortest lifetime of interest in RDM (anything shorter The solid line is a fitted curve which is calculated could be done by DSAM, as described in the using the nuclear and electronic stopping powers following paragraph) then at 4%-of-c recoil velocities shown in the upper inset and corresponds to a nuclear = the survival across the minimum gap is only ~ 50%. It mean-life, TVr 4.5 ps. would therefore be difficult to extract, a good value b) Nuclear-Lifetime Measurement Using the Doppler- for the lifetime under those conditions unless the true Shift-Attenuation Method (DSAM) zero reading of the target-stopping plate system were obtained very accurately from an independent As indicated in the preceding discussion the measurement. In practice the situation may be recoil-distance method is most useful for nuclear considerably worse than this, since in many experi- lifetimes ^ 1 ps. In these cases the stopped peak has a ments a self-supporting target foil is required and one well defined shape and a significant fraction of the could not achieve 0.5 mils controlled separation. recoiling nuclei will reach the stopper before de- Thus, it is seen that a recoil velocity of 4% of c excitation occurs. In the Doppler-shift-attenuation throughout the periodic table is a minimal require- method the target is prepared directly on the stopper. ment. Higher velocities are desirable but can only be Advantage is taken of the fact that even in solid achieved within the limitations of the reaction media recoiling atoms require a short but finite time mechanism itself; Le. the bombarding energy must be to dissipate their kinetic energy and come nearly to 12 chosen to yield a reasonable reaction intensity. rest; in typical cases this takes -Iff sec. The
-51 - 2 observed energy of the 7 rays emitted from nuclei correspond to high angular momentum (dag ~ £ ), during the slowing-down process is Doppler shifted and for a maximum orbital angular momentum by an amount given by the expression ^ 50, as is usually the case, this effect will dominate the small contributions from channel spin.
E(0,t) = Er |l + cos0-v(t)/c} Thus, since the evaporating particles carry off little angular momentum, most of the orbital alignment where v(t) is the atom velocity at the time t (t = 0 at will be preserved in the J value of the residual nuclear the reaction time) when the 7 ray is emitted and E^ is state. This alignment results in strong angular distri- the energy as observed from atoms at rest Since butions for the de-excitation 7 rays that are effective E(0,t) is a continuous function of t, the observed in determining the multipolarities of the 7 radiations. effect is a distortion of the normally Gaussian 7-ray In many cases the angular distributions of the line shape. An example of the effect is shown in de-exciting gamma rays can be simply interpreted Figure II-4-3 and the basis for analysis of such a line without coincidence demands (Ne67), but, if J is very shape is outlined in section II-8. In this example, in large, it is more difficult to deduce rigorously its which the target nucleus was Coulomb excited, the value since the angular distributions from completely conditions were chosen such that the maximum aligned states become insensitive to the exact value of target recoil velocity was 4% of c so as to minimize J. However, the angular distributions in conjunction the effects of the unreliable nuclear stopping power. with other arguments, can lead to J assignments if the The Mo isotopes were chosen for study because of 7-transition is 'stretched' (Ne67). the fact that the Mo recoil velocity is particularly 35 favourable with the 100 MeV CC beam presently MAGNETIC FIELD TO CAUSE A MEAN available. In order to study (i) lower-energy gamma- ANGULAR PRECESSION o.r =0.1 rays (ii) heavier target nuclei or (iii) multiply-excited ASSUMING A NUCLEAR g-FACTOR states, it would be desirable to use much heavier OF 0.3 projectiles. To achieve a minimum of 4% recoil velocity in this type of experiment throughout the periodic table while bombarding at the Coulomb barrier (in order to maximize the era's section for Coulomb excitation) an ion beam of A ~ 60, for example, would require energies of up to 5.5 MeV per nucleon.
c) Angular-Distribution Studies Following Heavy-Ion Reactions
The high momentum of heavy-ion beams gives rise to very high orbital angular momentum components at a reaction site; thus it is possible, in principle, to excite nuclear states with spins up to J ~ 50. While 100 the identification of levels with such high spin has not Recoil in Ferromagnetics so far been reported, some average properties of levels Recoiling Free Ion having J ~ 30 have been determined by measuring the time taken for gamma decay from a particular region Figure II-4-4 — The plot shows the relationship of excitation to the ground band (Ne70). The highest between nuclear lifetime, r, and the magnetic field spin reported so far for an individual level is 39/2 in strength which is required to cause a mean angular 21'At (Ma71). The (HI,xn) reaction has also been precession COT = 0.1 assuming a nuclear g factor o£ used to identify probable ground-state rotational- 0.3. The magnetic field strengths for T <^ 40 ps are band members with spins above the Mottelson- only realized in excited atoms recoiling freely in Valatin limit (Jo71). vacuum with velocities of v/c > 0.5%. Because of the geometry, the orbital angular momentum is aligned with respect to the beam direction: i.e. mp = 0. The largest cross sections
-52- d) g-Factors of Excited Nuclear Levels requirements such as large production cross section and low background. To be able to do this, maximum The strong 7-ray angular distributions associated versatility in the mass of available projectiles is with heavy-ion reactions, together with the very large required. hyperfine fields present in the partially stripped recoil atoms, permit g-factor measurements to be made by E. BEAM REQUIREMENTS the perturbed angular-correlation method (see e.g. G068) on many short-lived nuclear states. The mag- For the in-beam experiments envisaged here, netic field at the nuclear site in these recoiling atoms beams delivered at the target with a high duty cycle is found to be roughly proportional to recoil velocity are desirable. This would minimize counting losses in 8 1S0 and is ~ 10 gauss in a Sm atom recoiling from a singles experiments and randoms in coincidence target with a velocity of ~ 4% of c. The magnetic- experiments. For reasons discussed in section C, field strength necessary to produce a given rotation of compound-nucleus reactions should be studied at the angular distribution is plotted as a function of close to minimum excitation energy and transfer nuclear lifetime r in Figure 11-4-4. It is seen that the reactions at ~ 180° grazing incidence for reasons of fields attainable in the freely recoiling ion are as product specificity and low background. An ion much as two orders of magnitude greater than those energy of up to ~ 6 MeV/nucleon would satisfy these obtained by recoil into magnetized iron. At present conditions for heavy-ion in-beam studies on all stable the recoil of excited atoms in vacuum is the only targets. With gamma-ray techniques the energy resolu- method known for generating fields at the nucleus of tion of the machine need not be unusually good. A between 2 and 100 mega-gauss, and such strengths are figure of (AE/E)- 0.1% would be adequate for these necessary to produce measurable perturbations on the experiments; even (AE/E) — 1% would be acceptable 7-ray angular distributions from states with mean in certain studies. The highest usable current would lives of ^ 40 ps. The necessary recoil velocities (0.005 probably be ~ 100 "particle nA" but ~ 1 "particle < v/c < 0.04) must be produced at bombarding nA" could be acceptable in many cases; this is energies compatible with the other experimental equivalent to between 1010 and 1012 particles sec"1.
REFERENCES
Go69 H.E. Gove, in Proceedings International Con- A170 T.K. Alexander and A. Bell, Nucl. Instr. and ference on Properties of Nuclear Stales, Methods 81 (1970) 22, and references edited by M. Harvey, R.Y. Cusson, J.S. Geiger therein. and J.M. Pearson (Les Presses de L'Uni- De68 J. de Boer and J. Eichler, Advances in Nuclear versite de Montreal, Montreal, 1969) 35. Physics 1(1968)1. Je70 A.S. Jensen and C.Y. Wong, Phys. Rev. Cl Di70 K. Dietrich, Phys. Letters 32B (1970) 428. (1970) 1321. Di71 R.M. Diamond, G.D. Symons, J.L. Quebert, Jo71 A. Johnson, H. Ryde, J. Sztarkier, Phys. K.H. Maier, J.R. Leigh and F.S. Stephens, Letters 34B (1971) 605. Lawrence Radiation Laboratory preprint Li61 A.E. Litherland and A.J. Ferguson, Can. J. UCRL-20463 (1971). Phys. 39 (1961) 788. E148 L.G. Elliot and R.E. Bell, Phys. Rev. 74 Ma71 K.H. Maier, J.R. Leigh, F. Puhlhofer and R.M. (1948) 1869. Diamond, Phys. Letters 35B (1971) 401. Ew64 G.T. Ewan and A.J. Tavendale, Can. J. Phys. M06O B.R. Mottelson and J.G. Valatin, Phys. Rev. 42 (1964) 2286. Letters 5 (1960)511. Fr64 W.E. Frahn, R.H. Venter, Nucl. Phys. 59 Ne67 J.O. Newton, F.S. Stephens, R.M. Diamond, (1964) 651, K. Kotajima and E. Matthias, Nucl. Phys. A95 G068 G. Goldring, in Hyperfine Structure and Nuc- (1967) 357. lear Radiations, edited by E. Matthias and Ne70 J.O. Newton, F.S. Stephens, R.M. Diamond, D.A. Shirley (North-Holland Publishing Com- W.H. Kelly and D. Ward, Nucl. Phys. A141 pany. Amsterdam, 1968) 640. (1970) 631.
-53- Ro69 R.L. Robinson, F.K. McGowan, P.H. Stelson, St7O R.G. Stokstad, LA. Fraser, J.S. Greenberg, W.T. Milner and R.O. Sayer, Nucl. Phys. S.H. Sie and D.A. Bromley, Nucl. Phys. A156 A124 (1969) 533. (1970) 145. Ru68 M.L. Rustgi, J.G. Lucas and S.N. Mukherjee, St71 F.S. Stephens, J.R. Leigh and R.M. Diamond, Nucl. Phys. A117 (1968) 321 and references Nucl. Phys. A170 (1971) 321. therein. Wa69 D. Ward and W.G. Davies, Atomic Energy of Canada Limited Report AECL-3512 (1969)15.
-54- 5. HEAVY ION ELASTIC AND INELASTIC SCATTERING
A. Introduction
B. Optical Model Analysis
C. Microscopic Theories
D. Experimental Requirements
References A. INTRODUCTION
Since the observation at Chalk River of resonances ELASTIC SCATTERING I2 I2 in C + C elastic scattering (Br61) heavy-ion EXCITATION FUNCTIONS ec.m.*90' elastic scattering has received a considerable amount I ' ' • ' i • of experimental and theoretical attentian. A large variety of experiments has been performed on the elastic scattering of various projectile-target combi- nations in the mass range A < 40 and extensive analysis of the resulting cross sections has been undertaken on the basis of optical-model potentials and from more microscopic points of view. It is hoped that these studies will lead to a better understanding of the heavy-ion nucleus interaction and its relationship to the properties of nuclear matter, the fission process, nuclear structure and heavy-ion reactions in general. The following sections describe some of the activity to date in this subject, and indicate the need for an accelerator capable of exceeding the Coulomb barrier for the widest possible range of heavy ions with good beam intensity, energy resolution and emittance.
B. OPTICAL MODEL ANALYSIS
A general feature observed in a large number of the cases studied so far is a gross structure in the excitation functions showing peaks ivith widths of the order of two or three MeV. Data from a variety of ion-ion scattering studies are shown in Figure II-5-1 (from Go71) together with fits using a single set of Woods-Saxon optical model parameters with only the interaction radius scaled as Ala to correspond to the various cases. Although the exact positions of maxi- ma and minima and relative magnitudes are not well reproduced by the fits, the widths of the gross 20 SO structure and general trends of the data lead one to Ee.rn.tMtV) believe that optical-model fits may be able to approximate the gross structure if better parameters are chosen for the individual cases. A large number of Figure II-5-1 — Collected heavy ion elastic scattering detailed optical - model fits to the data have been excitation functions. The full lines represent data performed (see e.g. Go71, Si71) mainly as a conve- while the dashed lines are optical model predictions. nient parameterization of the data containing an results which were obtained at Chalk River (Fe71) explicit dependence on mass, charge and energy. It is for 28Si + 28Si elastic scattering and are shown hoped that systematic trends will be evident in the in Figure II-5-2. The dashed lines are the calculated parameters which will yield new insights into the cross sections for Coulomb scattering. The solid heavy-ion nucleus interaction (Si71). lines, which describe the available data quite well, General trends have already been observed in these are calculated from the simple Blair model (B157) optical-model fits which indicate that the nucleus as modified by Mclntyre et al. (Mc60). In this generally appears "black" for central collisions and model the nucleus is assumed to be completely "transparent" for grazing collisions (Si71). An absorbing for all partial waves which correspond to extreme case of this tendency was illustrated in the collisions within its classical radius; there is then an
-57- exponential increase to full transparency over a small in the '6 O + '6 O and '2 C + '2 C elastic scattering are range of angular momenta. This is presently the a consequence of the restricted number of open heaviest-mass study of identical particle elastic scat channels in these cases compared to, say, O + O tering. The statistical accuracy near the highest which shows almost no gross structure (Si71, Gr71). energies was insufficient to show the presence of any It is apparent that a complete description of the resonant structure, which points out the experimental process of heavy-ion scattering will require a know- difficulty of performing such experiments with a ledge of the properties of bulk nuclear matter as well Tan 'am accelerator near its maximum energy for a as considerations of the nuclear structure details for a given heavy ion. For the highest energy region (Ecm particular case. It would be particularly interesting to > 40 MeV or Ejab > 80 MeV) with 10 MV maximum see whether the resonant structure which
-58- (Gr71). A microscopic calculation (Gr71) based on Harvey (Ha71) is the role played by the Pauli the two-center shell model with many approxi- principle as the two nuclei merge. That is, how do the mations was found to introduce an Independence in individual nucleons intermingle as the centers of the the imaginary optical potential similar to that used by two nuclei approach coincidence? Harvey has been 16 16 Chatwin et al. (Ch70) to fit O + 0 elastic studying this problem by expressing the wave func- 6 6 scattering. Figure II-5-3 shows a fit to the ' O + * O tions of the two clusters in terms of the wave elastic scattering resonances with the real potential functions of two harmonic oscillators associated with determined from the sudden approximation using a the clusters. The total wave function is rendered generalized liquid-drop model, and an angular- antisymmetric for all nucleons at all cluster separa- momentum-dependent imaginary potential. tions and thus can properly represent the system as the two nuclei approach and possibly pass through each other. Calculations have been carried out (Ha71) for an 8-nucleon system which graphically portray how the density can vary as two alpha part Lies pass through each other. Greiner (Gr69) has speculated that abnormally high nuclear densities can be created so that nuclear particles are squeezed out in opposite directions from the overlapped region. Harvey's model suggests that the Pauli principle will prevent such behaviour and that the wave nature of the colliding nuclei will allow them to interpenetrate without any dramatic rise of the nuclear density. A recent experiment (Pu71) was designed to test Greiner's hypothesis by looking for a peak in the numbers of alpha particles emitted in opposite directions (at relative angles of 180°) from the reaction '6 0 + '6 O. No such peak was observed. Experiments and calculations of this type on heavy-ion scattering bear on questions of the com- pressibility of nuclear matter and the configura- tions of nucleons during the process of scattering. Other recent calculations by Jensen and Wong (Je71) have considered the effects of the Coulomb distortion \7 20 25 30 of heavy nuclei at energies near the Coulomb barrier CM. ENERGY (MeV) and of interference effects between Coulomb and nuclear fields at higher energies. Considerable defor- Figure 11-5-3 — Excitation function for the elastic 16 6 mations are found and it is likely that this is a fairly O-' O scattering. The theoretical curve is obtained good representation of the situation before nuclear with a real sudden potential and an angular momen- reactions take place. Work is in progress (Ha71) on tum dependent imaginary potential. incorporating Harvey's model for the interpenetration It is noted in the considerations of the two-center of nuclei into this type of calculation to extend the model that some configurations may occur that allow model to higher incident energies. Experiments decays to other open channels, thus giving rise to the designed to test these calculations should include imaginary components found in the optical poten- measurements of inelastic as well as elastic scattering tials. Some states are also found to have large widths in heavy-ion systems. The availability of an accele- for decay back to the entrance channel and thus form rator which could exceed the Coulomb barrier for all "quasimolecular" states as was suggested in early ion-ion systems would permit systematic studies of analysis of the I2C + I2C elastic scattering (Vo60, nuclear deformability using both spherical and highly Br61). distorted ions. The models described here have application in An important question in the interaction of two reverse for the latter stages of the fission process. At heavy ions which has been considered recently by
-59- present there is speculation on the effect of the Figure II-5-5 shows oscilloscope displays of 12 2 fragment shell structure on the fission process. It has C + ' C data accumulated in elastic and inelastic been suggested that the stabilizing effect of the scattering studies at Yale. Two position - sensitive doubly-closed shell structure of superheavy nuclei detectors located on opposite sides of the beam were 2 may result in their enhanced production by the used to detect both of the scattered ' C nuclei in fission of very heavy compound nuclear systems coincidence and give simultaneous energy and angle formed in heavy-ion reactions (see section II-2-B). information with good resolutioa The various en- Such effects could be studied through ion-ion col- hanced lines on the two dimensional displays of lisions of nuclei with varying shell structure. This position (p) (proportional to angle) and energy (E) again points out the need for an accelerator capable correspond to the cases where the two coincident 12 of performing such studies with a wide range of C ions are in their ground states, or one or both are projectiles. in an excited state. Provision is made far projecting a kinematic region on the position axis to display D. £XPERIMENTAL REQUIREMENTS angular distributions. The fine angular resolution is displayed in Figure II-5-5f which was accumulated It is apparent from the preceding discussion that with a grid of wires at 1° intervals over one of the the extension of elastic and inelastic scattering to all detectors. combinations of heavy ions and targets would greatly extend our understanding of the interactions of finite These examples point out the advantages which nuclear matter. Such studies must be systematic and would exist for all the experiments described in this widespread in scope because of the large number of report through the use of extensive on-line computer nuclear parameters upon which they depend. They facilities. Even the study of elastic scattering, which is must also be detailed, requiring good energy resolu- generally considered to be one of the simplest possible tion and fine energy steps to observe resonant experiments, can benefit greatly from the increased structure and good angular resolution to resolve the accuracy which can be obtained through computer deep dips and maxima observed in Mott-scattering control. angular distributions (see Figure II-5-4). A number of The main requirement for good energy resolution experimental techniques have been developed to use in these experiments is to resolve the fine structure computer control of experiments to achieve these which may occur in excitation functions. It is objectives. For example, a technique is in use at therefore sufficient that the energy spread of the Chalk River (La72) for automatically incrementing incident beam be less than the total energy loss in the the beam energy, refocussing the beam optics and target. Assuming that targets need not be self recording the data, which greatly facilitates the supporting, then thickness will be determined mainly accumulation of excitation functions. by yield requirements. If beam currents of 100
5 10% M -T-r-n I0 PELASTIC SCATTERING : P 28s, • 2Bsi • E, =20MeV =
o
i-
E 10
b|cj 1 10 I0
0 in ' ' ' i ' i • ' ' < ' . 10° 20 40 60 80 100 20 40 60 80 100
Figure II-5-4 — Angular distributions of 28Si + 2SSi elastic scattering at energies below or near the Coulomb barrier.
-60- Cl2+C12 DATA ANALYSIS
:."":. •::•...••::;:••»::= "HH::. ::::::..
: : :: : !:li::ll!l:!::i!!;l'i r :i! i :::»!ilillil: 1; ill
Yield
A /y i l" r ! A 1 i 1i Ill A J I l I _L 9 s 30.5 6lob 48.5
Figure II-5-5 —Photographs taken directly from the data acquisition display (from G071).
-61- particle nanoamps are available for all beams, then ~ good as possible in order to permit the strict 5 Mg/cm2 targets of the lighter elements would give collimation required to study the details of angular useable yields for studies requiring good energy distributions (such as Figure II-5-4) without reduc- resolution. For Si on Si at 120 MeV, AE = 50 keV for tion in beam current. 2 a 5 Mg/cm Si target, so AE/E = 0.04%. For U on U at An accelerator designed to ideally perform the 12 MeV/A, using a target with the same atomic 2 2 studies described in this section should be capable of density as 5 jug/cm of Si (i.e. 42 Mg/cm ) then AE = accelerating the widest possible variety of heavy ions 1.9 MeV and AE/E = 0.07%. Therefore an energy over the Coulomb barrier for all elements. It should resolution of 0.04% should be adequate although therefore exceed 8 MeV/nucleon for U on U but more patient experimenters could use better resolu- there will be interesting information to be obtained tion in some specific cases. for all energies higher than this. The emittance of the machine should also be as
-62- REFERENCES*
B157 J.S. Blair, Phys. Rev. 108 (1957) 827. La72 S.T. Lam and A.J. Ferguson, Nucl. Inst. Meth. Br61 D.A. Bromley, J.A. Kuehner and E. Almqvist, 99 (1972) 151. Phys. Rev. 123 (1961) 878. Mc60 J.A. Mclntyre, K.H. \Vang and L.C. Becker, Ch70 R.A. Chatwin, J.S. Eck, D. Robson and A. Phys. Rev. 117 (1960) 1337. Richter, Phys. Rev. Cl (1970) 795. Oe71 W. von Oertzen, ANL-7837 (1971) 121. Fe71 A.J. Ferguson, O. Hausser, A.B. McDonald Pu71 K.H. Purser, C. Gaarde, H.E. Gove, H. Kubo and T.K. Alexander, Proceedings of a and R. Liebert, ANL-7837 (1971) 57. Symposium on Heavy Ion Scattering, Ra71 G.H. Rawitscher, ANL-7837 (1971) 199. Argonne, ANL-7837 (1971) 187. Si71 R.H. Siemssen, ANL-7337 (1971) 145. Go71 A. Gobbi, ANL-7837 (1971) 63. St67 V.M. Strutinsky, Nuci. Phys. A95 (1967) 420. Gr69 W. Greiner, Nuclear Reactions Induced by St68 V.M. Strutinsky, Nucl. Phys. A122 (1968) 1. Heavy Ions, Heidelberg, 1969, ed. R. Bock and W.R. Hering (North-Holland Publishing Va71 R. Vandenbosch, Proceedings of the Inter- Company, Amsterdam, 1970) 748. national Conference on Heavy Ion Physics, Dubna (1971) 337. Gr71 W. Greiner and W. Scheid, ANL-7837 (1971) 1. Vo60 E.W. Vogt and H. McManus, Phys. Rev. Lett 4 (1960) 518. Ha71 M. Harvey, 1971 private communication. Je71 A.S. Jensen and C.Y. Wong, Nucl. Phys. A171 (1971) 1.
* ANL—XXXX — Argonne National Laboratory Report
-63- 6. TRANSFER REACTIONS WITH HEAVY IONS
A. Introduction
B. Nucleon Exchange in Heavy-Ion Scattering
C. Few-Nucleon Transfer Reactions
D. Multi-Nucleon Transfer Reactions
E. The Nuclear "Josephson" Effect
References A. INTRODUCTION
A heavy-ion accelerator capable of producing shown that the interpretation of the earlier work is heavy-ion beams of the order of 10 MeV per nucleon incorrect, and large contributions from the alpha provides opportunities for investigating nuclear struc- transfer reactions ' 2C(16O,'2C)16O must be in- ture through heavy-ion transfer reactions. The ciuded (Oe70) in the analysis. Apparently, for the considerable amount of spectroscopic information scattering of two non-identical nuclei A and B there is 3 obtained using light ions, e.g. (d,p), ( He,d), (p,d), always a certain probability for the transfer of (p,p') etc, has shown that scattering and transfer particles corresponding to the difference of the two reactions provide a valuable experimental technique nuclei, (B-A) = C. Since this transfer process A(B,A)B for studying nuclear structure. has zero Q-value and leads to the same final channel Until recently the use of heavy-ion beams for as potential scattering, A(B,B)A, it adds coherently to scattering and transfer studies has been limited by the latter and can strongly influence the angular low beam intensities, poor detection apparatus and distributions of the elastic scattering (Oe71). The difficulties in interpretation of the data. With im- importance of the transfer process depends upon the proved ion sources and advances in particle extent to which the wave function of B can be detectors — e.g. very thin, uniform surface barrier represented by (A+C) and, as in any transfer reaction, detectors for use in particle identification — many of is also related to the relative motion of the two parts these experimental problems are being overcome and A and C. high-flux heavy-ion beams of 5 to 10 MeV per nucleon would allow transfer reactions to be studied over wide ranges of energy and angle with reasonable
counting statistics. At these higher energies the 1O4 decreased specific energy loss of heavy ions places less stringent requirements on detector thicknesses than at lower energies, and assuming adequate energy resolution in the primary beam, many reactions involving a variety of different projectiles — but transferring similar nucleons — could all be studied with equal ease.
B. NUCLEON EXCHANGE IN HEAVY-ION SCAT- ioz TERING
One of the earliest heavy-ion scattering experi- ments was that of Bromley et al. (Br60) at Chalk River. They observed resonances in the elastic scat- 1 10 tering of '2 C on '2 C and suggested these were the result of the formation of quasi-molecular states. These measurements were quickly followed by measurements of the scattering of 16O by 12C by Kuehner et al. (Ku63) who made an optical-model 10° analysis (Ku64) of the data. They found that very shallow imaginary potentials were needed to explain the oscillatory structure in the angular distributions in contradiction with the belief that heavy ions were strongly absorbed particles. Since then a considerable amount of experimental data has been accumulated cr 20* 40* 6O* 80" 100* 12CC for the scattering of identical and non-identical particles such as I4N on 14C, 18O on 1&O, 19F on Figure II-6-1 — Angular distributions for the scat- 12 C etc. More recent results on the scattering of '6 0 tering of 19F, I6O and IOB on I2C taken at by l2C over a wider energy range (Go68) have bombarding energies corresponding to their respective Coulomb barriers (from Oe71).
-67- Figure II-6-1 shows angular distributions for the any desired accuracy (Sc70). The reactions analyzed scattering of three different projectiles on '2 C. It is were '"B^N,1 3N)" B, 27A1('6O,'5N)28Si and apparent that pure potential scattering dominates at 1' B(' 6O,'5 N)12C; incident energies were again near small forward angles while the transfer process shows the Coulomb barrier. The authors' conclusions were up as a steep rise in the angular distribution at that at these energies the theory provided a reliable backward angles. Therefore, one of the amplitudes is means of calculating angular distributions and extrac- negligible in the angular region where the other has its ting spectroscopic factors. They then proceeded to largest value and the two processes can be analyzed emphasize the importance of obtaining data at higher separately, typically with optical model analysis for energies since "above the Coulomb barrier increased A(B,B)A and DWBA calculations for A(B,A)B. In the sensitivity of the results to the optical potential intermediate angular region (~ 60° — 120°), where provides a test of these parameters". Furthermore both processes occur, the angular distributions can be "the central role of the optical potential at higher analyzed by adding coherently the two individual energies gives additional incentive for its study by amplitudes. Furthermore, the contribution of the other means. A non-locality, for example, would give transfer process is seen from the figure to have rise to a Perey effect (Pe62; this is the observed decreased quite significantly for the scattering of ' 9 F energy dependence of optical model parameters) on I2C where seven nucleons would have to be known to be important for nucleon-nucleus reactions. transferred. The results are sensitive to a repulsive core and could shed light on its importance in a broader survey of The development of techniques such as these data" (Sc70). should provide a much more quantitative description of heavy ion scattering and reactions. Already, in the Pairing correlations in nuclei can also be investi- case of '2 C on '3 C, "spectroscopic factors" for gated using heavy ion reactions. The (t,p) and (p,t) neutron transfer have been derived (Oe70) from reactions have given considerable information about experimental data taken at bombarding energies near neutron pairing; however, because of the experi- the Coulomb barrier. From comparison with results mental difficulty associated with (3He,n) and (n,3He) of the equivalent (d,p) reaction it can be established reactions, not as much is known about proton that particle exchange occurred in 2CR of the pairing. The (16O,14C) reaction has recently been heavy-ion collisions. Clearly many examples of this shown by Lemaire et al. (Le71) to be a suitable process must be examined before such an inter- reaction for studying proton pairing. In experiments pretation of the reaction mechanism can be bombarding Ca and Ti isotopes with a 48 MeV confidently believed, and extension to heavier oxygen beam, a correlation was found between the projectiles (and targets) could become crucial. The two-proton transfer cross section and B(E2) values energies so far studied have all been at or below the for the low-lying levels of 4fl's °Ti and s°'5 2Cr. Also, Coulomb barrier where it is hoped that the "two-state the levels populated by the (' 6O,'4C) reactions were approximation" is valid. In this approximation all not populated by alpha transfer reactions to the same other transfer reactions which lead to excited states levels, indicating the role of pairing correlations in the in either nucleus A or B are ignored, thus giving a structure of these levels. very small probabilitiy for processes which lead to the In the (l6O,'"C) reaction Lemaire et al. (Le71) same final channel via an intermediate state. Experi- found that the angular distributions to strongly ments at higher energies could establish the signifi- excited states had little structure, were all very similar cance of such higher-order effects and stimulate and did not show any spin dependence; therefore, all theoretical work to understand them. spectroscopic information must be contained in the cross-section intensities. Sample angular distributions C. FEW-NUCLEON TRANSFER REACTION are shown in Figure II-6-2. The most significant Considerable success has been achieved recently in difference between these results and those found in analyzing heavy-ion transfer reactions. The methods (t,p) two-neutron-transfer reactions is that all the 16 14 used have included diffraction theory (Da65) and states excited by ( O, C) in this energy region approximate distorted wave Born approximation have comparable intensity. In principle this should (DWBA) theories (for example Bu66) but the most lead to the extraction of more reliable spectroscopic successful technique was based on the use of DWBA amplitudes for states only weakly produced in (t,p) with which finite-range effects could be treated to reactions. In addition, of course, it would be inte-
-68- resting to examine heavy-ion two-neutron stripping (The same argument shows that very high-spin states 18 16 22 20 reactions such as ( O, O) or ( Ne, Ne) and will also be populated by (Hl.xn) reactions - see compare with the heavy-ion two-proton stripping section II-4). reaction as well as with (t,p). The availability of higher-energy and larger-mass projectiles would permit such studies to extend to a wide variety of 300 -f targetprojectile combinations thus improving our 200 1 1 knowledge of the reaction mechanism and our ability G sof 100 to obtain spet troseopic information. 90 Ji= z -\- •a B 40 \ D. MULTI-NUCLEON TRANSFER REACTIONS S 30 l n 200 - The importance of angular-momentum matching 1 i £ ioo of the incoming and outgoing channels on the 8 reaction cross section has been emphasized by s ° — 2*~ Chatwin et al. (Ch70). The angular momentum g 60 i «0 mismatch is given by V 30 A(kR) = (kR)j-(kR) 20 f 10 •If where k is the wave number, R the channel radius and 6 4 1 i and f indicate initial and final channels. If A(kR) 30 40 SO 60 30 40 50 60 matches the spin of a final state, the reaction will proceed strongly; otherwise it will be weak. Bromley 2 8 et al. (Br71) discuss several reactions which have Si Figure II-6-2-The 50Ti('6O,I4C)5:Cr two-proton in common as a compound nucleus. Part of a table transfer distributions for the most strongly excited from their work is included here as Table II-6-I. states of s 2Cr (from Le71). Evidently the first two reactions favour high-spin states in 24Mg and 27Ai since the outgoing alphas and protons can carry off little angular momentum.
TABLE II-6-I: Properties of several reactions involving 2 8Si as compound nucleus.
A(kR) Selective^) Reaction Ecm (kR); (kR)f (MeV)
'C+' 20.6 17.9 8.4 9.5 yes b) 25.7 20.0 10.2 9.8 yes
12^.16 o 25.7 20.0 4.6 15.4 yes c)
I4N+l4N->-24Mg+4He 10.1 12.7 8.3 4.4 no d) 14.0 15.0 9.8 5.2 no
a) Selective of high spin states in the final nucleus? b) Br71 c) Co71 d) Mi71b
-69- TABLE II-6-II: aThe excitation energies E are given for states in some N = Z even-even nuclei. For each nucleus A = 4 + 4(x+y+z) indicates x quartets in the Op shell, y quartets in the (Od.ls) shell, and z quarters in the (Of.lp) shell. The interaction between a quartet in the (Of.lp) shell and a quartet hole in the Op shell is denoted by V and left unspecified.
[xyz]E (MeV) [xyz]E (MeV) [xyz]E (MeV)
I6O [300] 0.0 DNe [310J 0.0 40Ca [360] 0.0 [210] 6.06 [220] 5.1 [351] 3.35 [201J11.1+V [301] 8.8 [342] 6.8 [120]15.0 [211J13.3+V [333]13.8 [130]17.0 [324]24.7 [102]20.0+4V [202J17.4+2V [261J23.7+V [030]23.1 [121J20.7+2V [252]22.4+2V [021]23.1+3V [112]24.2+4V [243]24.0+3V [012]23.1+6V [ 103] 26.3+6V [234J27.1+5V [003]21.5+9V [040J31.7 [162]45.0+4V [031]27.2+3V [153J41.8+6V [022]26.1+6V [144]40.9+8V [013]27.7+9V [004]27.3+12V
This table is taken from Ar70. One of the most interesting aspects of the produc- Similar evidence for the quartet nature of these tion of high-spin states by heavy-ion transfer states comes from the work of Marquardt et al. reactions is the possibility of determining quartet, or (Ma71); they studied the I2C('4N,6Li)20Ne reaction cluster, structure in even-even N = Z nuclei. Arima et which, as in the (12C,a) reaction, transfers eight al. (Ar70) have recently calculated quartet excited nucleons. Figure II-6-3 shows angular distributions states in N = Z even-even nuclei for ' 2 C to 5 2 Fe and which they observed to several low-lying levela The a sample of their results is shown in Table II-6-II. The shapes are not unlike those of direct (d,p) reactions, "quartet" is based on the strong interactions of 2 for example, where the stripping peaks move to larger protons and 2 neutrons occupying a four-fold degene- angles and become broader with increasing angular rate single-particle state (j4; J = 0, T = 0). As an momentum transfer. The authors feel that this may illustration, the neutron separation energy in '6 O is be understandable "in view of the fact that in both at 15.7 MeV while that for the alpha particle is at 7.2 cases the projectile is separated into two nearly equal MeV indicating that the last nucleon interacts parts in the transfer process". Most significantly, they strongly with the three others which make up the believe their evidence "is indicative of a preferential extracted alpha particle and much more weakly with direct transfer of eight nucleons" (Ma71). If this is so, the remaining nucleons. Evidence for quartet states in the relatively large observed cross sections of ~ 20 20Ne has recently been reported by Middleton et al. /ub/sr will make the reaction an ideal tool for (Mi71b) using the 12C(12C,a)20Ne reaction. Basing spectroscopy studies. their arguments on observed angular distributions and There are further important aspects of producing excitation functions they proposed that the 7.20 MeV high-spin states with four-nucleon transfer reactions. + + 20 0 and 7.83 MeV 2 levels in Ne are members of a From Figure II-6-4 it can be seen that in both the quartet configuration (two s-d shell alpha particles l60(7Li,t)20Ne (Og70) and 12C(14N,6Li)20Ne 12 outside a Ceore). (Ma71) reactions the lower members of the 20Ne
-70- ground-state band are populated; however, in the deficient side of the ^-stability line they are accessible (7Li,t) reaction the 8+ member of the band is seen only by heavy-ion induced reactions. weakly while in the (14N,6Li) reaction it is strongly excited. This suggests that transfer reactions such as | l60(7Li,t)zoNe (14N,6Li) could be used to identify rotational bands Li ) = 3O.3f in light- and medium-mass nuclei. In addition they might be useful in looking for states with spins 750- = 12 greater than the expected theoretical limit. As an + example, the SU(3) model indicates that J" = 8 is V) the limit of the ground-state band in 2oNe; if a 10+ 500 state were observed and it decayed strongly by E2 + gamma radiation to the 8 state, it would constitute a o significant failure of the model. 250 (I '1' •••• -^' '. I 12 10 C(" IN, U/ 1vie 50 100 150 200 ^/ CHANNEL NUMBER 4 = 0 h 0* 2 IBJT" 1 A >
40 • 120 S20 =SJMeV s- = 1J63M* 3. p ~10 24 c if) 80 o g 4 "^ 1 ' o o 40 U - 4.25 M*/ 4» 20
10 v 300 400 500 600 700 800 CHANNEL NUMBER i 6 7 40 60 Figure II-6-4 — Spectra from the reactions ' O( Li,t) 20Ne and 12C(14N,6 Li)20Ne (from Og70 and Ma71). Arrows mark the positions of the 0+, 2+, 4+, Figure II-6-3 — Angular distributions of strongly 6+ and 8+ members of the ground-state band. excited states in the reaction ' 2C('4N,6Li)20Ne (fromMa71). Heavy-ion transfer reactions can also be used to investigate isospin purity. In the reaction A+B -» With high-energy heavy-ion beams there is the C+C', if the isospin of either A or B is zero possibility of studying nucleon clusters on the nuclear (producing a definite isospin in the initial channel) surface with reactions such as (28Si,12C) or and if C and C' are members of the same isospin (24Mg,160). Reactions such as these, along with multiplet, the angular distribution will be symmetric (160,12C)(Ko71), (20Ne,l6O) (Si71) and (12C,t) about 90°. This theorem was first formulated by (Ce70) reactions, also allow the study of N « Z nuclei Barshay and Temmer (Ba64) and depends upon a) away from the line of stability: e.g. f-p shell nuclei conservation of isospin in the nuclear reaction and b) such as44Ti, 48Cr, s2Fe and heavier nuclei Similar "identity" of the members of isospin multiplets reactions could also be used to study new regions of relative to a statin rotation in isospin space. One test deformation predicted (Ma63) for Z ~ N ~ 65 and Z of these conditions tOe69) has involved the reaction 12 14 13 13 ~ N ~ 100. As these regions lie on the neutron- C( N, C) N with the result that the authors
-71- conclude that the difference between the value of the made by Dietrich (Di70) who found that two proton and neutron wave functions in l3N and 13C, mechanisms contribute to an enhanced pair transfer: respectively, is not larger than 0.8% at a radius of 1) two-particle tunneling and 2) transfer of a nucleon about L65 x A^ fm (the interaction radius). Tests pair from one nucleus to another through a residual involving many other (heavier) nuclei are possible and pairing interaction. Calculations by Hara (Ha71) are limited only by the fact that 40Ca is the heaviest along the lines of those by Dietrich have shown that stable projectile (or target) for which T - 0. There is the transfer current can be a.c. or d.c. The energy- no restriction to the transfer of only a few nucleons. change when a nucleon-pair jumps from one nucleus to another is twice the difference of the nuclear From the experiments already performed it is Fermi energies, namely o (putting h = 1). Thus, when apparent that the extraction of spectroscopic infor- the collision time is longer than the pair-transfer time mation from multi-particle heavy-ion transfer (1/M), oscillations of the pair can occur between the reactions will become even more fruitful in the two nuclei, giving rise to an a.c. current. Otherwise future. At the same time, it will be necessary to have the current is d.c. Further calculations (Di71) predict considerable freedom in the choice of projectile, that multiple-pair transfer can occur between "super- Urget and bombarding energy in order to exploit conducting" nuclei undergoing scattering below the fully the particular advantages of each type of Coulomb barrier. reaction and the momentum matching that it offers. An accelerator capable of producing heavy ions with The calculations suggest several experiments which energies above the Coulomb barrier for any target would investigate this phenomenon: (say ~ 6 MeV/nucleon) would provide the needed 1) Measurement of the enhanced transfer probability versatility. for neutron pairs just below the Coulomb barrier using reactions such as S8Ni + ' 20Sn or 120Sn + E. THE NUCLEAR "JOSEPHSON" EFFECT I20Sn.
Heavy-ion transfer reactions could be used to 2) Study of the transfer of pairs between excited investigate the enhanced transfer of nucleon pairs rotational states, possible since both nuclei will be which occurs in a manner similar to the flow of strongly Coulomb excited. current in a superconductor: i.e. the nuclear counter- 3) Study of the reduction of proton-pair transfer part (Di70) of the Josephson effect (Jo62, Jo64). A compared to two-neutron transfer as a result of number of nuclei in the mass region A ,> 100 exhibit the Coulomb barrier. properties of a superconducting system and sub- 4) Study of a possible ac. effect. If the two Coulomb barrier scattering of two such nuclei might interacting nuclei resonate in a quasi-molecular be viewed as a time-dependent Josephson junction; state, the probability of pair transfer should be the probability of pair transfer is expected to be large in the vicinity of the resonance. The transfer enhanced by the coherent nature of the nuclear states of several pairs and an a.c. effect might then be in both nuclei. Calculations for this effect have been observed.
REFERENCES
Ar70 A. Arima, V. Gillet and J. Ginocchio, Phys. Bu66 P.J.A. Buttle and L.J.B. Goldfarb, Nucl. Phys. Rev. Lett. 25 (1970) 1043. 78 (1966) 409. Ba64 S. Barshay and G.M. Temmer, Phys. Rev. Ce70 J. Cemy, C.U. Cardinal, K.P. Jackson, D.K. Lett 12 (1964) 728. Scott and A.C. Shotter, Phys. Rev. Lett. 25 Br60 D.A. Bromley, J.A. Kuehner and E. Almqvist, (1970) 676. Phys. Rev. Lett. 4 (1960) 365. Ch70 R.A. Chatwin, J.S. Eck, A. Richter and D. Br71 D.A. Bromley, L. Chua, A. Gobbi, P.R. Robson, in Nuclear Reactions Induced by Maurenzig, P.D. Parker, M.W. Sachs, D. Heavy Ions, edited by R. Bock and W.R. Shapira, R.G. Stokstad and R. Wieland, Yale Hering (North-Holland Publishing Company, University preprint 3223-243 (1971). Amsterdam, 1970) 76.
-72- Co71 E.R. Cosman, E. Grosse, A. Graue and C.H. Mi71a R. Middleton, J.D. Garrett, and H.T. Fortune, Britt, Bull. Am. Phys. Soc. 16 (1971) 644. Phys. Rev. Lett. 27 (1971) 950. Da65 A. Dar, Phys. Rev. 139B (1965) BI193. Mi71b R. Middleton, J.D. Garrett and H.T. Fortune, Di70 K. Dietrich, Phys. Lett. 32B (1970) 428. Bull. Am. Phys. Soc. 16 Series II (1971) 37. Di71 K. Dietrich, K. Hara and F. Weller, Phys. Lett. Oe69 W. von Oertzen, J.C. Jacmart, M. Liu, F. 35B (1971) 201. Pougheon, J.C. Roynette and M. Riou, Phys. Lett. 28B( 1969) 482. Go68 A. Gobbi, U. Matter, J.L. Perrenoud and P. Marmier, Nucl. Phys. A112 (1968) 537. Oe70 W. von Oertzen, Nucl. Phya A148 (1970) 529. Ha71 K. Hara, Phys. Lett. 35B (1971) 198. Oe71 W. von Oertzen, in the Proceedings of the Heavy Ion Scattering Symposium, Argonne Jo62 B.D. Josephson, Phys. Lett. 1 (1962) 251. National Laboratory Report ANL-7837 Jo64 B.D. Josephson, Rev. Mod. Phya 36 (1964) (1971) 121. 216. Og70 A.A. Ogloblin, in Nuclear Reactions Induced Ko71 H.-J. Korner, L.R. Greenwood, G.C. Morrison by Heavy Ions, edited by R. Bock and W.R. and R.H. Siemssen, Bull. Am. Phys. Soc. Hering (North-Holland Publishing Company, Series II 16(1971)646. Amsterdam, 1970) 231. Ku63 J.A. Kuehner, E. Almqvist and D.A. Bromley, Pe62 F.G. Perey, in Direct Interactions and Nuclear Phys. Rev. 131 (1963) 1254. Reaction Mechanisms, edited by E. Clementel and C. Villi (Gordon and Breach Science Ku64 J.A. Kuehner and E. Almqvist, Phys. Rev. Publishers, Inc., New York, 1962) 125. 134B(1964)B1229. Sc70 F. Schmittroth, W. Tobocman and A.A. Le71 M.-C. Lemaire, J.-M. Loiseaux, M.C. Mermaz, Golestaneh, Phys. Rev. Cl (1970) 377. A. Papineau and H. Faraggi, Phys. Rev. Lett. 26(1971)900. Si71 R.H. Siemssen, M.L. Halbert, M. Saltmarsh and A. van der Woude, Phys. Rev. C4 (1971) Ma63 E. Marshalek, L.W. Person and R.K. Sheline, 1004. Rev. Mod. Phys. 35 (1963) 108. Ma71 N. Marquardt, W. von Oertzen and R.L. Walter, Phys. Lett. 35B (1971) 37.
-73- 7. STUDIES WITH LIGHT ION BEAMS
A. Introduction
B. Nucleon-Nucleon Scattering
C. Many-Body Final States D. Quasi-Free Scattering on Nuclei
E. Meson Production in Nuclei
F. Summary References A. INTRODUCTION
A large theoretical effort is presently being con- of two spin 1/2 particles at a certain energy and centrated on the properties of the fundamental angle, involves 16 coefficienta Six of these can be nucleon-nucleon interaction and the associated eliminated if charge symmetry holds, five are odd problem of mesonic effects in nuclei. The majority of under parity (P), time-reversal (T) or (PT), and five the present information on the nucleon-nucleon coefficients are invariant. To completely determine interaction has come from nucleon-nucleon scattering these coefficients measurements must be made with experiments and from reactions with three-body final both polarized and unpolarized beams and targets. states, but many gaps still exist in the available information which limit our knowledge. The details The data at one energy can be decomposed into of nuclear structure associated with the presence of angular momentum eigenstates by a phase-shift mesons in the nucleus are also related to the exact analysis (Ar66, Si69). Much of the available infor- form of the nucleon-nucleon interaction within the mation is of insufficient accuracy to determine the nucleus. Further information essential for detailed higher partial waves and of course the very important 3 3 nuclear structure calculations is the "off the energy mixing parameters such as the Si- D, parameter e\ shell" behaviour of the interaction, which can only be which provides information about the tensor force properly studied by reactions with three-body final (see Figure 11-7-1). Only the 'SQ-'DO states have states. Reactions such as (p,2p) on heavier nuclei been studied in n-p scattering and then only at a few relate to off-shell effects of "bulk" matter as well as energies (Si69, Si71b). providing information on shell structure of nuclei. The following sections describe these subjects in more detail and provide examples of the more important experiments which could be undertaken with light ion beams in the energy range 50 to 300 MeV. I- B. NUCLEON-NUCLEON SCATTERING 5 Detailed knowledge of the nucleon-nucleon (NN) scattering provides the basis for all models of the __LF nuclear force and thus for calculations of nuclear i*~——~-»_ BGT structure. In spite of decades of intensive study of NN scattering a number of vital questions are still • ..i . 1 unanswered. One of the reasons for this situation is the fact that NN data have been accumulated in the past in a somewhat random manner with fixed energy Figure U-7-1 — The nuclear bar coupling parameter 3 3 machines. Even though a large amount of data exists T, for the Si — D, states (Si69). The curves are for p-p scattering there are still many gaps in our predictions of various N-N potentials. knowledge, particularly between 50 and 100 MeV The availability of an accelerator that provides and between 200 and 350 MeV in the laboratory high-intensity beams of (polarized) protons with an frame of reference (Si69, Ma67). The situation is energy resolution of 0.1% in the range from 50 to much worse for n-p and n-n scattering. Most of the 300 MeV would make a more systematic study of the higher energy information for n-p scattering has been NN interaction possible and would ideally comple- obtained from the study of final-state interactions in ment programs planned at the meson factories 3-body final-state experiments such as proton (LAMPF and TRIUMF) in the energy range 300-800 scattering from deuterium. Such final-state inter- MeV. actions have also provided all of the information on the n-n system. A direct measurement of the scattering of neu- trons by protons is very important as a probe of the The second reason for the so-far relatively slow T = 0 components of the NN interaction and ulti- progress in this field lies in the complexity of the NN mately provides a test of the charge independence of interaction itself. The general expression for the nuclear forcea An intermediate - energy proton scattering matrix, M, te. the amplitude for scattering accelerator could provide substantial beams of
-77- neutrons (polarized and unpolarized) by charge- phase shifts for nucleon-nucleon scattering has been exchange reactions on targets such as liquid deute- discussed by Schumacher and Bethe (Sc61). rium. For example, with an unpolarized beam of 300- The need for more accurate nucleon-nucleon MeV protons of 100nA and a liquid-deuterium target scattering data at intermediate energy has recently of 10 cm length, fluxes of 107 neutrons/(cm2 s) 6 2 been emphasized by Signell and Holdeman (Si71a) in a (unpolarized) or 3 x 10 neutrons/(cm s) (polari- discussion of the ambiguity which exists in fits to zation ~ 25%) can be obtained (La64). present data near 330 MeV. Figure 11-7-3 shows the Polarized proton targets prepared by nuclear goodness of fit parameter X2 plotted versus ei for orientation in lanthanum magnesium nitrate (LMN) two selections (with and without Si56) of fitted data (Je63, Be68) could be used for measurements of the (solid curves). The differences in overall determination scattering of unpolarized or polarized neutrons from of parameters for the two minima of the lower curve in polarized protons, which might also include the Figure II-7-3 are indicated in Table II-7-I. In addition, it measurement of the polarization of these neutrons, as is evident from Figure II-7-4 that the majority of po- shown in Figure II-7-2. The proton-recoil coincidence tential models presently used favor the lower value of is required in this experiment in order to eliminate NEUTRON POLARI METER NEUTRON SEAM \ POLARIZED LMN TARGET 50 cm SCALE Figure II-7-2 — Diagram of polarization transfer experiment in n-p scattering using polarized LMN target. The cm. angle is 135°, corresponding to 65.7° in the lab. The final neutron detectors S3 and S4, should be visualized as lying above and below the plane of the paper. -78- polarization (P(0)) every 10° from 60° to 160° to ± employ 2TT exchange or vector-boson contributions 0.01, plus the spin-spin correlation parameter for h/ 2111^0 < r < h/i%c. CNN(120°) measured to ± 0.05. If such experiments were to confirm solution 2 of Table 1I-7-I, the so-called tensor/central ratio in the twonucleon- triplet-even states would be substantially increased, which would signiflcantiy weaken predicted nuclear binding energies (Si71a, Si69). In addition, all of the potential models shown in Figure II-7-4 would be eliminated. Nucleon-nucleon scattering measurements may therefore be expected to provide new fundamental information concerning the short-range and spin- dependent parts of the nucleon-nucleon interaction. The conventional dynamics of nuclear structure considers only a system of protons and neutrons with WO C-T DATA a two-body potential between any pair of particles, but there is an inherent understanding that mesons are responsible for a part of the dynamics. The basic €, (DEGREES)-* understanding of the two-body potential is quite Figure II-7-3 —The goodness-of-fit parameter, x*. incomplete. The long-range part of the potential (i.e. versus the 3S -3Di nuclear bar coupling parameter IT, for r greater than the pion Compton wave length 1 at 330 MeV, with and without the old Carnegie-Tech h/m^c) is believed to stem from one-pion exchange. data (Si56). The dashes are curves predicted by the For r < ^VrrijjC, it is usual to employ a phenomeno- curvatures at the minima. The dots show the effect of logical description in terms of a static potential with a adding certain proposed measurements. hard or a soft core. An alternative description is to TABLE II-7-I: Phase parameters corresponding to the two minima in the lower curve of 3 Figure II-7-3. Note the separation of the two solutions in the e3 and G4 phase parameters. Solution Si 5.7 ± 4.2 13.3 ±3.2 8.9 ±2.7 21.2 ± 3.1 -29.2 + 3.0 -21.4 ± 1.6 -43.3 ± 2.1 -27.6 ± 3.8 17.6 ±4.0 21.5 ± 3.4 3.5 ± 1.7 2.6 ± 1.1 4.0 ± 1.1 e"3 8.6 ± 1.8 3 G3 -4.7 ± 2.6 -6.2 ±1.9 -2.6 ± 1.6 -5.4 ± 1.6 0.8 ± 1.6 10.3 ± 1.1 3 -0.9 ±0.7 G5 -1.6 ±0.7 -2.5 ± 0.8 'H5 -2.5 ± 1.6 -79- these can only be studied experimentally in reactions TABD with three or more particles in the final state. 10 MAW-IX j; BS in ' I""I"1 Lj ' T U ' In order to determine the nuclear potential MJD [YALE completely, or, more realistically, in order to test 0 • LF BKD RIHC) If whether a semi-empirical or a "theoretically derived" to- D potential is correct we must know a considerable n GREEN MAW-X ! ,_ AM-IV^ -10 IDSMJ amount about its off-shell behaviour. Such infor- mation would provide very important and perhaps -20 1 I 1 ) 1 crucial guide posts for theorists currently trying to 0 10 20 30 develop a field-theoretical nucleon-nucleon inter- «, (DEGREES)—» action. Figure II-7-4 — The solid error bars show the solu- In addition, current theory necessarily predicts tions of Si71, the dashes those of Ma69, Ma68, Ar66. that three-body and higher-body forces exist, The boxes show the predictions of a number of especially at short range or, equivalently, for large potential models (Ta64, Br69, Lo68, Br67, Ha62, momentum transfer (De69, Br68a, Br68b). At present Re68, La62, St71). there is virtually no experimental information con- cerning the off-the-energy - shell behaviour of the Phenomenological descriptions for the two-body nuclear forces or of the existence of three-body potential introduce spin-dependent terms through a forces in nuclei (De69, Si69). Three-body effects have tensor and a two-body spin-orbit term. The tensor been investigated for bound systems (De69), i.e. the t force is essential to explain the ground-state quadru- and 3 He systems, but detailed studies of these forces pole moment of the deuteron, but in the lowest order as a function of energy necessarily involve reactions of perturbation theory it has no effect on polari- with three-body final states. zation in nucleon-nucleon scattering. A two-body spin-orbit force of the type (r, —t2) x (p! -p2 )-((?i + Three-body final states are also the simplest 02) cat: give rise to polarization in lowest oraer and it system for studying off-shell effects in the nucleon- is found phenomenologicaily that its range is less than nucleon interaction. Nucleon-nucleon bremsstrahlung h/m^c. The one-pion exchange potential does not give reactions, any spin-orbit contribution but it has been conjec- 1) p + p ->• p + p + 7 tured by Sakurai (Sa60) and Breit (Br60) that the exchange of vector mesons (p and co) can give a 2) p + n spin-orbit force of the right range and about the right 3) n+n -n+n + magnitude. Detailed cross-section and polarization although difficult experimentally are potentially the measurements should provide sufficient information easiest to analyze for off-shell effecta The scattering to determine the contributions of these various matrix involves terms (Br69b) such as: exchange potentials to the basic nucleon-nucleon interaction or at least to distinguish between the various phenomenological potentials currently in use. j AEJ C. MANY-BODY FINAL STATES where Vem is the electromagnetic potential between the nucleons and VJ^N is the nucleon-nucleon poten- Even if complete and accurate data for p-p, p-n tial. The initial and final wave functions for the and n-n scattering were available it would still be scattering system are x+i and 0 . The off-shell impossible to determine completely a phenomeno- f effects arise from the sum over intermediate states. logical potential required to describe interactions The usually stated advantage of bremsstrahlung within a nucleus (Ba67, Si69). This is because the experiments in a study of VNN is that Vem is well two-body scattering data only determine the "on the understood theoretically. However, this is really only energy shell" behaviour of the interaction, i.e. the true in the low-energy photon limit where it can be "elastic" behaviour. Interactions involving virtual shown that these experiments are not very sensitive particles, wherein energy is not explicitly conserved to the desired off-shell effects (Kh71). For higher between the two nucleons involved (off-shell effects) energy photons Vem is presently not as well under- are an important part of nuclear interactions, and stood (He71). -80- Another way to investigate both off-shell and on-shell effects of the NN interaction is to study reactions with three-particle final states. As an example of the amount of information which could be obtained from a systematic study of such reactions, we shall consider reactions produced by bombarding 3He and t with deuterons at energies between 10 and 300 MeV. Possible three-body final states would include: d + 3He->-3He + p+n -» t + p + p ->• d + d + p and d+t->t+p + n -• 3 He + n + n Although a number of experiments of this nature have been performed (Do65, S168), none of these experiments was designed to look for off-shell effects and many (S168, Co64, Ba66) were not E-MeV kinematically complete. Figure II-7-5 — (from Br69b). Integrated cross section The relations for conservation of linear momen- dold£lidQ,2 calculated with the Hamada-Johnston tum and energy for a 3-body final-state reaction in (Ha62) (dashed curve) and the Bryan-Scott(Br69a) the laboratory frame are: (solid curve) potentials for coplanar symmetric angles of 30° and 40 . P, +(?2 =0)->P3 + P4+Ps Figure II-7-5 indicates the extent of the data pre- Tj +(T2=0)->T3 +T4 + TS +Q sently available for p-p brerasstrahlung (Br69b). A quo- where Pj and Tj are the linear momenta and kinetic tation from a review article by Signell (Si69) describes energy of the particles. Since we know P,, P2, Ti and the knowledge of off-shell effects derivable from T2 it is sufficient to measure any two of P3, P4 or Ps present data. "Although there have been calculations to determine completely the kinematics of the final of p-p bremsstrahlung with at least three or four state. In practice P3 and P4, say, would be deter- different potentials, one can only conclude at this mined by measuring the energy and angles with time that no experiment has been either sufficiently respect to the beam direction of these particles; such precise or sufficiently off-shell to distinguish between an experiment is said to be kinematically complete. different types of potentials which have similar Thus we are faced with measuring third order on-shell matrix elements. On the other hand, the differential cross sections i.e. d'a/dfiidftjdE]. The theoretical calculations have used unjustifiable advantage is that we can choose the region in phase approximations, have failed to prove adequate on- space that enhances the type of interaction we wish shell agreement among the potentials used, or have to study. merely compared potentials of the same general type For example, at low energies one can measure the such as those with hard and "soft" (hard) cores". p-p, p-n and n-n scattering lengths by choosing a This statement, combined with the scarcity of data in geometry that leaves the two nucleons of interest (i.e. Figure II-7-5, indicates the need for much more p-p, p-n or n-n) travelling together with small relative accurate p-p and p-n bremsstrahlung data in the velocities. As the relative velocities are increased the energy region between 50 and 300 MeV, particularly experiment becomes sensitive to the effective range for geometries which maximize off-,°hell effects, and parameter and is eventually dominated by the effects for more extensive theoretical studies of the resulting of the core. information. -81- A comparison of potentially a lot easier to perform, makes the theoretical analysis more difficult. 3He->3He+p At stil1 other geometries in the reactions discussed above, one becomes sensitive to the properties of the d+ t-»- t+p+ n excited states of structures such as 4He viz d + 3He 4 d +t->3He + n+ n ->• ( He* + P) ->• t + p + p (Wa71, Ba71). in the geometry mentioned above and extending over It is possible by a proper choice of geometry and 3 energy to study off-shell effects on the t+p inter- a wide range of incident d, He or t energies should 4 provide accurate information regarding the on-the- action at the He* resonance. This is analogous to energy-shell properties of the n-n interaction. The inelastic electron scattering where the exchanged known p-p and p-n scattering data would be used as a photon is off-the-energy shell and therefore allows a test of the accuracy of the analysis. For large momen- study of the excited state of the nucleus as a function tum transfers at the higher bombarding energies this of momentum and energy of the photon. Such comparison is essential since off-energy-shell terms off-shell nuclear-structure effects could involve some become important. very interesting and presently unknown phenomena. A significant advantage of this type of measure- Particular types of nucleon-nucleon interactions ment is that the experimental arrangement is may exhibit symmetry properties which enable parti- essentially identical for the n-n, p-n and p-p measure- cularly simple tests to be performed to determine the ments. The symmetries of the reaction mechanism will extent of their influence. One example of this is the also help reduce some of the problems with the Treiman-Yang test for the one-pion exchange potential analysis of the data. (Tr62) which predicts that the angular distribution obtained by rotating one of the detectors in the Final-state interactions are the only means of azimuthal plane should be isotropic. The properties gaining information about the neutron-neutron inter- of other types of exchange interactions are much action and the information presently available on the more complicated but may exhibit some symmetries n-n scattering length has come from reactions such as through which one could distinguish between such n+d -»• p+2a (For a summary see (He69).) interactions at various values of the range of the Further information can be obtained from d + t nucleon-nucleon interaction. and d + 3He reactions if the geometry is chosen for In summary, many-body final state interactions which the reaction proceeds by "quasi-free scat are difficult to study experimentally and theore- tering" wherein the third particle is nearly unaffected tically, but can justify extensive effort on both by the interaction of the other two. The interaction is fronts for they contain information on off-shell not sensitive to off-shell effects at this point but as effects of the nucleon-nucleon interaction which is we move away from this geometry the sensitivity to essential for a basic understanding of nuclear off-shell effects increases and these effects become structure. large at high bombarding energies i.e. 150-300 MeV. The analysis of this data would involve expansions D. QUASI-FREE SCATTERING ON NUCLEI similar to those for p-p bremsstrahlung. That is There is a class of experiments involving light projectiles impinging on heavier target nuclei that Tf, have many features in common with the quasi-free scattering experiments described in the previous section. Those are reactions such as (p,2p) or (a,2a) where we have replaced Vem by VNN, the extra at high bombarding energy where one assumes that momentum and energy being transferred to the the projectile intt acts strongly only with the nucleon spectator particle rather than to the photon. These or cluster being eje. fed leaving the residual nucleus experiments have the advantage that the cross sec- otherwise undisturbed. Historically these experiments tions will be much higher than for p-p or p-n have been analyzed using the plane wave (PWIA) or bremsstrahlung since we replace the weak electro- distorted wave (DWIA) impulse approximations magnetic interaction by the strong nuclear (Ja69, Wa71). These (p,2p) or (a,2a) reactions must interaction. This factor, which makes the experiments be performed at higher energies than the 3He + d -82- quasi-free scattering described in the previous section Assuming that picn production on nuclei results since it is more difficult to ensure that we are dealing from the interaction between the incident proton and only with this simple reaction mechanism. One one of the target nucleons, then the cross section for criterion is that the de Broglie wave length of the pion production depends on the momentum distri- projectile must be short enough that there is a bution of nucleons in the nucleus. This distribution negligible chance of the projectile interacting with may be written as more than one of the ejected clusters For (p,2p) 2 reactions the proton bombarding energy must be F(Pl) = /l^(Pl,P2)...PA)! dP3...dPA greater than 100 MeV. where F(Pt) is the probability of finding a nucleon of Because the ejected nucleon or cluster (e.g. an momentum Pi in the ground state of the target alpha particle) is bound to the target these reactions nucleus and $ is the ground-state wave function in automatically contain components that are off-the- momentum space. Pion production by protons at energy shell. This provides a mechanism for studying energies up to 300 MeV is mainly dependent on the the off-shell effects that arise in "bulk" nuclear high-momentum components which reflect the short- matter in contrast to the earlier discussion involving range properties of the nucleon-nucleon interactions only a very few nucleons. There may be important in the nucleus. The saturation properties of nuclear differences between the few-nucleon and many- matter are known to depend very sensitively on this nucleon systems. short-range behaviour. In the past (Ja69). these reactions have not been The information to be obtained at LAMPF and used to study off-shell effects but rather to look at TRIUMF on the production of pions by p-p scat- the "deep shell" structure of nuclei (Cu72), that is to tering at energies from 300 to 800 MeV will be find the energies of the fundamental single-particle essential for a detailed analysis of pion production on states of the nuclei. Similarity, the (a,2a) reaction has nuclei. Once this pion-production process is under- been used mostly to look for the probability of alpha- stood pion production in nuclei may be used to map particle clusters in nuclei (Cu72). However, there is a out the proton Fermi surface in much the same way recent case where this was combined with a study that positron annihilation in metals provides us with of the off-energy-shell behaviour in the reaction details of the momentum distribution of electrons in 6Li(a.2a)d (Wa71). When studying heavier targets, the metals. Coulomb barrier for the alpha particles makes the Pion production on nuclei may also provide tests (a, 2a) cross section very small at energies below of soft-pion approximations which give definite about 150 MeV (Ga62), so high-energy alpha particles predictions for the pion-production cross sections. are required even though the de Broglie wave length The accuracy of such approximations is a matter of of the alpha particles is 1/2 that of the proion at considerable interest as they are often used in the same energy. calculations of meson effects in nuclear structure. An accelerator capable of producing intermediate- Pickup reactions such as (p,d) at high bombarding energy beams of a variety of light projectiles could be energies are also sensitive to the high-momentum used very effectively in the study of quasi-free components of the nuclear wave functions since the scattering, providing a wide range of information on pickup only occurs for low relative velocities of the the topics discussed in this section: off-shell inter- incident proton and picked-up neutron. A com- actions in nuclear matter, "deep-shell" nuclear parison with momentum distributions derived from structure and clustering. meson - production experiments would test the accuracy of the two methods of analysis which E. MESON PRODUCTION IN NUCLEI describe quite different effects in the exit channel. The threshold for pion production in nucleon- F. SUMMARY nucleus collisions is approximately equal to the pion 9 rest energy (e.g. 152 MeV for Be (p.ir) and 129 MeV An accelerator capable of performing the variety 63 for Cu (p,7r)), significantly lower than the thres- of experiments described in this section should have hold for pion production in nucleon-nucleon col- variable energy in the range from 50 to 300 MeV for lisions (290 MeV) where half the laboratory kinetic beams in the mass range from protons to lithium. energy goes into center of mass motion. Energy resolution of 0.1% or better is essential and -83- beam intensities of up to 100 n* for protons would The use of polarized beams and targets would be be useful for some experiments. At this intensity an important part of any research program involving usable neutron beams could be produced and meson light ions. For the production of high-intensity beams production on nuclei could be studied. of polarized ions, positive-ion injection would be very advantageous, particularly for deuterons and tritons. The experiments described herein are very complex to perform, generally requiring coincidence An accelerator with these characteristics would be measurements and often being dependent on accurate ideal for extensive, systematic studies with light-ion angular determinations. Such measurements respec- beams at intermediate energies. The results of such tively require a duty cycle close to 100%, and beam studies can be expected to enrich our knowledge of i) emittance as small as possible, certainly less than 0.3 the basic nucleon-nucleon interaction, ii) two-body cm mr. The complexity of the experiments will and many-body interactions in nuclei, iii) funda- require that extensive on-line and off-line computing mental nuclear-structure properties such as "deep facilities be available. In cases such as many-body shell" binding energies and cluster structure and final-state reactions the worth of the data is highly perhaps iv) details of nuclear structure which cannot dependent upon the completeness of the experiment presently be predicted, but which are always the as well as on its accuracy. object of extending studies into regions which have not yet been fully investigated. REFERENCES Ar66 R.A. Amdt and M.H. MacGregor, Phys. Rev. De69 L.M. Delves and A.C. Phillips, Rev. Mod. 141 (1966) 873. Phys. 41 (1969) 497. Ba66 E. Baumgartner, H.E. Conzett, E. Shield and Do65 P.F. Donovan, Rev. Mod. Phya 37 (1965) R.J. Slobodrian, Phys. Rev. Lett. 16 (1966) 501 and the 7 following papers in this journal. 105. Ga62 H. Gauvin, M. LeFort and X. Tarrago, Nucl. Ba67 M. Baranger, Proc. of the Inter. School of Phys. 39 (1962) 447. Phys., E. Fermi, Varenna 1967. Ha62 T. Hamada and I.D. Johnston, Nucl. Phys. 34 Ba71 G.C. Ball, W.G. Davies, A.J. Ferguson, J.S. (1962) 382. Forster and R.E. Warner, Atomic Energy of He69 E.M. Henley in hospin in Nuclear Physics Canada Limited Report AECL-3912 (1971) 8. (North-Holland Publishing Company, Amster- Be68 A. Beretvas, Phys. Rev. 171 (1968) 1392. dam), (1969) 15. ,^-'- He71 L. Heller, Proc. Gull Lake Symposium on"the Br60 G.Breit, Phys. Rev. 120(1960)287. Two-Body Force in Nuclei (1971). Br67 C.N. Bressel and A.K. Kerman, quoted in P.C. Ja69 A.N. James, P.T. Andrews, P. Kirkby and Bhargava and D.W.L. Sprung, Ann. Phys. B.G. Lowe, Nucl. Phys. A138 (1969) 145. (New York) 42 (1967) 222. Je63 CD. Jeffries, Dynamic Nuclear Orientation Br68a G.E. Brown, A.M. Green and W.J. Gerace, (Interscience, New York) (1963). Nucl. Phys. A115 (1968) 435. Kh71 F.C. Khanna, private communication (1971). Br68b G.E. Brown, A.M. Green, W.J. Gerace and La62 K.E. Lassila, M.H. Hull, Jr., H.M. Ruppel, E.M. Nyman, Nucl. Phys. A118 (1968) 1. F.A. McDonald and G. Breit, Phys. Rev. 126 Br69a R. Bryan and B.L. Scott, Phys. Rev. 177 (1962) 881. (1969) 1435. La64 LAMPF — A Proposal for a High-Flux Meson Br69b V.R. Brown, Phys. Rev. 177 (1969) 1498. Facility, Los Alamos (1964) 78. Co64 H.E. Conzett, E. Shield, R.J. Slobodrian and Lo68 E.L. Loman and H. Feshbach, Ann. Phys. S. Yamabe, Phys. Rev. Lett. 13 (1964) 625. (New York) 48 (1968) 94. Cu72 R.Y. Cusson and H.C. Lee, Annals of Physics Ma67 M.H. MacGregor, Rev. Mod. Phys. 39 (1967) 72 (1972) 353. 556. -84- Ma68 M.H. MacGregor, R.A. Arndt and R.M. Si71b P. Signell, Proc. Gull Lake Symposium on the Wright, Phys. Rev. 173 (1968) 1272. Two-Body Force in Nuclei (19ri 1). Ma69 M.H. MacGregor, R.A. Arndt and R.M. S168 R.J. Slobodrian, H.E. Conzett and F.G. Wright, Phys. Rev. 182 (1969) 1714. Resmini, Phys. Lett. 27B (1968) 405. Re68 R.V. Reid, Jr., Ann. Phys. (New York) 50 St71 R.W. Stagat, F. Riewe and A.E.S. Green, (1968) 411. Phys. Rev. 03(1971)552. Sa60 J.J. Sakurai, Phys. Rev. 119 (1960) 1784. Ta64 F. Tabakin, Ann. Phys. (New York) 30 (1964) 51. Sc61 C.R. Schumacher and H.A. Bethe, Phys. Rev. 121 (1961) 1534. Tr62 S.B. Treiman and C.N. Yang, Phys. Rev. Lett. 8 (1962) 140. Si56 R.T. Siegel, A.J. Hartzler and W.A. Love, Phys. Rev. 101 (1956) 838. Wa71 R.E. Warner, G.C. Ball, W.G. Davies, A.J. Ferguson and ,!.S. Forster, Phys. Rev. Lett. 27 Si69 P. Signell, Adv. Nucl. Phys. II (Plenum Press (1971) 961. 1969) 223. Si71a P. Signell and J. Holdeman, Jr., Phys. Rev. Lett. 27 (1971) 1393. -85- 8. RANGES, STOPPING POWERS AND ATOMIC COLLISIONS PART 1: RANGES AND STOPPING POWERS OF HEAVY IONS A. Introduction B. Applications and Inadequacies C. Future Development PART 2: PROPERTIES OF UNITED ATOMS References PART 1: RANGES AND STOPPING POWERS OF HEAVY IONS A. INTRODUCTION The calculation of the stopping powers of ions in gaseous and condensed materials has been a challenge STOPPING POWERS to theorists for several decades. While there has been 100 IN Ni considerable success in understanding the stopping- power mechanism, it remains necessary to normalize the theoretical models with accurate data from experiment. Prior to 1960 most of the effort in measuring and understanding energy losses was con- CM fined to the light ions of A < 4. With the advent, in E the late 1950's, of the HILAC's and the tandem Van o 10 de Graat'f's, which are capable of accelerating heavier ions, the need for heavy-ion stopping powers became e more urgent. In I960 Northcliffe (No60) reported an extensive experimental study of the stopping powers of 4He, 10B, UB, 12C, 14N, I6O, )9F and 20Ne in aluminum absorbers at ion energies of up to 10 MeV/amu. In the same year Roll and Steigert (Ro60) reported data for the same set of ions and energy range, stopping in O2 gas and Ni foils. These measurements, augmented by more recent experi- 0. L I.J. mental data on lower-energy ions of A < 127, have 0.3 I 3 provided the basic input data for the semi-empirical MeV/AMU tabulations of Northcliffe and Schilling (No70). The tables include predictions of stopping powers S(E) for Figure II-8-1 — Stopping powers in Ni from the all ions in the range 1 < Z < 103 at energies of semi-empiricaJ tabulations of No70. The lines are 0.0125 < E/A < 12 MeV/amu in 24 different dashed in the regions for which there is no direct stopping media from Be to U where S(E) is given by experimental data. 2 : S(E) - dE/(pdx) in MeV cm mg" [1] where p is the density of, and x is the distance in. the B. APPLICATIONS AND INADEQUACIES stopping medium. a) Coulomb Excitation The Northcliffe and Schilling tables "provide useful and reasonable estimates in the overwhelming It should be noted that the majority of measured number of cases where there are no data at all" but values of stopping powers are accurate to only ~ "it cannot be expected that all of these values will be 10%. In many heavy-ion measurements, of which of high accuracy" (No70). The tabulated stopping Coulomb excitation is a case in point, the accuracy of powers in Ni for five ions are plotted in Figure II-8-1. the cross sections deduced from experiment is The lines are dashed for energy regions in which there directly dependent on the accuracy with which are no direct experimental data. There is a paucity of stopping powers are known. Consider the case where 35 direct experimental information for ions of A > 40 in a flux 0 of C1 ions/sec at an incident energy Eo = the energy range plotted here. The only exception is 100 MeV is impinging on a thick target of Mo as the ORNL data (M066, Br67a, Br67b) for 127I ions shown in the upper part of Figure H-8-2. After of up to ~ 200 MeV stopping in Be, C, Al, Ni, Ag, Au traversing a distance x, i.e. a surface density depth px, the ions will have an energy (in MeV) of: and UF4. -89- E(x) E0-/oS(E)pdx [2] of 7-ray lines emitted from recoiling short-lived excited target atoms as they slow down and come to as shown in the central plot of Figure II-8-2. The rest in the chosen stopping medium. Heavy- ion reaction yield from the next element pdx is: reactions give initial recoil velocities of up to several per cent of c. Thus a 7-ray, of energy E~ in the moving frame of reference, will be observed in the where No is Avogadro's number, A2 is the atomic laboratory frame to have an energy which is altered weight of the target atoms and o(E) is the reaction by the Doppler effect: cross section. The curves L and H in the lower part of E(0,t) = E |l + cos0-v(t)/cJ. [5] Figure 11-8-2 show the energy (depth) dependence for 7 exciting typical low (~ 0.1 MeV) and high (~ 1 MeV) energy states in Mo by a single-step Coulomb- where v(t) is the atom velocity at the time t (t = 0 at excitation process. The total reaction yield for the reaction time) at which the 7-ray is emitted. For the full range, R, of the incident ions will be given by: example of Figure II-8-2, a head-on Coulomb-exciting ,R, collision near the surface gives rise to an excited Y=/^(No/A2).0.a(E[x])pdx 14] 94 Mo atom with a recoil energy of Er = 78 MeV and i.e. by areas under the curves L or H. In this example a recoil velocity vr — 4% of c. Mo atoms of this energy when stopping in Mo(p = 10.2 g/cm2) are a 10% uncertainty in S(E) at Eion £ 80 MeV results predicted (No70) to have stopping powers of S — 22 in a corresponding uncertainty in predicting or 2 1 2 interpreting reaction yields. MeV cm mg" and a total range of ~ 10 mg/cm i.e. ~ 10~3 cm. They will lose half their energy within ~ 0.2 ps and come nearly to rest in ~ 1 ps. Thus, for THICK Mo TARGET nuclear lifetimes T^ ^ 10 ps an appreciable fraction FLUX 4, OF of 7-rays will be emitted with a Doppler-shifted 100 MeV energy. These will appear as a high-energy shoulder on the 7-ray line if viewed by a counter at forward 35 CilONS angles. Only a tiny fraction of the 7-rays will have the full 100 (4%) Doppler shift in energy. In most cases the full 35 Ci ION Doppler shift will be attenuated or altered by: ENERGY sol— i) the loss of incident ion energy before reaching a MeV reaction site; 0 ii) a reaction scattering angle less than 180°, giving ER < 78 MeV; COULOMB EXCITATION iii) the loss of recoil-atom energy before 7-ray emis- sion; and CROSS SECTION iv) the loss of nuclear alignment with time. (ARBITRARY UNITS) This method of measuring nuclear lifetimes from the '0 5 10 15 analysis of 7-ray line shapes is known as the Doppler 2 Shift Attenuation Method or DSAM. DEPTH Px (mg/cm ) Figure II-8-3 illustrates the DSAM (Si71). The data Figure II-8-2 — Illustration of the origin of thick were taken in coincidence with 3SC1 ions back- 3 5 target Coulomb excitation yields with energetic Cl scattered at angles of 135° to 175°. This selects those ions. 94 Mo target atoms which were Coulomb excited in the 2 mg/cm2 layer nearest the surface (Figure 11-8-2) b) Doppler-Shift Measurements and recoil forward at 6 <^ 7° with energies of 63 to 78 MeV. This set of atoms has a mean recoil velocity of v A second example of the usefulness of accurate = 3.6% of c. The soiid line fitted to the data points stopping powers is in the interpretation of the shapes (Si71) was deduced by interpolating the Northcliffe -90- and Schilling tabulations (No70) to give the stopping getic heavy ions has prompted the development in powers for Mo in Mo, and corresponds to a nuclear this laboratory of new techniques for the accurate lifetime of rjj = 4.5 ps. The statistical errors of the measurement of heavy-ion stopping powers in solid data points imply an uncertainty in r^j of only ~ 2%; media (Gr71, Wa71). The comparison of the mea- the main uncertainly in T^ is believed to be ^ 10% sured stopping powers of 35C1 ions in Ge and in Ag and arises from using stopping-power values which are with the tabulated values of Northcliffe and Schilling not based on experiment. If accurate experimental is given in Figure II-8-4, and shows that for these values did become available, many nuclear lifetimes, specific cases the tabulated values deviate from the including those for which data already exist, could be direct measurements by up to "- 10%. obtained with significantly improved precision. STOPPING POWERS FOR 35Cl IONS LINE SHAPE FOR 2*-0* y.RAY (871 keV) in ^Mo BACKSCATTER COINCIDENCE WITH KCt (lOOMeV) 9, = 45 90" COUNTER INGOING OUTGOING 150* • INGOING OUTGOING 20 40 SO 80 100 120 140 160 3^ ENERGY (MleV) Figure II-8-4 — Stopping powers of Cl in Ge and Ag. The data points are raw output numbers from Gr71 and Wa71. V/C % The tabulated stopping-power values for most 0 I 5 10 20 30 40 50 70 energetic ions with A > 35 involve much larger E co.L(MeV) RE predicted extrapolations from experimental data than those shewn in Figure II-8-1. The techniques deve- Figure II-8-3 — Illustration of the DSAM method of loped here are capable of providing measured measuring nuclear lifetimes. Assuming the stopping stopping powers, accurate to ~ 4%. They are readily power curve shown in the inset for Mo atoms in Mo, applicable to any" heavy ion, stopping in a wide the best fit to the data points yields a mean life Tj^ = 94 variety of solid target materials and if beams of more 4.5 ps for the 871 keV 2+ level in Mo. The energetic heavy ions were to become available, it accuracy would approach the 2% statistical value if would then be possible to fill the void which now the stopping powers were accurately known. exists for reliable directly measured values. These data would permit more accurate analyses of heavy- C. FUTURE DEVELOPMENT ion reaction yields and should lead to an improved understanding of the energy-loss mechanisms. The paucity of directly measured data for ener- -91 - PART 2 : PROPERTIES OF UNITED ATOMS One aspect of atomic-collision physics that is Ordinarily, the lifetime of the excited state is currently attracting a great deal of interest, and that longer than the collision time (~ 10"'6 seconds) and could benefit from the availability of high-energy hence de-excitation effects are not observed until heavy-ion beams, is the testing of the so-called after the atoms have completely separated. However, "united atom" concept. Whenever the internuclear Saris (Sa71) has recently reported direct observation separation between two colliding atoms becomes of Kr L-X-rays in the above Ar-Ar collisions. He has significantly less than the sum of the radii of a accomplished this by using a solid Ar target and a specific electron shell (K, L, M, etc.), then for the sufficiently energetic Ar+ beam that its equilibrium duration of the collision the electrons in this shell charge state in passing through the solid would behave as if they belonged to the much heavier involve at least one or two L-shell vacancies. When "united atom", i.e. to a hypothetical atom having an such an ion has a violent collision, the L-shell of the atomic number given by the sum of the two nuclear united-atom (Kr) may sometimes retain one of these charges. Suppose, for example, two Ar atoms collide L-shell vacancies and, since the lifetime of the Kr L sufficiently violently that their L-shells overlap. Their vacancy is somewhat shorter than the collision time, a 16 L-electrons must redistribute themselves among Kr L X-ray would then be emitted. the available Kr energy levels; since only 8 can remain This opens up many exciting possibilities in in the L-shell, the other 8 are promoted to higher atomic-collision physics. The use of heavier ions may levels that satisfy certain selection rules (no change in well enable X-rays to be observed from "united atoms" angular momentum, etc.). In many cases this involves considerably heavier than the known elements and several level crossings and, as the nuclear separation may indeed provide a test of atomic-structure theory increases again after the collision, the electrons do in a completely new atomic - number regime (see not necessarily find their way back to the Ar L-shells. section II-2). For these heavier elements the higher The resulting L-shell vacancies then produce X-ray energies are obviously necessary in order to achieve a emission, Auger electrons, etc. This united-atom significant equilibrium vacancy concentration in the picture has been extremely successful in describing inner shells. the inelastic energy losses that accompany violent single collisions. REFERENCES Br67a L.B. Bridwell, L.C. Northcliffe, S. Datz, CD. No70 L.C. Northcliffe and R.F. Schilling, Nuclear Moak, and H.O. Lutz, Phys. Rev. 159 (1967) Data Tables A7 (1970) 233. 276. Ro60 P.G. Roll and F.E. Steigert, Nucl. Phya 17 Br67b L.B. Bridwell and CD. Moak, Phys. Rev. 156 (1960) 54. (1967) 242. Sa71 F.W. Saris, W.F. van der Weg, H. Tawara and Gr71 R.L. Graham, D. Ward and J.S. Geiger, Bull. R. Laubert, Phys. Rev.vLett 28 (1972) 717. Am. Phya Soc. Series II, 16 (1971) 565. Si71 S.H. Sie, J.S. Geiger, R.L. Graham, H.R. Mo66 CD. Moak and M.D. Brown, Phys. Rev. 149 Andrews and D. Ward, Atomic Energy of (1986) 244. Canada Limited Report AECL-4068 (1971) 50. No60 L.C. Northcliffe, Phys. Rev. 120 (1960) 1744. Wa71 D. Ward, R.L. Graham and J.S. Geiger, Atomic Energy of Canada Limited Report AECL-4068 (1971) 29. -92- 9. FUNDAMENTAL INTERACTIONS AND SYMMETRIES A. Introduction B. Strong Interactions C. Nuclear Gamma Decay D. Nuclear Beta Decay References A. INTRODUCTION In the past three decades the study of elementary polarization in nucleon-nucleon scattering in the symmetries has greatly increased our understanding energy range 50-300 MeV has been discussed in of the three interactions basic to nuclear physics, section II-7. Experiments of this sort may also be i.e. the strong, electromagnetic (EM), and weak specifically tailored to examine the fundamental interactions. A well-known example is the violation of symmetry properties of the strong interaction with parity in beta decay (Le5fc>) which was first observed regard to time reversal, parity inversion and charge in a low-energy nuclear-physics experiment (Wu57) symmetry. and which contributed in an essential way to a formulation of the current-current theory of weak All phase-shift analyses so far have assumed the interactions (Fe58). To choose a more recent full validity of all symmetries in order to reduce the example, let us consider the apparent CP violation in number of coefficients required to describe the the decay of the long-lived Kj meson into two pions scattering matrix. The measurement of fundamental (Ch64). At present, the dominant question of the symmetry properties is predominantly dependent on origin of the CP-violating interaction is not answered high accuracy in a specific measurement. However, although a number of speculative theories have been the interpretation of the results often depends on a more accurate knowledge of nucleon-nucleon phase advanced (St69). It is possible that experiments in shifts than is presently available. This again points out low-or intermediate-energy phyr-ics may well provide the need for systematic studies of nucleon-nucleon decisive answers which may help to distinguish scattering at intermediate energies. between these theories. If the CP violation is of EM origin as has been suggested (Be65), the nuclear Interaction invariance with respect to time reversal wave-function will have a time-reversal-violating implies the equality of polarization and asymmetry, amplitude of typically 10~3. From a recent survey of P(0) = A(0), where P(0) is the polarization resulting nuclear tests of time-reversal invariance (Ri70) it from a collision of unpolarized particles and A (9) is appears likely that such small amplitudes can be the asymmetry in the scattering of a completely isolated experimentally. It is evident that low- and polarized beam from an unpolarized target (see intermediate-energy experiments can contribute to Gr68). A similar equality has been tested for p-p the solution of problems which are of fundamental scattering by Handler et ;1. (Ha67) who found a importance not only to nuclear physics but to physics difference of 0.0006 ± 0.0028 between proton in general. Furthermore, violation of a certain polarizations for two geometries related by time symmetry in a specified interaction may show up in reversal. The interpretation of the data requires experiments in which any of the three basic inter- knowledge of the phase angle between time-reversal- actions is dominant. For this reason the following conserving and-violating terms which can only be text is subdivided into three parts according to obtained by recourse to phase shifts. The results are 3 3 whether the strong, EM, or weak interactions domi- particularly sensitive to the P2- F2 and, at higher 3 3 nate the experimental situations. There are a number energies, to the F4- H4 phase shifts. The time- of experiments discussed in previous chapters which reversal-violating amplitude and phase were found to relate to fundamental problems. For the sake of be respectively less than 0.5% and 6% of the completeness these points will be briefly reiterated. time-reversal - invariant values. Uncertainty in the The discussion to follow assumes the availability of phase shifts leads to perhaps a 50% uncertainty in heavy-ion beams of stable nuclei throughout the these limits. periodic table with energies in excess of 6 MeV/A. A recent paper by Bryan and Gersten (Br71) dealt For the study of strong interactions variable energy with the question of where the greatest sensitivity to beams of protons in the energy range from 50-300 time-reversal-violating effects may be obtained in MeV appear most worthwhile. nucleon-nucleon scattering. Figure II-9-1 shows their predicted results for the difference in polarization B. STRONG INTERACTIONS and asymmetry as a function of energy and angle. Although these predictions are based on a specific a) Nucleon-Nucleon Scattering model for CP violation (Su68) they state that the The detailed information which may be obtained enhanced sensitivity in n-p scattering near 140° for from accurate measurements of cross sections and energies above 145 MeV is a general feature of any -95- very short-range time-reversal-violating interactions. test of charge symmetry. Information on the n-n Only the magnitude of P-A would be affected by the interaction must come from final-state interactions in particular model used. reactions with many-body final states. As discussed in section II-7-C, systematic studies in similar geometries The evidence for parity conservation in p-p scat- of three-body final-state interactions in systems tering has until now been restricted to the J = 0 states involving n-n, n-p and p-p pairs may provide more (coupling of * So and3P phases) and only surprisingly 0 accurate information on a . Accurate knowledge of crude limits have been obtained (Th65). A number of nn the n-p and p-p interactions could provide "cali- significant improvements Tor the design and analysis brations" of the analysis used to extract a . of experiments on P violation have been suggested nn (Th65) but the experiments still remain to be done. The direct evidence for charge dependence of the b) Symmetries in Nuclei and Nuclear Reactions N-N force rests mainly on the difference in the The ability to observe deviations from funda- scattering lengths a_p and a , which provide an np mental symmetries in many cases requires that a estimate of ~ 2% for the forces violating this fortuituous arrangement of nuclear energy levels or symmetry (He69). The violation of charge indepen- reaction threshold energies exist. For example, the dence for the strong interaction is believed to result largest parity-mixing effects should occur between from a variety of electromagnetic effects other than closely spaced energy levels with the same spin but the obvious effect of the charge of the proton. different parities. The experimental difficulties The major contribution is thought to arise from the associated with tests which require such a high degree difference in mass of the charged and neutral pions, of accuracy also prevent significant measurements for which affects the range of the one-pion exchange all but a few "best" cases. potential (Du66). Other properties such as the nuclear mass difference, vacuum polarization and magnetic It is therefore possible that cases may occur in effects also make small contributions (see He69a for a presently unknown nuclei which would enable more full discussion). precise measures of symmetry properties to be obtained. The extension of the "known" limits of Measurements of p-p and n-p scattering cross the chart of the nuclides as discussed in sections II-l sections, and measurements with polarized beams and and II-2 could provide these cases. targets are described in section II-7-B. Results of this type could determine the T = 1 phase shifts suffi- hospin symmetries in nuclei have been a subject ciently accurately to exhibit charge dependent effects for extensive investigation in recent years (for a at intermediate energies. summary see (Wi69)). The object of many of these The present value of the n-n scattering length is studies has been to determine nuclear effects resulting not sufficiently accurate to provide a very stringent from the large number of interactions which break Figure II-9-1 — Graphs of polari- zation minus asymmetry (P-A) predicted by the extended one- boson-exchange model (Br71) (Su68) at E,ab = 50, 145, 425 and 635 MeV. The solid and dashed curves correspond to plus or minus sign for a parameter of the theory (see Br71). The p-p data at 142 and 635 MeV came from (Zu70). -96- the charge-independence of nuclear forces. The vation of isospin. If in a nuclear reaction A(B,C)C'. Coulomb interaction arising from the electric charge isospin in the entrance channel is unique, and if the of the proton has been by far the largest effect in all two reaction products C,C' are members of the same cases studied so far. Very thorough calculations of isospin multiplet, then the angular distributions for C Coulomb contributions to asymmetries observed in and C' will be symmetric about 90°, provided isospin isospin-forbidden particle decays (Ad69) have been is conserved throughout the reaction. This rule, performed (Ar71); however, they are not yet accurate derived by Barshay and Temmer (Ba64) has been enough to permit information to be obtained on the tested in only a few reactions, and strong violations smaller effects resulting from charge dependence of of isospin conservation have been observed in the the strong interaction. d(4He,3He)t reaction at various energies (Gr70, Wa71). In Figure II-9-2 the asymmetry W(0) = A recent experiment (Co71) attempted to detect (oc(0)-ac'(n-8))l(oc(6)+oc'(ir-U)) is shown for this isospin-forbidden decay from the 5.36 MeV T = 1 reaction at E = 48.25 MeV and E = 82 MeV. WiLh a 6 a Q state of Li to a + d. This case was chosen because in high-energy heavy-ion accelerator such studies could an L-S coupling model the only nearby T = 0 state of be extended to considerably higher masses as has the same spin and parity cannot be mixed by the been discussed in section II-6-D. Coulomb interaction. This should result in an enhanced sensitivity to other charge - dependent Time-reversal invariance in nuclear reactions gene- effects. An upper limit of 2% for the deuteron rally implies the validity of the symmetry of the branching ratio was obtained, which is not sufficient scattering n-.atrix S under time-reversal accuracy to observe charge-dependent effects. It is transformation, i.e. conceivable that other cases of this type will turn up | -97 - 10 1 ' 1 1 ' 1 ; 3 o-d(a, He)t Eo« 48.25 MeV - EB«82MeV I s (GROSS tt_2L • d(a,t) He (WAGNER tl»L PHYS. REV. LETT. 24 , 473 PR1V. COMM.) gf (1970))' 8 » • »a 8 8 0.1 - 1 - 9 8 * * 8 ' - - 8 8 ; 1 . 1 i i i i 0.01 0.1 0.16 0.16 - - 0.12 0.12 - - 0.08 0.08 - - 0.04 0.04 - £ 0 0 -0.04 -0.04 - h -0.08 -0.08 - - -0.12 -0.12 - - -0.16 -0.16 L i . i 40° 80 120" 160 40' 80' 120 160 "cm. Figure II-9-2 — Experimental test of thu Barshay-Temmer theorem (see text). are estimated to be about one order of magnitude In contrast to time-reversal invariance, parity lower than the accuracy of the tests listed in Table violation in nuclei has been observed and is known to II-9-I. be caused by the weak interaction. In the framework TABLE IL9-I: Strung liUeruttum Tests of Tinu- Krvrrsat and Pnrity Invariant- of the current-current theory (Fe58) the effective Hamiltonian can be wiitten as tfilCtlOll Knetey Prin -.plf K 'suit Ref Hwk ' GUnJn+ + Jsi K ..T"l ,•„„ F' \ ^ where G is the universal weak coupling constant, js I'M 1 h A (1 i-j'.-'iiiiar, and jn are strangeness-changing and strangeness non- ' n*il MN.II TIltiH changing hadronic currents. The importance of nuclear parity-violation experiments stems from the + E ,, "«rp ,!,•,. ilril 1 nir WrfiS fact that jnjn behaves like an isoscalar and an > hnln ur n VlTVll EMf, isotensor (i.e. AT = 0,2) whereas j^ is predomi- nantly isovector (i.e. AT = 1). Experiments which are Al-p sensitive to only AT = 0 or to only AT = 1 parity- violating forces can thus provide information on the currents jn and js. The relative strengths of isovector and isoscalar parts of Hwk vary greatly from theory -98- to theory (Mc70) — for example standard Cabibbo only be observable in very- advantageous circum- theory (Ca63) predicts the isovoctor part to be stances, such as in this "'0 case where "'N beta weaker by a factor of 16. decay populates the 2" level much more strongly than the underlying background. It can only be conjec- r2000 tured that new suitable examples for parity-violation experiments will emerge in the course of studies of nuclei off the stability line. •s 1000 a C. NUCLEAR GAMMA DECAY IT. T T The interaction of nuclei with (he EM field is well \ understood and the study of nuclear gamma transi- tions has therefore been one of the backbones of I— nuclear speclroscopy. Undoubtedly the study of nuclear gamma decays will prove invaluable in 1 1 attempts to understand the structure of nuclei in new i i regions of the periodic table which will become 1000 accessible with a new heavy-ion accelerator. It is the purpose of this section to single out a few problems of general importance which have not been men- tioned in section 11-4 on the more standard aspects of 1200 1250 O00 13S0 U00 U50 gamma spectroscopy and also to point out 2000 •keV [' information on fundamental symmetries which may 10 15 JO 25 30 35 iS IS 50 55 —•• channel no be obtained from studies of nuclear gamma decay. Figure II-9-3 — Deviations of the pulse-height distri- a) Time-Reversal Invariance bution, from the approximating exponential function The suggestion of Bernstein. Feinberg and Lee (= AN"). The error bars indicate tne mean statistical (Be65) that the EM interaction of the hadrons might error of the measured points. The horizontal scale be responsible for the CP violation in the K; decay shows alpha energy in keV. The dashed line shows the has prompted a number of searches lor time-reversal expected decay energy of I6O (8.87). The exponen- violation in nuclear gamma decay. The experiments tial background at 1280 keV was 1.5 x 105 counts have not been completely successful so far. because per channel. the accuracies obtained are rot < 0. V •. There are no selection rules which would enhance time-reversal A definite parity violation has now been observed violating effects and these difficult experiments ff in the alpha decay of the J = 2" state at 8.87 MeV in require the measurement of quantities such as the 16 12 O to the C ground state (Ha70). Since admixed correlation between two momentum vectors in the T = 1 states cannot strongly emit alpha-particles, the plane perpendicular to a polarization axis I i.e. decay rate is only sensitive to the AT = 0 part of the o-P! s p;). This correction should be zero if time N-N force. Figure II-9-3 shows the peak observed at reversal invariance is valid. An odd time-reversal w>rm an alpha energy of 1280 keV which corresponds to will allow a finite phase-difference, -q, between E2 and the parity-violating alpha decay of the 8.87 MeV Ml components of a gamma ray transition, which level. The points shown are deviations from an should be 0" or 180" (He59, Bo68d) if time-reversal exponential function approximating the background invariance holds. The experiments usually use an from the allowed decay of the 9.61 MeV r level. initially polarized nucleus which decays by a 7-7 cas- From the measured alpha decay width (Ha70), V = cade. The primary gamma ray is mixed and the \C2 and (2.2 ± 0.8)x l(Tl0eV, the probability for the admix- Ml components should have approximately equal ture of i" = 2+, |F|2 * Iff"'3, can be deduced and is amplitudes since the size of the interference term, sin in agreement with theoretical estimates (Ga69, 17, is proportional to the multipole mixing ratio 99 - quired to test the suggestions of Bernstein, Feinberg (Ab68, Wa69, Ba70) or circular polarization of and Lee. In-beam studies of time-reversal violation gamma rays emitted by a randomly oriented using the (p,yy) reaction with beams of polarized pro- ensemble of nuclei (Ba70, Lo67,Bo68b, L066). In all tons might also become feasible. A further possibility is the chosen examples, the normal gamma decay mode the study of (p,7) and (7,p) reactions in thegiant-dipole is strongly inhibited for nuclear-structure reasons. All resonance region using the principle ot detailed balance. the measurements were performed wilh heavy nuclei (A > 100) and even after the experimental errors Although the low-energy cests already described have been reduced, it is doubtful that the nuclear- are performed with high precision, they may lack structure aspects of the problem can be evaluated sensitivity to the matrix elements of the electro- with sufficient accuracy to derive quantitatively the magnetic current far off the energy shell (He69e). On terms present in the parity-violating Hamilton;?n. the other hand, very accurate high-energy tests which More experiments on light nuclei are therefore desir- do have this sensitivity are difficult to perform. At able. As already mentioned, cases of AT = 1 present, all high-energy electromagnetic tests are parity mixing are particularly valuable because they consistent with no time-reversal violation, but the provide information on tne strangeness-changing part accuracy is less than that achieved in the low-energy of the Hamiltonian Cases in light nuclei in which this tests listed in Table II-9-II. (For a summary see Ri70). For example, a detailed balance test of 7+ 3He=^p+d mixing is probably strong are the T = 0 states at 5.11 MeV in :0B(J" = 2"), at 9.13 MeV in 14N(,F = 2") (Ra67) has only been performed with 10% accuracy. 1S These experiments are difficult because they and at 1.08 MeV in F (S" = 0"). Unfortunately, generally involve two different types of accelerator to none of these levels is fed by beta decay, and it is produce high-energy particle beams and high energy therefore doubtful whether sufficient accuracy could gamma-ray beams. be obtained. Again it can reasonably be hoped that new odd-odd nuclei with N = Z will furnish more TAIILK 11-911: Tries nt t irne rt'vt'rsa* tnva:nan«* in EM interneUoi favorable examples, especially since T = 0 and T = 1 levels are expected (Ja65) to be at comparable excitation energies for nuclei heavier than A = 40. Niu-lrus Priru-iplr x 1 IT' lU-feri-nci' The possibility also exists of searching for parity- violating admixtures in nuclear levels through in-beam ""itu h..m M*nsgh:iiirr i 1 • i ". KMiT .ii iMirpliun experiments, using the properties of nuclear reactions to produce polarization of the recoiling nuclei. One 1 "ir :ta i | • 1 K Alii." ;;;™iiy "- such attempt (Mo69) searched for anisotropy in the gamma-ray angular distribution from the first-excited '""I'll ,,.,.r,,ht,,,n 1 • IK I'i'lis state of ' "F(110 keV, Ji" = 1/2T) which was excited "l'l I1. .I.,r,/|-,I n I-^IIMI K • L' :: by Coulomb excitation. An asymmetry coefficient of i 1 (6.1 ± 5.6) x 10~" was measured, compared to a '" < 1 I'iu.) I *'() illi-n-IH-i- in Wiilln 4 i'l.iili-cl Uilanri' i-:1 K'2 pha-i- predicted coefficient of 4.3 x 10" , calculated by Mill- •-. Ill assuming the existence of a parity-violating, weak- ' Hi- •'llr.-pni KutiT interaction nucleon-nucleon force (Mo69). Such K^ur.Mi.v !ii.il hi 10 accelerator-based experiments are more difficult to perform than those using radioactive sources, but may have advantages in studying otherwise- b) Parity Violation inaccessible cases. Theoretical estimates (Mc70) indicate that the c) E.M. Studies of Isospin Symmetries parity mixing of nuclear states has an amplitude in the rangt 10"6 <^ F <^ 10"7. There is now experi- There are a number of problems related to isospin mental evidence, particularly from nuclear gamma in nuclear gamma decay which can be tackled with a decay, that F is of this order of magnitude although heavy-ion accelerator, three of which are mentioned individual measurements of the same transition may here. differ as much as a factor ten in F. Searches for parity i) One of these concerns the separation of EM matrix violation in gamma decay are based on detecting elements into their isoscalar and isovector parts. For either gamma asymmetries from polarized nuclei E2 transitions this would determine whether the - 100 - E2 effective charge comes from low-lying T = 0 or T traced back to the presence of mes.iii.-, in tin- nucleus. = 1 excitations. The simplest example involves the Microscopically, the total current operator in tin- observation of analogous E2 transitions in a T = 1 nucleus is j = j^ « jj. + }p > .... The terms other than triad. The experimental difficulty lies in measuring j>j result in a two-body part in the EM transition the transition in the Tj = 0 nucleus because the E2 operator and are commonly called exchange currents. transition is usually much weaker than competing AT Calculations indicate that these currents contribute = 1 Ml transitions. The data from the mass-26 triad significantly to the anomalous magnetic moments of (Ha68, Sc70) indicate that only the isoscalar contri- 3 He and 3H (Ch71l and to the n-p capture cross bution is enhanced. In odd-odd nuclei with A > 40 section at thermal-neutron pner»ips l.N'oiia). It is the experimental difficulty should not arise to the therefore of considerable interest to idenlih same extent because of the closeness of T = 0 and T = exchange currents in heavier nuclei. 1 states (Ja65). A systematic study of isovector and The exchange currents contribute a piece to the isoscalar effective charges could therefore be under- interaction HamilIonian that behaves as an isotensor taken in these nuclei. of rank 2. Although these terms are possibly quiU- ii) The mixing of states of the same T by the small they can be sensitively searched for in AT = 2 isovector part of the Coulomb and other charge- transitions which are strictly forbidden for states of dependent forces generally depends on T3. Such pure isospin. However, admixtures of different iso- mixing will cause a violation of selection rules for spin, which can decay by allowed AT = 1 transitions, gamma decay: for example AT = ± 1 transitions of also contribute to the gamma decay widths of the any multipolarity (or AT = 0 El transitions) will no levels of interest. These admixtures due to the longer have identical matrix elements in conjugate Coulomb interaction must be accurately calculated nuclei. Calculations by Lane and Soper (La62) before information can be obtained on exchange predict that isovector mixing should increase for currents. Such calculations (Ar71) can be most easily medium and heavy nuclei. Again an enlarged sample performed for light nuclei or near closed shells where of nuclei near the N = Z line will be essential for a wave functions are reasonably well understood. systematic study. It may well be easier to identify exchange currents iii) The study of isobaric analogue states with T > from their isoscalar and isovector parts which contri- Tg s + 2 is at present extremely limited (Ce68). bute typically 10-20'V to EM matrix elements. Since Coulomb - energy systematic^ ;Ja(59) indicate, magnetic moments and Ml matrix elements are not however, that states with T = 3 and 1 will be narrow very sensitive to small collective contributions, their in T3 = 0 nuclei with A ^ 40. Investigation of these measurement may provide conclusive evidence for states by T-forbidden resonance reactions and by mesonic currents in heavy nu-lei, particularly in the T-allowed multiple-particle transfer reactions, as well region of closed shells. For example, the exchange as studies of their gamma-decay matrix elements contributions to the g.s. magnetic moment in "'Hi promise to be both feasible and interesting. (Ch69) are of the same size as the perturbaliw one-body corrections (Ma67) and their sun can nearly d) Exchange Currents account for the anomalously large value. It has been predicted (Ch69) that the exchange contributions are In the conventional formulation of the interaction strongly dependent on the angular momentum of the between nuclei and the EM field (Ro67) the nuclear states although there is no strong experimental charge and current distributions are approximated by evidence. The influence of exchange currents on M 1 the sum of the individual - nucleon free-space transitions in the Pb region has recently been investi- quantities. Consequently the operators tor gamma gated (Kh72, Ha72). A new heavy-ion accelerator and beta decay are one-body operators with isoscalar would undoubtedly be extremely valuable in and isovector components. obtaining magnetic matrix elements relevant to the problem of exchange currents (see section ll-.'Sl- However, the presence of the strong interactions changes the EM interaction current. For example, if the phenoinenological N-N interaction has a Majorana D. NUCLEAR BETA DECAY exchange term, then the electric-dipole sum rule in the nuclear photo-effect is increased by about 40'} Production of nuclei far from stability will make (Le50). The origin of such exchange terms may be available many more examples of nuclear beta decay. -101- and the study of these decays will probably be one of the nuclei far from stability could prove to be ideal the first tasks to be tackled as accelerators become examples for such a study. available. Therefore it is worth summarizing the present status of our understanding of nuclear beta To date there is no positive evidence for a term in decay and indicating the significance of new data weak interactions which is not time reversal invariant. that could be obtained specifically from the decay of Experiments (BuBO, Te60, C160, C161, Ca67, Er68) nuclei far from 0-stability. As such, this section is not have attempted to observe an asymmetry (J-pe x pv) in isodoublet (3-derays such as n -* p + e" + De and intended to be a complete study, but simply an ly 19 + indication of a few important problems. Ne -* F + e + ue using polarized nuclei and detecting the direction of the electron and a) Weak Interactions neutrino (i.e. recoil nucleus). The experimental diffi- culty is in detecting the recoil nucleus;however, if ths In analogy with electromagnetic theory, a current- daughter nucleus were unstable to particle emission, current interaction is assumed and the Hamiltonian it would be possible to infer the direction of the density for nuclear beta decay is written (Sc66, recoil nucleus from measuring the direction and K066) energy of the emitted particle. No isodoublet beLa decays are currently known in which the daughter nucleus is particle unstable, but it is very likely that an example will be found among nuclei far from stability. On the other hand, if an asymmetry is measured in such an experiment, Kim and Primakoff (Ki69) warn against an immediate interpretation in where G is the universal weak-interaction constant, P^ are combinations of Dirac matrices, and C^ and terms of time-reversal violations, since an asymmetry C'x' are coupling constants. The subscript X stands may be produced by the presence of a 'second-class' fur scalar (S), vector (V), tensor (T), axial-vector (A) current (to be discussed later) in the axial-vector part and pseudoscalar (P), and the Dirac matrices are Pg = of the interaction. In an attempt to eliminate the presence of Mch a current, Kim and Primakoff 1, Py = V rT = om. PA = 75 -^ and PP = 75. The interaction depends on 10 complex coupling con- suggest looking for asymmetries in the decays of the slants (here lepton conservation has been assumed; two extreme members of an isotriplet with the 32 > 3:2 otherwise there would be 20 complex coupling daughter state being an isosinglet, e.g. CI- - S + + 3 2 3 2 constants). Furthermore if time reversal invariance is e + ve and P ->• S + e + ve or any other similar assumed then the coupling constants are real and the case for which the Gcmow-Teller matrix clement is interaction depends on 10 real parameters. A recent hindered for nuclear structure reasons. attempt has been made by Paul (Pa70) to determine the best values of the coupling constants from all b) Induced Interactions relevant measurements on allowed decays (75 data), by a least-squares adjustment program. The results he Assuming a pure V-A interaction which is time obtained by assuming Cp = Cp' = 0; Cg = Cg' and Op reversal invariant, the interaction Hamiltonian density = Cj' are can be rewritten in the form C /C = 0004 Cs/Cv --0.001 ± 0.006 T A -° ± 0.0003 + ly/'-V- 0.82 £}° CA-/CA= 1.10 10.06 which implies that the interaction is pure V-A (viz. = ^X ^X'- Cg = Op = Cp = 0) to a very good where the coupling constants have been incorporated approximation. Paul (Pa70) concludes that a consi- into the nuclear vector and axial-vector currents derable reduction of the errors for the ratios Cy' Cy J^/^ and JL/A'. The term "induced interactions" re- and l'^' C^ would be obtained if accurate measure- fers to higher order effects due to the presence of ments of the circular polarization and shape factors strong interactions and these are proportional to the + + for pure Fermi 0 — 0 transitions were available. momentum transferred, k^,. Thus the nuclear currents The high energy decays which will be found among are written -102- V) + V " B V TM *WM V weak maenesium induced scalar A)= V s V " induced tensor induced pseudoscalar According to the conserved vector current (CVC) theory (Fe58, Wu64) the nucleon current J^I is a conserved current (i.e. 3^J^^ = 0) and is propor- tional to the plus component of the total isolopic- 40 60 spin current. By analogy with electrodynamics, the SUM OF ENERGY RELEASED (me* UNITS) magnitude of the "wtak magnetism" coupling Figure 11-9-4 — Asymmetry 6 as a function of sum o! constant g-\^y[ can be inferred to be (Ge58) energy released from positron and electron decay. Each point represents a mirror pair; number is A value. Inclined lines is lhat expected if b wire caused by a simple single-particle tensor term. in units of h " c = m = 1, where Kp - Kn is the diffe- rence of proton and neutron anomalous magnetic moments, and m and M are masses of electron and Here Wo~ is the maximum energy released in the + nucleon. The CVC theory also predicts that the negatron emission and Wo the maximum energy induced scalar coupling constant gjg must vanish. released in the mirror positron decay. The available experimental evidence is summarized in Figure li-9-1 The behaviour of the 0-interaction under the where the asymmetry 5 is plotted as a function of the transformation G = C e'71^,, (the product of charge sum of the energy released in the two decays, Wo + symmetry and charge conjugation) permits the + Wo , and it is found that a sloping straight line separation of the terms of H^ into two classes (We58), passing through the origin is consistent with this data. those which are invariant under G-transformation and This simple picture was thrown into disarray by a those which are not. The induced-tensor term and the rather elegant experiment on the mass-8 system by induced - scalar term are not, and hence are in a Wilkinson and Alburger (Wi71b). The special thing separate class from the other four terms: they are about this system is that the first excited stall- of h :!H called 'second-class currents'. If it is assumed that the is very wide — many MeV — so KLi and HH do not 0-decay interaction like the strong interaction, is decay to a well defined excitation in KBe; rather they invariant under G, then one must set gjg = gj-p = 0. go into the broad continuum that break:; up into the The CVC theory required the V interaction to be G alpha particles at excitations in sBe revealed by tin- invariant (i.e. gjg = 0); however, there is no good energies of those breakup alphas. By measuring the evidence (We58) for apph ng this invariance principle coincident alpha spectra for both "Li and "H decay, to the A interaction, since the axial-vector current is the ratio of ft+/ff can be deduced, and Wilkinson and not conserved under strong interactions. Alburger's result is shown in Figure 11-9-5. The The whole question of 'second-class' currents experimental points clearly appear to fall on a recently reopened by Wilkinson (Wi70b, Wi71a) has horizontal straight line; the sloping line shown is what. led to a flurry of activity as reported in Physics would be expected if the energy dependence shown Today (September 1970 and November 1971). One in Figure II-9-4 were correct. Thus if second class consequence of a simple theory with one-body currents are to explain mirror asymmetry then the induced tensor currents is that an asymmetry, S, in simple theory has to be substantially modified, the ft-values for mirror ^-transitions is expected and perhaps incorporating meson-exchange effects which should be proportional to the energy released as are of many-body character. Lipkin (Li71| suggests exhibited by the formula that meson exchange with u> - 3it decay in the nucleus might be one such mechanism. Other pffecls. such as binding energy differences, can produce mirror asymmetries; however the calculations to date (Wi7 1 a) ft" - 103 - suggest that these effects by themselves are insuffi- (a) To compare experimentally deduced matrix cient to account for the experimental asymmetries. elements with predictions from various nuclear As an alternative to looking at mirror decays, models. A typical example has been the explanation Holstein and Treiman (HoTl) suggest examining the of the retardation in unique first-forbidden decays an single allowed 0-decay between the mirror states of an being due to the repulsive nature of the T = 1 isodoublet. They claim that with a complete set of particle-hole force (To71). measurements of shape factors, electron angular (b) To compare (3-decay and 7-decay matrix ele- distributions from polarized nuclei and £S-7 circular ments; in particular a comparison of allowed polarization, it would be possible (on the basis of the Gamow-Teller decays with Ml 7-decays has already simple theory) to separate induced tensor terms from been extensively pursued. (Ha69). This can be weak magnetism and other recoil effects. Other extended to other multipoles, and if the experimental experiments of this type, in particular on nuclei far data is sufficiently accurate, the con.parison could from stability, since these are characterized by large furnish a test of the CVC theory. energy release, may well shed some light on this interesting problem of second-class currents. This (c) To compare two different beta-decay matrix would also have an important bearing on time-reversal elements. For example in first-forbidden non-unique studies as mentioned previously. beta decay, CVC theory predicts a relationship between matrix elements /a and Jir which could be tested if the experimental determination is suffi- ciently accurate (Sm70). Once again the production of nuclei with higher decay energies would signifi- cantly improve experimental access to these quantities (To72). ii) A systematic study of superallowed 0+->0+, AT = 0, Fermi decaya For these decays the nuclear matrix elements (being the expectation value of T+, the isospin raising or lowering operator) are the same for all decays involving states of a given isospin T; from the transition intensities a value for the universal 25 35 45 55 SUM OF ENERGY RELEASED (mc2UNITS) weak-interaction constant G can be deduced (B169). All ft-values for these decays are expected to be the Figure H-9-5 — Comparison of spectra of excitation same irrespective of the nuclei involved; thus any in Be from Li and "B decay. 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SUMMARY OF OPTIMUM ACCELERATOR PROPERTIES 1. INTRODUCTION 2. MASS AND ENERGY RANGE OF PROJECTILES 3. ENERGY RESOLUTION 4. CURRENT AND EMITTANCE References 1. INTRODUCTION 300 In the preceding chapter a variety of topics in physics was discussed. Each discussion led to the determination of characteristics that an accelerator 100 must possess in order to have the greatest potential for the future, and although the problem was approached from different directions the conclusions reached have much in common. They could certainly E all be satisfied by a single accelerator. a In this chapter we shall outline characteristics that would make an accelerator capable of achieving the varied goals set in previous sections. For the moment < this will be divorced from the actual features of w 10 existing or technically feasible accelerators; that V connection will be made in the next chapter. Suffice \ REGION OF FUTURE it to say that none of the properties described here would be unattainable. Furthermore they would, if combined in one accelerator, result in a uniquely powerful tool for frontier research. 2. MASS AND ENERGY RANGE OF PROJEC- 80 160 TILES PROJECTILE MASS Both "light ions" (isotopes of hydrogen, helium Figure IH-2-1 — Energy range of projectiles return and lithium) and "heavy ions" (those heavier than mended in this report. lithium) have been considered as important in this report. The most demanding conditions for light ions 3. ENERGY RESOLUTION were set in section II-7, where variable energies from 50 to 300 MeV were deemed necessary; this range In addition to prod-icing exotic nuclides whose easily accommodates the requirements discussed in decays may be studied subsequently, heavy-ion trans- section II-1 for producing nuclei far from stability.. fer reactions can also provide information on tin- masses or energy levels of these nuclei. However, For heavy ions, the highest>energy demands tome since both residual nuclei can be left in an excited from sections II-l and II-2 and are to facilitate the slate, such measurements will require a beam-energy production of exotic nuclei. For all A 3= 40 this resolution, AE/E, of between 0.01r; and 0.1'r com- amounts to a projectile energy of ~10 MeV/nucleon bined with a careful selection of target and projectile but with lighter ions increases rapidly to ~50 so as to minimize competition from unwanted states. MeV/nucleon for lithium. To makepossibleCoulomb- excitation studies, energies should also be variable The feasibility of studying heavy ion transfer down to a lower limit which lies, as discussed in reactions at incident energies of 10 MeV/amu using section II-4, somewhat below the energy of the a solid-state counter telescope and/or a magnetic Coulomb barrier experienced by each projectile on a spectrometer is presented in this section. In gene- target of similar Z. ral, target-thickness and kinematic-broadening effects will limit the experimental energy resolution to The complete range of desired energies is illus- being greater than about 0.03%; therefore a beam trated in Figure III-2-1. It should not be interpreted as resolution of -0.01% would be ideal for most meaning that an extension of the range towards experiments. higher energies would not be desirable but simply Even if a beam of projectiles is monoenergetie as it that any reduction in the described range could only impinges upon a target, the reaction products will lead to significant compromises in the scope for have a finite spread in energy when they are detected. study. -Ill- The principal causes are kinematics and energy losses i) angular effects dominate for all projectiles in the target and the effect becomes quite significant with Z > 10; as the mass of the projectile increases. This is ii) since geometry effects cannot easily be illustrated in Table 111-3-1. limited to <|0.1°, it is unnecessary to use targets thinner than 50 Mg/cm2; at this thickness the multiple-scattering angle is also ~0.1°; iii) the absolute energy resolution for a given projectile is approximatley proportional to t'2/E (E in MeV/amu); and iv) at 10 MeV/amu, with 50 ug/cm2 targets, all reactions with projectiles having Z ^ 60 Variations in angle, dtf.are caused by i) multiple are characterized by a "beam-independent" scattering in the target and ii) geometry effects such energy resolution of LJ O.I AE «idE/dfl)(Z U!-7K m t 10 MeV/amu < where Zt is the atomic number of the target, t is its 0.01 thickness and E is the energy in MeV'amu. For a CONTRIBUTIONS TO given projectile: i) dE/dS is approximately constant ENERGY SPREAD for all energies between 7 and 10 MeV/amu, and ii) AT E=IO MeV/amu AEni is approximately constant for any target provi- ding its 7. is greater than that of the projectile. The energy spread caused by geometry. AE,,, Wl" De assumed equal to AE . m 0,1 For heavy-ion transfer reactions detection will usually be at or near the classical gra/.ing angle, and with a bombarding energy of 7 to 10 MeV/amu this 0.01 always occurs at less than -10°. Since the Q-values will 20 4 0 60 be much less than such bombarding energies, both PROJECTILE Z incoming and outgoing ions will have approximately Figure III-3-1 — The percentage calculated experi- equal rates of energy loss. By appropriately rotating mental energy resolution AE/E is plotted as a the target the total energy loss can be made indepen- function of projectile Z for ail heavy ion reactions for dent of the depth at which the reaction takes place, which the target Z exceeds that of the projectile. The and proportional only to target thickness. Thus, the curves were calculated at 7 and 10 MeV/amu for only contribution to energy spread. AEU, will be a targets of 100 fig/cm2 (solid lines) and 50 fig/cm2 small effect of target non-uniformity. Finally, the (dashed). A breakdown of the terms contributing to effect of statistical fluctuations (or straggle) in energy the total resolution at 10 MeV/amu and with a 100 loss, AE . is given by (Se6-1) AE aZ tl;! where Z is S s p p ^g/cm2 target is also given; these terms include the atomic number of the projectile. multiple scattering AEm, geometry AEg = AEm, The terms contributing to energy resolution are energy straggling AES and target non-uniformity shown in Figure II1-3-1 together with the total (assumed ± 10%) AEU. resolution, AE. for heavy-ion transfer reactions at 7 and 10 MeV/amu; target thicknesses of 50 and 100 : r The best percentage resolution attainable under ug;cm are assumed with ± 10 7 deviations. The the described conditions appears from Figure III-3-1 salient characteristics evident from the figure are: to be 0.03cc providing the atomic number of the -112- projectile is greater than 10. Thus, for these projec- The most .stringent requirements on heavy-ion tiles, a beam resolution of ~0.01% would be beam current are set b> the subjects considered in appropriate. As discussed in section II-7 such resolu- sections 11-1. 11-2 and 11-3 since these in general tion would be entirely adequate for light ions as well. involve the bombardment of relatively thick targets. Thus, heal dissipation will present few difficulties and 4. CURRENT AND EMITTANCE only the experimental counting rate need be consi- dered. Under these conditions, 10'2 particles per Both current and emittance are beam properties second would certainly be desirable, although some for which no upper limit on performance can be set. reduction could probably be tolerated for the heavier For any accelerator the available current should ions. For the light-ion experiment.1: di.-« ussed in always be as high as possible with the emittance as section 11-7 much higher currents might be required, low as possible. There are undoubtedly many experi- ranging in some cases as high as 101 % particles per ments, such as those involving thin targets, which second. would require only a small fraction of the current The necessity for accurate angular determinations available, but such reduction could never cause is discussed particularly in sections 11-5 and 11-7. A difficulty. Thus we must set limits here which beam emittance of less than ()..'] cm mr was deemed represent minimum requirements without which an important prerequisite. some aspect of the experimental program already described would materially suffer. REFERENCES Ma6S J.B. Marion and F.C. Young, Nuclear Reac- Seti4 E. Segre. Nuclei and Panicles (VV.A. rti-mamin tion Analysis (North-Holland Publishing Com- Inc.. New York. 19fi4). pany, Amsterdam, 1968). -113- Chapter IV. SOME HEAVY ION ACCELERATORS 1. INTRODUCTION 2. THE MP TANDEM VAN DE GRAAFF AS A PREACCELERATOR 3. A HELIX LINEAR ACCELERATOR FOR HEAVY IONS 4. A HEAVY ION CYCLOTRON 5. A HEAVY ION SYNCHROTRON References 1- INTRODUCTION The increased interest in heavy ion physics and one stage of stripping is used. Thai is. the beam is acce- chemistry, and the desire to accelerate the heaviest lerated and then passed tnrough a gas or foil where ions to energies sufficient to overcome the Coulomb ionization is increased by multiple atomic collisions. barrier of any target nucleus, have resulted in the When a Tandem Van de Graaff is used as a preaccele- upgrading of at least two accelerators and the rator two strippings are used, one in the terminal, production of about a dozen proposals for new ones. changing the negative ions to multiply charged positive Nevertheless only two accelerator projects capable of ions, and a second at ground where the positive accelerating all ions to energies greater than 8 MeV/A charge is further increased. have been funded (Super Hilac (Ma71) and the UNILAC (Bo70)) and will be the only ones in the foreseeable future with this capability. The Super- Hilac (Ma71) at Berkeley and the Tandem cyclotrons (Ph72) at Dubna fall into the category of upgraded machines. Large isochronous cyclotrons being built at the University of Indiana (Ri71) and Dubna (Sh71), and a hybrid linac-cyclotron system (ALICE) (Ca71) at Orsay are examples of new machines with a wide range of heavy-ion acceleration capabilities — al- though not to the extent of accelerating the heaviest ions over the Coulomb barrier for all target nuclei. The most ambitious (and expensive) heavy-ion pro- ject at present is the UNILAC (Bo70), a heavy-ion linac being built in Germany. When completed in 1974 it will be capable of accelerating all ions to energies above the Coulomb barrier of any target. Fig. IV-1-1 (adapted from B171) summarizes the maxi- mum energy capabilities in MeV/amu as a function of ion mass for heavy ion accelerators, operating or under construction around the world. Also shown in Fig. IV-1-1 are three turves showing BO 120 IGO the maximum ion energy capabilities of three hybrid- ION MASS iAMU) accelerator systems that would meet the requirements of the experiments proposed in this report. These Figure IV-1-1 — Heavy ion energy range for three consist of a Tandem Van de Graaff preaccelerator and possible CRNL accelerators discussed in this report either a cyclotron., synchrotron or a helix linac as a (solid lines); Tandem Van de Graaff-cyclotrcr post-stripper accelerator. The curves shown cones- Tandem Van de Graaff-synchrotron and Tandem V pond to a 13.5 MV terminal and foil stripper in the de Graaff-Helix combinations. In all cases a l.'J.f> MV terminal and at ground. terminal and foil stripping in the terminal and at ground are assumed. Also shown are the energy 2. THE MP TANDEM VAN DE GRAAFF AS A ranges for all relevant accelerators either operating or PREACCELERATOR under construction around the world (dashed lines). This figure is based on one prepared by M. Blann The present day ion sources of the Von Ardenne or (B171). The two curves for the UNILAC correspond Penning iype are capable of producing beams of to the use of a gas stripper (lower) and a foil stripper highly ionized light elements, but for heavier (upper). elements they seem to be limited to the production oi charge state (q) to atomic mass (A) ratios % = q/A Charge - to - mass ratios achievable in this way of not much larger than 0.05. Acceleration to high depend on the terminal voltage. Calculations based on energies of ions with such low £ is expensive, so in most empirical formulas of Betz (Be6(i) and Nikolaev and heavy-ion accelerators, operating or proposed, at least Dmitriev (Ni68) show that with a gas stripper in a -117- 13.5 MV terminal and a foil stripper at ground, the Heidelberg designers predict a buncher capture most probable charge state (q) for uranium ions is efficiency of 70% for a double-drift buncher. 28 . A foil in the terminal gives an even higher charge For light ions with £ approaching 0.5 the specific + state, 34 ,but in this case the design of the stripper energy will reach only four times that for the heaviest must take into account the damage to the foil by ions (e.g. protons could be accelerated to 82 MeV.) intense beams. If the intensity is not to be limited, a This limitation is not eas'ly lifted because the energy mechanism for rapid foil changing must be gain per section is restricted by the accelerating incorporated in the terminal and methods of gradient that can be achieved and because the extending foil lifetimes must be investigated. A particles pass through the structure only once. In a Tandem accelerator with two foil strippers and with cyclic machine, by contrast, the number of transits an ion source capable of delivering time-averaged through the accelerating cavity is not fixed sc that negative-ion currents near 5 jiiA will fulfill the intensity the final energy is limited by other factors, such as requirements of the experiments proposed in this magnetic rigidity and isochronism. report, provided that the capture efficiency of the post accelerator is high. In 1970 the estimated hardware cost for each section was $90,000. A helix pos^accelerator for 10 3. A HELIX LINEAR ACCELERATOR FOR MeV/A ions would therefore cost a minimum of $5.0 HEAVY IONS M for the structure, RF supply and focussing magnets. The cost of the buncher and interface The helical wave guide structure has been between Tandem and helix is roughly estimated at developed in recent years at the University of $200 k. A 10 MW substation would be required for Frankfurt fur the acceleration of heavy ions (K171K the RF power supply which would cost about $200 An accelerator of this type at the University of k. (See Table 1V-3-I). Heidelberg using an upgraded MP Tandem as an injector has been proposed. It has been demonstrated TABLE IV-3-1: Principal Parameters of a Helix Linear Accelerator for Heavy Ions that the structure can be adapted for low particle velocities corresponding to specific energies of 0.8 Injection Energy II.H Mi'V A MeV/A or greater. The modified CRNL MP Tandem £ min 0.15 with a terminal voltage of 13.5 MV will easily be Filial Energy '• HIMvV A capable of delivering beams of heavy ions of all Accelerating Gradient 1.25 MVtim species including uranium with specific energies equal Number of sections 56 to or exceeding 0,8 MeV,A. Length 7:).2 m RF puwenl'lVI 5.6 .MW The Frankfurt design employs helix sections 1.3 m Frequency 108.-IH MHz long, each of which gives an energy gain of 1.08 MeV per unit of charge. To reach the objective of 10 I'ost tMimal e lli>70*r MeV/A for uranium ions the energy gain in the helix Helix including KF supply control must be 9.2 MeV/A. Assuming that solid strippers in and cooling at S90 k, section 5.U M the terminal and at ground potential will yield a Huncher .2.M + useful quantity of, say. q = 36 ions, the number N Substation (10 MW) .2 M of sections required is S 5.1 M N * 9.2 x 238/(36 x 1.08) = 50.7 * 56 At 1.3 m pei section the total length is 73.2 m. 4. A HEAVY ION CYCLOTRON The Frankfurt-Heidelberg type of accelerator In recent years a number of groups have proposed section operates at a frequency of 108.48 MHz and the combination of a Tandem accelerator injecting each requires 100 kVV of cw RF power. If designed into a cyclotron to provide proton energies up to for a charge-to-mass ratio j - U.15 (q = 36+, A = ~300 MeV and energies up to 8 MeV/A for all heavy 238), the accelerator could be tuned to accept all ions. (For a summary see Li70). The following ions with a larger charge-to-mass ratio. discussion is based to a large extent on the Oak Ridge The capture efficiency of the helix for a dc beam is APACHE proposal (Or69) but considers the possi- increased by the use ofabuncher. The Frankfurt- bility of producing such a machine in two stages. The - 118- machine described below contains a number of Three of the gaps between magnet sectors are used economy measures, whose effect is primarily to for beam injection and extraction, extraction restrict the energy of light-ion beams (maximum deflector and accelerating cavity. The fourth gap is proton energy 70 MeV) while providing energies up vacant, but could in future be used either for another to 10 MeV/A for all ions. Future additions to the extr<.-tion channel or for a harmonic cavity to machine could provide for the acceleration of protons provide some flat topping of the accelerating voltage, to 350 MeV at total costs roughly equivalent to those to reduce energy spread in the output beams. of APACHE. The accelerating cavity is similar to that of the APACHE proposal, that is, a half-wave resonator The following design assumes that the injector can capacitively loaded at the centre by the delta-shaped provide ion beams with a charge-to-mass ratio, accelerating electrodes. The peak RF voltage on (he q/A, (corresponding to q = 36+ for uranium) greater electrodes is 250 kV and since there are two gaps, the than 0.15 and energies greater than 0.53 MeV per total ion-energy gain per turn is roughly U.5 MeV nucleon. Figure IV-4-1 is a plan view of the times its charge state. cyclotron. It is a four sector machine with 50% of the c.rbii in the magnetic field. The azimuthally varying Beam extraction is done at a fixed radius; therefore field provides axial focussing and the radial-field the magnetic field and acceleration frequency must profile is adjusted to maintain isochronism. For all be varied to provide a variable energy output. A but the lightest ions the profile is flat. Overall tuning range of 10 MHz to 30 MHz for the RF dimensions of the magnet are diameter, 11.5 metres, system, and operation on the 5lh, 15th and 25th height 3.6 metres, and weight approximately 1900 harmonics of the ion-rotation frequency allow the tons. Maximum magnetic field is 1.5 T. Trim coils on beam-output energy to be varied from 1 MeV/amu to the magnet pole faces allow adjustment of the radial 70 MeV/amu. The latter energy however can only be profile. achieved for protons. ELECTROSTATIC DEFLECTOR 6 I ME'RE SCALE HEAVY ION CYCLOTRON Figure IV-4-1 — Plan view of the heavy-ion cyclotron. -119- As shown in Fig. IV-4-1 the beam is injected into TABLE IV-4-1: Tentative Characteristics of a Heavy Ion Cyclotron the cyclotron by passing it through a sector gap, into a 110° bending magnet The radius of the initial orbit is 0.8 metre and the orbit spacing at injection is for MAGNET all cases greater than 3.2 cm. The orbit spacing Overall Diameter 11.6 m decreases with increasing ion energy to a minimum Height 3.6 m Weight 1900 tons orbit spacing on the final him of 1.3 cm. This should Number ol Sectors •i make 100% beam extraction relatively easy. Sector angle 45° Maximum Magnetic Field 1.5Tesla The extraction system shown in Fig. IV-4-1 is % Orbit in Magnetic Field 50% similar to that of the APACHE proposal. A one-metre electrostatic deflector operating with an electric field RF SYSTEM of 4 MV/m, deflects the beam approximately 4 cm No. uC Accelerating Cavities I from its equilibrium position into the entrance of the No. of Gaps 2 Maximum Gap Voltage 250 kV first septum magnet, whose field is about 1.5% Frequency Tuning Range 10 MHz.10 MHz smaller than the main sector field. In the succeeding RF Power (cw) 250 kW magnet sector another septum magnet with a field 15% lower than that of the sector, deflects the beam BEAM 20 cm from the equilibrium orbit and into the first Minimum £ For 10 MeV/amu GiK-iut .15 extraction bending magnet A second magnet bends Injection orbit radius .8 m Extraction orbit radius 2.67 m the beam clear of the cyclotron. Ion Frequency 0,5-4.5 MHz With the orbit-spacing restriction, the maximum Output energy 1 MeV IA to 10 MeV/A or 70 MeV/A (heavy ions) (protons) energy to which an ion can be accelerated depends on its charge state and the energy gain per turn. The graph shown in Fig. IV-1-1 gives maximum attainable ion energy as a function of ion mass, assuming a TABLE IV-4-II: Heavy Ion Cyclotron Cost Estimates minimum turn spacing of 1.3 cm and an energy gain per turn of 0.5 MeV. Table IV-4-1 summarizes the Cost Estimates dimensions and other characteristics for the cyclotron. Item CRNL APACHE The numbers are necessarily tentative and may change with a detailed design study. Magnet and Power Supply 1.70 M$ 1.70 M$ No attempt has been made to do an independent Trim Coil and Power Supply .25 .75 cost estimate of the cyclotron. A fairly detailed cost Beam Injection and Extraction .-15 .64 estimate for a similar cyclotron was however made at Oak Ridge for the APACHE proposal. Using their RF Cavities .22 .43 numbers and modifying them to reflect the difference RF Power Supply .46 .92 in trim coil requirements, RF-cavity and-power Vacuum System .66 .66 requirements, allows us to make the cost estimates Control .35 .35 which appear in Table IV-4-II. The costs are in 1970 dollars. No factor for escalation or contingency is 4.09 M$ 5.45 M$ included. The equivalent APACHE estimates are included for comparison. 5. A HEAVY-ION SYNCHROTRON Modification of the cyclotron to increase the maximum energy of light ions is an open option for Although it has been recognized (Li70) for some the future. In particular, modifying the magnet poles, time that a modern strong-focussing synchrotron increasing the number of trim coils, and adding provides by far the lowest cost per unit of final another accelerating cavity, would allow a maximum field-radius product, the very high vacuum require- proton energy of 350 MeV. ments and the inherently low duty cycle have discouraged development. A thorough study of a -120- heavy-ion Alternating Gradient Synchrotron system 83 f/A to give a final current of 100 n.A, well below was carried out at Berkeley under the name the space charge limit). OMNITRON (Uc66). Recently, the weak-focussing Pulsing of (he negative ion source of (he Tandem synchrotrons, Princeton-Penn Accelerator and UCRL accelerator al these repetition rates should therefore Bevatron, have accelerated small currents of N ions to be investigated as a means of increasing the over 100 MeV/A. An interesting variant of the A.G. instantaneous injected current. It should be noted synchrotron, described below, would use the that pulsed operation of the Tandpm, providing H3 upgraded CRNL MP Tandem as an injector and would MA for 20 /is at 60 Hz, gives an average beam accelerate the heaviest ions to 10 MeV/A and protons current of only 1 pA (if the charge state of interest to 350 MeV. comprises 10'", of the total beam from the Tandem). The principal difficulties mentioned above can be This is well below the point where beam loading overcome or ameliorated. The vacuum requirement affects accelerator operation. (~10~9 T i similar to that of theCERN Intersecting orr) S A separated-function magnet lattice is proposed for Storage Ring. In the ISR the vacuum chamber is the heavy - ion synchrotron. Separated - function bakeable and cryopumping is used. For a rapid- magnets were suggested by Danby et al. (Da66,Da67) cycling synchrotron, a ceramic vacuum chamber as at BNL in 1966 and subsequently adopted at NAL used on the Cambridge Electron Accelerator (cycling for the 200 GeV synchrotron. Th's arrangement has rate 60 Hz) would be suitable. the advantage in a universal heavy-ion synchrotron of The problem of the low duty cycle can be solved, providing more flexibility in tuning the ring for a in principle, by two devices, viz. by pulsing the variety of ions. The simple lattice, F O D O. is Tandem ion source and by employing a long spill proposed with one focussing, and one defocussing, time for the accelerated beam. Taking these in reverse quadrupole per normal period (Fig. IV-5-1). A order, the technique of spilling the beam from a bending or dipole-magnet guides the beam in the 0 synchrotron for up to 50% of its period has been spaces between quadrupolps. The dipoles could be extensively developed and employed in most, if not either window-frame or H-frame type. There are 16 all, high-energy proton and electron synchrotrons. normal periods of this lattice and four straight The method involves the controlled excitation of an sections. The injection septum, acceleration cavity integral or a one-third integral resonance in the and extraction septum each occupy one of the betatron oscillations by energizing special quadru- straight sections. poles and sextupoles while the field in the guide magnets is kept constant. The growth of the radial oscillations of an individual particle causes it to pass into a septum-magnet channel at a random time. The spill rate can be adjusted to extract all particles in the time available. A more difficult problem is the capture of sufficient charge in each cycle if a Tandem accelerator is used as an injector. The mean current, Io, captured in the synchrotron, is Io = Ijnrfe where Ij is the instantaneous injector current, n is the number of orbits captured, T the orbit period at injection, f the cycling frequency and e the capture efficiency in the RF buckets. Since e can be made unity, f = 60 Hz is a convenient value, and heavy ions from a Tandem will have orbit times r of the order of 2 /is (see below), then I-, = 8333 Io/n. Thus to reduce the number of turns injected to a reasonable value like 10, the peak injector current Figure IV-5-1 - Plan view n!" heiivy-inn synchrotron. must be 833 times the mean accelerated current (e.g. -121- l0(—I I I I 11 I I I M I I 1 1 1 I M I I 1 • —1000 X-INJECTIJN WITH 13.5 MV TERMINAL 100 SPECIFIC ENERGY (MeV/A) Figure IV-5-2 — Magnetic rigidity Bp, ion velocity )3 and rotation frequency fo as a function of specific energy for various charge-to-mass ratios. Fig. IV-5-1 is a plan view of the synchrotron TABLE IV-5-I: Tentative Principal Parameters of a Heavy-Ion Synchroton layout. Each quadrant has four normal periods, each of which extends from the center of a focussing (F) quadrupole to the center of the next focussing Peak guide field 1.5Tesla quadrupole. The F quadrupoles adjacent to the Bending radius 2 m straight sections have half the strength of the others. Injection field minimum 0.3 Tesla The sextupoles, S, and possibly some additional Average radius 4.3 m quadrupoles will be required for the resonant Circumference 26.85 m extraction procedure. The accelerating cavity is Proton rotation frequency 2.6 to 8.8 MHz similar to that proposed for the OMNITRON, a U40 rotation frequency 0.46 to 1.78 MHz ferrite-tuned cavity whose tuning tracks the guide Cycle rale 60 Hz field throughout the accelerating cycle. The maxi- 50 kV mum energy gain per cycle is 50 keV for singly Peak accelerating voltage 4 charged ions. By operating on harmonics of the Number of sLraight sections rotation frequency varying from the 4th to the 22nd Number of normal periods 16 the tuning range can be kept between 10 MHz and 35 Structure of normal periods FO DO MHz. Number of dipoles (guide magnets) .12 Number of quadrupoles 36 The variation of magnetic rigidity, ion velocity and Number of sextupoles I rotation frequency vs specific energy for various Vertical aperture 5 cm charge-to-mass ratios £ are shown in Fig. IV-5-2. The Radial aperture 9 cm initial guide field required with the 13.5 MV-terminal Injection energy minimum 0.8 MeV/A Tandem as injector shows a surprisingly small variation from protons to uranium ions. Charge-to-mass ratio minimum 0.15 Extraction energy U40 12MeV/A For a summary of design parameters and estimated Extraction energy protons 360 MeV costs, see tables IV-5-i and IV-5-I1. Ratio of injected to extracted rurrent (n = no. iif injected orbits) -122- TABLE IV-5-II: Cost Estimate Summary of a Heavy Ion Synchroton (based on the Omnitron Proposal Uc66) Magnets 32 dipoles at $6k $ 192 k 36 quadrupoles at $4k 144 k 4 sextupoles $8k •VI k L owei" supply dt £ ok^uipult k $ 4k;quad 1 14 k Flat-topping 1 ISO W SHIS k S !> 1 :< k RF Resonator and supply 184 k IS 1 k Vacuum Chamber at $15JiO/m 41.6 k Pumps at S4000/m 1(17.4 S 149 k Mil k Control Jol) k afiii k $1601 k 5% Escalation per annum to 1970 (x 1.275) S 2.D M REFERENCES Be66 H.-D. Betz. G. Hortig, E. Leischne;-. Ch. Ma71 R.M. Main, Nuclear Instruments and MiMhorls Schnelzer, B. Stadler. J. Weihrauch. Phys. 97 (1971) ol. Lett. 22(1966)643. Ni6H V.S. Nikolaev and l.S. Dmilriev. Plus. Lett. B171 M. Blann, Nucl. Instruments and Methods 97 28A (196H) 277. (1971) 1. OrH9 Accelerator for Physics and Ohemistn nf Bo70 D. Bohne and Ch. Schmelzer, Linear Accele- Heavy Elements (APACHEl, A Pmpnsal rators, North Holla-id (1970) p.1047. ORNL 1969. Ca71 A. Cabrespin and M. Lefort, Nuclear Instru- Ph72 Physics Today. 25 (Jan 19721 19. ments and Methods 97 (1971) 29. Ri71 M.E. Rickey and M.B. Sampson. Ntirli'ar Da66 G.T. Danby, J.E. Allinger and J.W, Jackson, Instruments and Methods 97 (19711 lio. BNL unpublished report AADD-115 (1966) Sh71 I.A. Shelaev. E.D. Vorobiev. B.A. Zagi-r. S.I. (BNL-10508). Koslov, V.I. Kuznetsov. R. Tz. Ogancssian. Da67 G.T. Danby, S.T. Lin and J.W. Jackson, IEEE Yu. Tz. Oganessian. K.I. Semin, A.N. Kilip^in Trans, on Nuclear Science NS-14 (1967) 442. and V.A. Chugreev. Nuclear Instruments =• tirl K171 H. Klein, H. Herminghaus, P. Junior. J. Methods 93 (1971) 557. Klabunde, Nuclear Instruments and Methods Uc66 The OMNITRON, Lawrence Radiation Labor- 97 (1971)41. atory Report UCRL-16828 (J%6). Li70 R,S. Livingston, Particle Accelerators 1 (1970) 51. -123- Chapter V. EXPERIMENTAL FACILITIES AND TECHNIQUES 1. INTRODUCTION 2. COMPUTING FACILITIES 3. TARGET-MAKING FACILITIES 4. GAMMA-RAY DETECTION 5. BETA-RAY DETECTION 6. CHARGED PARTICLE DETECTION AND IDENTIFICATION 7. BEAM-PULSING FACILITY 8. ISOTOPE SEPARATOR 9. POLARIZED BEAMS AND TARGETS References 1. INTRODUCTION The study of the diverse topics that have been V-4 to V-6 and provide good examples of necessan described in Chapter II would require a wide variety general-purpose detection equipment. There are many of experimental equipment and techniques. In many modifications, however, that could be envisaged to cases, specialized equipment must be manufactured provide more useful and versatile instruments. The for one particular experiment, but any laboratory use of large volume Ge(Li) detectors rather than Nal planning to undertake such studies should also detectors on the LOTUS should be possible at contain a variety of general-purpose apparatus. The reasonable cost within a few years. A more auu>- complexity of these siudies wuuiu also require maled and iarger-radius scattering chamber could sophisticated equipment for data accumulation and provide more extensive and more accurate dala in a analysis as well as for automatic control of the number of instances. For the very high-energy li^ht accelerator and experiments. ions involved in some of the experiments described in II-7 and 11-9, the magnetic-rigidity capability of ihe This section attempts to describe the types of J equipment that would be necessary to accomplish the QD magnetic spectrometer < E •' 156.3 q" m) would be insufficient and additional equipment would lie objectives of Chapter II. In many cases such equip- required. However, as will be seen below, the existing ment exists, or will shortly exist, in the MP Tandem equipment is well suited to most of the proposed laboratory. These specific examples are described and studies. Although there would need to be additions, a their advantages and limitations are pointed out. laboratory designed specifically to carry out the Sections V-7, V-8 and V-9 describe facilities which do physics program outlined in Chapter II would not presently exist at CRNL, but which would be undoubtedly have to include a substantial investment desirable for the pursuit of a number of future in the types of equipment presently in use intheMP- studies. In these cases the slate-nf-the-art in such Tandem laboratory. devices is described. The topics discussed include detectors for all The last three sections of this chapter (V-7 to V-!ii nuclear radiations: gammas, betas, neutrons and all describe facilities that have recently been considered charged ions. The electronic components associated as additions to the present laboratory. Even with the with such detection equipment are usually available present accelerator, these facilities could increase the commercially today, and so these details have not scope of the experimental program. For experiments been discussed. at the higher beam energies considered in this report, their existence could become crucial. In particular, Computer control of apparatus will be an impor- the beam-pulsing facility would permit unambiguous tant aspect of future experimental techniques and particle identification wiLh the QU' spectrometer for will require extensive interfaces as well as versatile even the heaviest ions. The on-line isotope separator hardware and software in the computer itself. Section becomesvital at higher incident ion mass and enert;\ V-2 describes the system in use at the MP Tandem since the number and variety of nuclei produced laboratory, which combines on-line control abilities increases and the production cross section decreases with ease of programming and considerable reserve as one attempts to study nuclei farther from capacity for detailed data analysis off line. ^-stability. Finally, many of the studies of nucleon- The preparation and handling of targets for accele- nucleon interactions and fundamental symmetries rator experiments, discussed in Section V-3, requires that could be performed with intermediate-energy specialized equipment and techniques. Many future light-ion beams require polari/.ed beams and or studies could require radioactive targets, or produce targets. polentiallv dangerous amounts of radioactive In summary, the efficiency with which a func- material. The organization and equipment avail- tioning program of studies at higher beam energies able at CRNL would be a valuable asset in the could be established would depend upon the exis- safe handling and monitoring of such material. tence of proven experimental equipment and techni- The LOTUS goniometer, brange'and iron-free n\J 2 ques, as well as on the availability of new and (3-spectrometers, Ortec 19" scattering chamber and improved facilities. Both aspects of this prescription QD3 magnetic spectrometer are described in sections for success will be discussed in Ihe following sections -127- 2. COMPUTING FACILITIES scopes (one with light pen), Calcomp plotter, one 7- track '•••" tape unit and six DEC (addressable) A • Introduction magnetic tape units. It is usually programmed in Decal language (a mixed assembler compiler). The experiments oroposed in Chapter II almost all involve multi-parameter data recording and in many The PDP 10 is a fast third-generation computer cases high accuracy and stability is required, thus with 82-thousand words of 36-bit memory (1 jus necessitating extensive monitoring throughout the memory cycle), a very extensive command repertoire experiment. These requirements can only be carried including full hardware floating-point arithmetic, five out effectively by means of a flexible on-line com- typewriter terminals, one alphanumeric display ter- puting system, in addition, subsequent data analysis minal, a 500-thousand word disc, three 7-track tape requires convenient off-line facilities for interaction units, four DEC tape units, a display oscilloscope with with the computer in the inspection and fitting of the keyboard and light pen, a Calcomp plotter, a 128- data. Both on- and off-line facilities must be properly point programmable process scanner, a general- "human engineered" for ease of data handling. purpose interface capable of controlling and receiving The accelerators that have been described in information from a very large number of devices of Chapter IV will also have *i number of sophisticated all types (sealers, kicksorters, detector gain control, control functions requiring computer control. For all magnetic-spectrometer positions and field settings, on-line applications the interfacing of the computer angular-correlation tables, etc.) and 8 fast data to the equipment is a major concern and must be channels, 3 now in use and 5 reserved for future specifically tailored to each particular case. Such on-line interaction. The PDP 10 is programmable in a considerations are as important as the speed of variety of high-level languages such as FORTRAN, operation and ease of programming of the computer ALGOL, BASIC, AID and has a variety of utility itself. programs maintained by the manufacturer for data transfer, program editing and debugging as well as an The wide variety of possible applications of extensive and growing library of locally produced computers in a research laboratory cannot be fully data-manipulation programs. It operates under a fully described in this report. However, the computer time-shared real-time operating system (Monitor) that system currently in use at the Tandem accelerator among many other things gives the privileged user laboratory is an example of an operating system writing in FORTRAN or MACRO (a powerful as- which satisfies the majority of the requirements outlined above. The following section is a detailed sembly language) full access to the 5-level priority description of this system. interrupt system. The PDP-1 computer is used to control and, or B. Detailed Description monitor almost every experiment performed with the Tandem accelerator and has been found to be an At. present the bulk of on-line computing and data extremely reliable and useful instrument. Two accumulation for experiments is performed byaPDP- methods of data accumulation can be used concur- 1 computer which was installed in 1962. For off-line rently: (i) spectra may be accumulated directly into data analysis a PDP-10 time-sharing system (installed 8K of memory at high rates from up to 8 separate late in 1968) is primarily used, together with the analog-to-digital converters (ADC) through a deran- extensive facilities available at the CRNL computing domizing buffer by means of the Fixed Program center, which include a CDC H60U. The use ot the Processor (FPP) facility; (ii) multiparameter related- considerable on-line capabilities of the PDP 10 is address data may be accumulated sequentially from rapidly expanding and the existing data links between an array of up to 9 other ADC's into a buffer area the PDP 10 and the PDP 1 and the all-but-completed assigned by program. Full buffers are written on link to the CDC 6600 will soon be in use to provide magnetic tape, with concurrent selection of data and considerable flexibility in computing activities of all accumulation of spectra in memory for monitoring types. purposes. The program structure of the PDP 1 is The PDP-1 computer has a memory cycle time of designed to allow functions requiring special data 5 /us and a capacity of 24-thousand 18-bit words of accumulation and experimental control to be which typically S thousand arc usi'd for programs and incorporated into standard programs which deal with the resi for data storage. It has iwo display oscillo- aspects common to all experiments: data display. -128- plotting, storage and retrieval on magnetic tape etc. system essential for experiments of the type Instrumentation has been developed for the described in Chapter 11. computer control of a wide variety of experimental equipment such as (i) beam-transport elements, (ii) The possibility of direct interaction with the the angles of detectors, (iii) the gain of electronic computer during off-line data analysis is anoiher equipment, and in some instances, (iv) the energy of extremely attractive feature of the present PDP 10- the accelerator. These control capabilities together PDP 1 system. The use of one or more display with the excellent qualities of the beam-transport oscilloscopes, disc storage and plotter enables multi- parameter data to be re-examined in a variety of system have greatly reduced the difficulties of configurations. The complexity of the proposed obtaining detailed data on excitation functions and experiments would necessitate this approach to data • angular distributions (La72). analysis and the PDP 10 has already proved itself in All of the on-line functions currently performed this capacity. It should become even more useful by the PDP 1 will soon be available directly or when the results of large computation jobs done on indirectly with the PDP 10 to make use of its greater the CDC tifiOOar e readily accessible via the direct link speed, ease of programming, memory size and flexi- between the two computers. bility of peripheral equipment. The additional abilities of the PDP 10 will also permit much more 3. TARGET-MAKING FACILITIES extensive control and monitoring than was possible with the PDP 1. For example, one of the fast data A. Solid Targets channels is presently being used to monitor 128 In many cases the success or failure of nuclear- parameters associated with the accelerator and experi- physics experiments rests upon the quality of avail- mental equipment. If any of these parameters, such as able targets. The preparation of thin, uniform, pure, beam-line vacuum or quadrupole-magnet temperature self-supporting targets from a variety of elements i.s exceeds preset limits, this information is transmitted an art which requires the extensive development of a to a display screen at the accelerator operator's variety of techniques. At CRNL, facilities exist for console. An additional general-purpose interface target preparation, storage and transfer in vacuum or permits interaction with a very large number of in an inert atmosphere. Thin films can be deposited in different experimental devices through 36-bit input vacuum from materials vaporized by resistive heating, and output registers. This interface currently interacts sputtering or electron bombardment. Targets of with 4 sealers (16 more to be added soon) and two radioactive materials can be produced, notably r •''' Pu kicksorters (one more to be added soon). The and other actinides as well as self-supporting foils of monitoring of up to 7 magnetic fields plus precise I4C (Ga71). The extensive facilities that exist at control of up to 10 currents as well as the angular CRNL for handling radioactive and toxic materials setting for the QD3 spectrometer will be done and the associated protective monitoring have been through this interface. essential in this work. Facilities also exist for the Data from the 4096-and 1024-wire focal-plane routine determination of target thickness and unifor- Charpak counters on the QD3 will be handled mity by the measurement of alpha-particle energy through one of two fast scanners, one built, the other loss and for the non-destructive determination of target composition through X-ray fluorescence soon to be constructed. The scanner planned for the measurements. PDP 10 will combine the features of the FPP and fast scanners on the PDP 1 by sending related-address New techniques have been developed in a number (coincidence) data through the 8-channel fast-data of cases (Ga71) such as the preparation of very thin multiplexor to memory. "Singles" events will enter (~50 Mg/cm2 ) self-supporting films of Au. Ag and directly through a special memory port on an other metals by the use of zapon support films which add-one-to-memory (half word) basis. The scanner are later removed. The production of thin flat can handle both modes concurrently. The new stretched foils of a variety or target materials scanner recently completed for the PDP 1 is similar (including in addition to many metals, titanium but cannot handle both modes concurrently. hydride, deuteride and tritidel has enabled a variety The implementation of this and other planned of nuclear lifetimes to be measured by the recoil- on-line facilities will result in an extremely versatile distance method (Ga70). -129- B. Differentially Pumped Gas Target The methods which have been developed for measuring the electromagnetic properties of nuclei A differentially pumped window/less gas target can be directly applied to extended studies using system (Li67, AI72) has allowed high resolution higher-energy heavy ions. In many cases the higher 4 studies of resonance reactions. For ( He, 7) experi- recoil velocities and enhanced cross sections will ments it has been found that the use of heavy-ion permit much greater sens', ivity and higher accuracy 4 beams on a He target results in considerably lower than is presently attainable. A detailed description of background than is attainable for the inverse reaction. these techniques has been presented in Section II-4. The present facility permits the detection of gammas, neutrons or charged particles and would be very 5. BETA-RAY DETECTION useful for the study of heavy-ion reactions on gaseous targets in cases where the energy loss, energy straggle Two magnetic spectrometers are currently in use and background reactions introduced by beam at CRNL for measuring 0-ray and conversion-electron entrance foils would be intolerable, spectra up to energies of ~ 4 MeV. One is the iron-free nsjl (3-spectrometer constructed during 1. GAMMA-RAY DETECTION 1956-58 (Gr60). It is located in a non-magnetic building about 200 metres from the Tandem Labora- The precision gamma-ray detection apparatus tory. It has an optic-circle radius of 1 metre and can presently in use in the Tandem accelerator 'ab be operated at momentum resolution of Ap/p ~ 0.3S7r, includes an array of six 5" x 6" Nal (TV) scintillation to ~ 0.01% with corresponding transmissions in the detectors associated with the LOTUS goniometer, range ~ 60 to ~ 5 millisteradians (0.4% to 0.03% of and a large variety of lithium-drifted germanium An). This instrument is ideally suited to the study of (Ge(Li)) detectors of various sizes and geometries the internal-conversion electron spectra from medium The use of Ge(Li) crystals for gamma ray detection and heavy nuclei. In favourable cases transition was pioneered at, CRNL (see e.g. Ew64) and the energies can be measured with absolute accuracies of Tandem accelerator facility still benefits greatly from ~ 1 in 10s (Mu63, Mu65). From the K to L and L to the work of the Counter Development Section who M etc. energy differences one can deduce the Z of the are actively engaged in the development of solid-state nucleus in which the gamma-ray transition occurs. detectors of many types. For example, a recent The relative intensities of the L-subshell and M- development by this section is a detector in the form subshell lines are often extremely sensitive measures of a long annulus which is being used in one of the transition multipolarity (Ge65a, Gr72). When experiment to achieve nearly 4tr detection geometry operated at a momentum resolution of Ap/p s 0.05% and in another experiment to detect gamma rays with the L lines can be resolved for transition energies up. cylindrical symmetry at 0° and 180°. to ~ 250 keV at Z = 50 and up to ~ 800 keV at Z =-• The LOTUS goniometer is a precision instrument 90 (GrbS). Additional multipolarity information can designed to locate up to six detectors, which may be be deduced by comparing the measured conversion- either Nal(Tt!) or a mixture of NaI(T«) and Ge(Li), at line and gamma-ray intensities, i.e. combining spectro- various positions over a spherical surface surrounding meter data and Ge(Li) gamma-ray data (Gr72). the target. The target chamber can contain a number The n\/2 spectrometer requires "massless" sources of particle detectors for particle-gamma coincidence for optimum performance. The sources normally have studies, and the associated electronics allows multi- dimensions of 2 mm wide by 20 mm high for parameter recording of data to handle all combi- operation at Ap/p = 0.05% and have strengths of ~ nations of multiple-coincidence events. This target 20 to 200 nC This source-strength requirement can location is used, in addition to two other less be met for the more abundantly produced activities complex ones, to perform experiments of the type in heavy-ion reactions, e.g. for partial cross sections of described in Section 11-4. The ability to use an array ^ 0.1 barns with beams of ~ 100 particle nA. The or Nai(Tt!) or Ge(Li) detectors to collect data at many angles simultaneously greatly facilitates the conventional point>by-point mode of spectrometer measurement of gamma-ray angular correlations and operation using a single counter restricts the rate of measurement of nuclear lifetimes by the recoil data acquisition. A sixteen-counter array is being Doppler-shift method or Doppler-shift attenuation developed for this spectrometer in order to improve method. its data collection efficiency, which is low compared to that of a Ge(Li) gamma-ray spectrometer. -130- The second instrument is a seven-gap "orange' 0-ray Gas-filled proportional counters are sometimes spectrometer situated on-line (Ge65b). As currently used in preference to solid state detectors. Although operated it has a momentum resolution of Ap/p a they have poorer energy resolution than solid-state 0.59c and a transmission of ~ 0.4 steradians. It detectors, they are much less sensitive to radiation requires sources having dimensions ^ 1 mm high by < damage by heavy ions and can be made very thin 5 mm wide and strengths ~ 1/10 that needed for the when used as transmission detectors. n\/2 spectrometer. The transmission can be increased to ~ 1.4 steradians with the resolution degraded to The discussion in this section is confined to th;> Ap/'p ~ 2%. This instrument is particularly well suited two most common types of charged-particle detector, the magnetic spectrometer and the solid-siaU> to studying conversion electron spectra in-beam. detector. When used in conjunction with the proposed pulsed- beam facility it will be possible to study delayed B. Solid State Detectors activities with half lives^ Id8 sec. A variety of types of solid-stale chargedparticle 6. CHARGED PARTICLE DETECTION spectrometers are in usu today, some with energy resolution as good as 17.3 keV for 12 MeV protons A. Introduction (Mc68). Usable depletion depths of detectors have The techniques used for the detection and identifi- been gradually increasing over the years and at cation of charged particles may vary considerably present it is possible to obtain detectors for protons r from one experiment to another. The information with energies up to 80 MeV (Ge(Li) detectors with l.» sought may have rigid requirements for any or all of: mm sensitive depth). Very thin surface-barrier detec- (i) good energy resolution, (ii) broad energy range, tors for particle-identification purposes have also (iii) large solid angle, (iv) high count-rate capability, become available, and uniform detectors as thin as h (v) unambiguous particle identification, (vi) high H (± 0.5/J) are available commercially. For detection selectivity in the presence of unwanted background, at 0° and 180°, which is extremely important for (vii) kinematic compensation of dE/dfl, (viii) large, gamma-ray angular-correlation work, annular surface- accurately adjustable angular range including 0° and barrier detectors and detector telescopes are available. 180°, (ix; low sensitivity to radiation damage, (x) Linear and radial position-sensitive detectors are good timing for coincidence measurements. extremely convenient for obtaining detailed angular distributions and for kinematic compensation to 3 The QD (one quadrupole, three dipole magnets) increase energy resolution. magnetic spectrometer about to be installed meets all these requirements (Mi70) and is therefore an ideal All of these detector types have been used in instrument for high - resolution charged - particle experiments with the Tandem accelerator. The small detection. The properties of this spectrometer are size of these detectors has meant that they could be described in Section V-6-C. For many other experi- conveniently included in a variety of relatively small ments, particularly those which require simultaneous target chambers permitting good geometric efficiency detection at many angles, solid-state detectors are for particle-gamma coincidence studies. For experi- generally used. Details of their application to particle ments requiring an array of solid-state detectors, the detection are described in Section V-6-B. Ortec 19"' scattering chamber has proven to he a versatile instrument. This chamber has independently For heavy-ion reactions, charged-particle detection rotatable detector platforms top and bottom, which systems must be capable of providing unambiguous can be reproducibly positioned to ± 0.05°. Targets particle identification. The details of the use of solid •are mounted in an eighUposition turret, with provi- state detectors and the QD3 spectrometer for this sion for the transfer of targets from the targeUmaking purpose are presented in Section V-6-D. laboratory to the scattering chamber under vacuum There are a variety of other types of detectors or inert atmosphere. which are used for special-purpose applications — for This 19" target chamber could be conveniently example, "Makrofoils", or mica can be used to detect used for the majority of experiments described in heavy ions. After exposure the tracks are made visible Chapter II, although in some rases benefits could be by controlled etching through which many particle obtained from a larger, more automated chamber. types can be identified. -131- For example, the 9.5" radius may be too short a meter, consisting of a quadrupole and three dipote flight path to provide particle identification by magnets (see Figure V-6-1) has an energy resolution time-of-flight in some cases. Computer control of AE/E ~ 2 x 10~4, a solid angle of ~ 15 msr, an energy detector position could be used to advantage in range Emax/Emjn 1.5 and a maximum analyzable obtaining detailed angular distributions such as would energy of 156.3 q2 /M MeV. A multi-wire proportional- be required in heavy-ion elastic and inelastic scat- counter system (Charpak counter) (Ch68) is being con- tering experiments. structed which is expected to be able to operate at counting rates up to 107 counts per secoi.^ for each Particle identification through dE/dx measurement wire. Such a counter would be capable of detecting in AE-E counter telescopes will form the basis for very low counting rates even in the presence of high many experiments with a high-energy heavy-ion background in other portions of the focal plane. The accelerator. This technique is discussed in Section pulse from the wires will be read directly to the PDP- V-6-D where it is pointed out that at E = 10 10 computer through one of the fast data channels MeV/amu all isotopes with Z < 22 can be resolved by and it is expected that total count rates of ~ 106 /s presently available telescope systems. The use of can be handled by this system. automated arrays of detector telescopes, or else telescopes with position-sensitive E detectors would The spectrometer can be operated over the angular greatly facilitate the acquisition of angular- range from -20° to +160° and will be usable at 0° by distribution information in heavy-ion reactions. intercepting the transmitted beam at an intermediate focus point before it reaches the focal plane. Opera- For many applications a counter telescope would tion at 180° would be possible through the addition provide sufficient particle identification and energy of a "reflecting" (Koertz) magnet which would allow resolution. For more stringent requirements the QD3 the beam to be incider t on the target without passing magnetic spectrometer could provide belter mass and through the spectrometer. energy resolution as well as rejecting much unwanted background. Provision is also made for the kinematic compen- sation of dE/dd over the large available solid angle. C. QD3 Magnetic Spectrometer This feature will be very valuable in maintaining good energy resolution in heayy-ion reactions with large The high-resolution, broad-range magnetic spectro- dE/d0. meter which is to be installed in the Tandem accelerator laboratory during 1972 could be used to The large solid angle of this instrument will make advantage in the performance of many of the it particularly valuable for use in coincidence with experiments described in Chapter II. This spectro- gamma detectors or other particle detectors. The high 7—7 /' / s TOP a BOTTOM Y0KE3 / / / /-/TUtm THK. TOP a BOTTOM YOKES 5i40cm PUMPING 36 cm TMRr SLOTUCO .TOP » BOTTOM Figure V-6-1 — Schematic plan 8 (6T0P.6B0TT0M) J K //// //**• "I'.'l? view of the QD3 spectrometer ~ I ' I' Sfc\\\' TOPS BOTTOM V/Vtgi'J and a section through a pole edge showing the position of the coils and the clamps. 7 7T r • . •. i -132- resolution attainable with the spectrometer will make MeV. The focal-plane delecting system can be it possible to study in detail the decay processes of tailored to the particle-identification requirements of individual levels. particular experiments (see Section V-6-D), and can One of the main uses of the QD3 in experiments provide unambiguous particle identification lor nil associated with a higher-energy accelerator would be masses at energies of 10 MeV, amu. the detection of heavy ions. The maximum analyz- able energy of 156.3 q2/M MeV will enable it to D- Particle Identification handle the majority of heavy ions produced by the a) Solid-State Counter Telescopes accelerators discussed in Chapter IV; for example, for fully ionized heavy ions the charge state, q, can The rate of energy loss in a thin solid-stale approach Z ~ 1/2 M giving Emax ~ 39.1 MeV/amu. detector can be used to determine part ide typo quite Important advantages of using a magnetic spectro- reliably for light ions. Particle-identification methods meter for detecting heavy ions are the higher count- have been developed (Go64) which parameterize the rate capability resulting from the elimination of data using empirical range-energy relationships which elastically scattered ions which can overload can be simulated by analogue circuitry. In particular, conventional counter telescopes, and resistance to the relation R I range) = aE*1 has been used where a is radiation damage. The first advantage is reduced if characteristic of particle type, and b is nearly the the elastic events are distributed over the focal plane same for all light ions (Z < 6) at energies above 10 as a result of (i) charge changing processes taking MeV. Although this procedure works well in the place over the seven-metre flight path through the region of constant b. it is inadequate for lower spectrometer or (ii) a distribution of charge states for energies, or heavier ions where the range-energy ions leaving the target However, the design aim of relations deviate from this simple relation. 10~7-Torr vacuum in the spectrometer is expected to result in a total charge-changing probability less than In recent experiments at Chalk River (Ba71) a 2 x 1CT5 for all heavy ions at energies of 5 to 10 more detailed method (Hi69) has been used In MeV/amu (Ba72). At high energies (E « 10 achieve better mass resolution for heavier ions. In this MeV/amu) the distribution of charge states leaving method the most accurate available range-energy the target is less of a problem, because a large information is stored in tabular form in the PDP-1 proportion of the ions are fully stripped. At 10 computer and on-line identification is made evenl- MeV/amu all ions with Z < 26 should exist primarily by-event through comparison with this table. Data is in < 3 charge states; for heavier ions (Z > 26) the also accumulated on magnetic tape for subsequent number of prominent charge states increases to « reanalysis on the PDP 10 using range-energy relations 6-10. most appropriate to the various mass regions observed. The multiplicity of charge states and masses The limiting factor in resolving isotopes of a given produced in heavy-ion reactions results in a compli- nuclear charge for heavier ions is the nonunifonnily cated spectrum at the focal plane since all particles of the very thin i\E detectors required by the short with the same value of ME/q2 are focussed to the ranges of the heavier ions. Detailed considerations of same point. Therefore the detection system used to the effects of nonuniformities and energy straggling determine the position on the focal plane must also (Ba72) lead to the conclusion that at 10 MeV amu be capable of providing further information to adjacent isotopes should be resolvable for all ions distinguish between the various particle types. The with Z < 22. use of various types of focal-plane detector in particle However, in this identification technique, ambi- identification is discussed in Section V-6-D. guities still remain between high-mass isotopes of a In summary, the QD3 magnetic spectrometer will given Z and low-mass isotopes of Z + 1. An inspection be a very versatile instrument for use in studies of of the range-energy relations of Northcliffe and heavy-ion transfer reactions, accurate mass and Schilling (No70) reveals that this ambiguity occurs nuclear-structure measurements of nuclei far from between ions differing in mass by about 6 amu. The stability, particle-particle and particle-gamma coinci- measurement of the time of flight between ^K and K dence studies. Coulomb excitation and high- detectors has been used successfully (PoMI to resolve resolution light-ion spectroscopic and fundamental- this ambiguity. With the flight paths available in the interaction studies below energies of 156.3 q2 ,'M Ortec scattering chamber, assuming that a time -133- resolution of 200 ps could be attained, it should be improvement can be obtained by reduction in solid possible to resolve all ambiguities for masses M < 60 angle. Another method would be a two-counter at energies of 10 MeV/amu. focal-plane detection system to determine the angle of incidence, thus enabling the actual path length to For ions with Z > 22, or for lighter ions with be calculated (Mi70). energies < 10 MeV,amu. it may no longer be possible to resolve one mass unit by means of the AE-E A variety of focal-plane detection systems could be measurement. (It should be noted however, that at 10 used, each having certain advantages and limitations MeV/amu the counter-telescope system is capable of for particle identification. The multi-wire propor- defining the nuclear charge Z for even the most tional counter system presently being constructed massive ions.) In these cases the time-of-flight system will be very well suited for high-resolution studies, must be able to resolve one mass unit, and longer particularly with lighter ions. Large counting rates flight paths are generally required. The solid angles can be tolerated in one section of the focal plane with involved then become very small and particle identi- no effect on other regions of interest. This system fication with the QDJ magnetic spectrometer is a may present problems in the extraction of useful more efficient method. pulse-height information, particularly because of large energy straggling in the thin active region necessary for good position information. However, an appro- b) QD3 Magnetic Spectrometer priate proportional-counter system could be used (see for example Ha72a) followed by a detector capable of The QD3 magnetic spectrometer can also be used accurate energy information to identify particle type to provide particle identification for the study of from range-energy relations (see Section V-6-D-a). A heavy-ion reactions. All particles with the same value counter telescope with good total energy resolution of ME/q2 (where M, E and q are the mass, energy and (6E/E < 0.01) in the focal plane of the spectrometer ionic charge, respectively) are focussed to the same need only be capable of resolving isotopes differing by point on the focal plane and so the detection system four mass units to remove all ambiguities. The accurate must be capable of providing further information to 2 distinguish between the various particle types. knowledge of E and position defines q /M, and the nearest ambiguities in this quantity occur for AM = 4. For example, an accurate determination of the Mass determination by time-of-flight measurement energy E of particles at the focal plane, as well as would then only be required when the counter 2 their position, determines the quantity q /M (E = telescope could no longer resolve AM = 4. For a 2 const x q /M). However, ambiguities still exist and telescope composed of two solid-state detectors, some additional parameter must be measured to counter nonuniformity is the main limitation. resolve them. The measurement of the time of flight However, for E = 10 MeV/amu such a system can through the spectrometer determines Mq (t = const x resolve AM = 4 for all ions up to Z = 45 (Ba72). For a M/q) which then defines M and q. The only remaining transmission proportional counter backed by an array ambiguities are isobars with the same q such as of solid-state detectors, which could cover a much J :o Ne' and Na' larger region of the focal plane, the limitation would When the magnet is used for coincidence studies, be energy straggling and energy resolution in the the time of flight may be easily determined from the proportional counter. Energy resolution as good as time relationship with the other detected particle. 3% might be obtained which would resolve AM = 4 For singles experiments the time of flight could be for all ions up to Z = 30 (Ba72). most easily determined by pulsing the beam in bursts For the heaviest, most energetic ions, the best of a few nanoseconds every few hundred nano- identification method would be a counter telescope seconds. Such a pulsing system is described in Section in the focal plane to define nuclear charge Z, and V-7. measurement of time of flight to define the mass. In The main limitation in time resolution attainable this way the QD3 could be used for the unambiguous with the QD3 is the variation in path length for identification of 10-MeV/amu uranium ions, with an various trajectories. For the full angular acceptance available solid angle of ~ 0.2 msr. The long flight (15 msr) the trajectory can vary by one.metre about a paths required for time-of-flight measurements mean path length of 7 metres. The resolution is without the spectrometer (see Section V-6-D-a) directly proportional to the solid angle used so that would result in solid angles more than a factor of 10 -134- smaller than this. determined through independent measurements nf In summary, the QDJ spectrometer possesses the dependence of q on 'L and velocity. many desirable qualities for particle identification, The pulsing of the beam on this time scale will also including the reduction of unwanted background. A permit neutrons and gamma rays to be distinguished variety of focal-plane detection systems are suitable through their time of flight from the target to Hie for various mass regions, extending up to the heaviest detectors. For experiments attempting to observe low ions at the highest energies discussed in Chapter II. gamma counting rates in the presence of neutrons or general room background the ability to count gamma 7. BEAM PULSING FACILITY rays only during the short time that the beam is on There are many experimental techniques which the target can greatly enhance the peak to hai-k would benefit greatly from the availability of a ground ratio. repetitive time structure in the incident beam, capable The determination of neutron energy through time- of bursts as short as one nanosecond at intervals of-flight measurements permits nuclear speclrosrupy of a few hundred nanoseconds. to be performed in many otherwise inaccessible cast's. For a Tandem accelerator, this beam structure can Since time-of-flight spectroscopy provides the only be imposed by means of a radio-frequency bunching accurate means of determining neutron energy, reac- and chopping system located at the low-energy end of tions with neutrons in the final state can only be the accelerator. Such a system has been proposed for studied in a very restricted manner in the absence of a installation on the present Tandem accelerator pulsed beam. (Ha72b) and its desirable properties could be super- The measurement of the lifetimes of nuclear slali-s imposed on the beam structure of any higher-energy in the region T> 10~* sec through electronic timing accelerator which used the Tandem as an injector. would benefit greatly from the availability of apulsed- The uses of such a beam structure are extensive, as beam facility. The knowledge of beam arrival lime it would permit definitive particle identification, fast would permit the direct measurement of the lifetimes neutron time-of-flight measurements, measurement of of levels populated in reactions, doing away with the lifetimes of gamma-ray and fission isomers and usual requirement of coincidence with a particle or determination of electric and magnetic static mo- gamma populating the level. This technique would ments of nuclear energy levels. have applicability both for studies of gamma-emitting isomeric states, and for fission isomers which have The use of time-of-flight measurements for particle created considerable current interest (see Section identification has been discussed in some detail in the II-3-D). previous section. It is expected that the proposed beam-pulsing system could provide time spreads as Another very important use of the pulsed-beam low as 2 to 3 nanoseconds for heavy ions, particularly system would be in the measurement of magnetic- if the system includes a post-accelerator chopper. dipole and electric-quadrupole moments of excited Resolution of this order would be sufficient for use states through their interaction with homogeneous with the QD3 spectrometer, where the main limi- magnetic fields and with electric-field gradients, tation in mass resolution will be due to variations in respectively. These measurements would involve path length through the spectrometer. observations of perturbed angular correlations or the use of nuclear magnetic resonance (Qu69) and For time-of-flight measurements with AE-E tele- stroboscopic methods (Ch70) which have been demon- scopes, better time resolution than this should be strated to give very high accuracy (< 0.5%). Measuri1- obtainable by extracting timing signals from both AE ment techniques may be applied to levels with and E detectors. However, for heavy ions whose lifetimes (T) varying from ~ 10"8 sec to 10 * sec. energy is too low to allow them to pass through the thinnest available AE detectors, then the only avail- For T < lCT'1 sec, recoiling nuclei mav he able mass identification is through the u=e of the implanted in metallic diamagnetic cubic lattices for pulsed beam. By using an electrostatic deflector which the nuclear relaxation time is about 2.5 x 10"*1 between the target and a position-sensitive detector sec at 20°C. For lifetimes in the region 10"* to 10* the average charge state q could also be determined. sec, longer relaxation times can be obtained with Provision for such a deflector exists in the QD1 liquid targets such as gallium and mercury (Qu(i9, spectrometer. The nuclear charge Z could then be Ch70). -135- These techniques for lifetimes T> 10* sec will be sec but preferably < 100 ms| and efficient. The ion complementary to those described in Section II-4-D source must also be efficient, and the separator which are applicable for much shorter lifetimes. should have a resolution of at least 2000 with a dispersion at mass 300 of ^ 5 mm. The ion source 8. ISOTOPE SEPARATOR ON LINE (ISOL) and separator conditions can be met by commercially One of the most important uses of a high-energy available units—the "high-temperature, hollow- heavy-ion beam will be in the production of nuclei cathode ion source, model 911" and the "isotope which are far from the region of /3-stability. Study of separator, model 9000", both sold by Danfysik. An these nuclei and their decay will frequently depend adequate transport system appears technically upon the extent to which the desired activity can be feasible but must be designed and built here. isolated from competing radiation. To some extent If a constant flow of helium gas is established from the production technique itself can provide selectivity a small-volume target chamber through a capillary- (see Sections II-l and II-4), and in certain cases tube to the ion source, then the recoil nuclei can be through a judicious choice of target, projectile and transported at the sonic velocity of helium, in ur - 136 — hydrogen-isotope work has been the subject of several being made to produce a polarized 'He beam by reviews (G169, Ha67: Da65). Both negative-ion and extraction of polarized ions produced by a weak r.f. positive-ion beams have been produced for accele- discharge in an optically pumped 'He cell (BaliS). ration in Tandem or other accelerators. Polarized The authors report an extracted beam of 3-4 niA of proton or deuteron beams have been produced by 3He+ with a measured polarization of about 5'>. This state selection of an atomic beam in a Stern-Gerlach was equal to the polarization of the 3He gas in the apparatus followed by suitable r.f. transitions and pumping cell which was determined by optical means. ionziation (C163) or by the Zavoiskii-Lamb method Another approach to 3He polarized beams is the use (Za57). The latter, which appears particularly suited of an atomic beam with magnetic state selection, hi to producing negative beams, achieves the state this case, because only the small nuclpar moment is separation by working with the 2S^2 metastable available, the atomic-beam source must be cooled to state of hydrogen. The metastable atoms are the liquid-He temperature region. The results of produced by the passage of a proton beam through Cs experiments with the low-lemperalure source have vapour. The beam passes through a suitable static been presented in the literature (Vy70). magnetic field which produces a level crossing (degeneracy) between the short lived 2P j m "levels and TABLIC V-9-I the lower two 2S]/2 levels. The mixing is produced by a weak static electric field. The negative ions are Ion M, P3(ma\) P33(m.x, i' Fr;i produced selectively from the metastable polarized atoms as they pass through argon gas. Impressive H" •., 1.0 - s»; ;MI performance figures for proton and deuteron beams H" '•! -0.12 !..!. have recently been reported for such an ion source by D + \ 1.0 1.0 7 1 Ml the Los Alamos Group (I,a69, Mc70). The authors iy 0 0.012 •l.iiHH 7 i Ml . report a maximum current on target of 107 nA for n 1 -0.1181 7 1 stv : protons and 208 nA for deuterons after passage through a Tandem accelerator. Table V-9-I presents In summary, it is clear that copious positive and the maximum polarization available for proton and negative beams of protons and deulerons can be deuteron beams as a function of the choice of nuclear produced and practical sources of polarized "" He and magnetic substate with largest population. The popu- " Li are in the offing. lation of the chosen magnetic substate is maximized Most polarized targets, with the exception of by inducing appropriate radio-frequency transitions optically pumped gaseous 3He targets (Ba69), in- following the level-crossing depletion of the two volve the use of temperatures in the 1°K region or lower 2Sij2 substates (Ha67). The vector polari- lower. Because of this low-temperature operation, zation, (N+ - N_), is denoted by P3 and the tensor heat input from the beam and the coupling of the polarization, (1 - 3NO), by P3J. N+ are the nor- cryostat to the beam-transport system present com- malized populations of the Mj = ± 1/2 and ± 1 states plicated experimental problems. Good results are for protons and deuterons respectively. No is the being obtained for polarized-proton and -deuteron normalized population of the Mj = 0 substate for the targets by dynamic orientation of the hydrogenU: deuterons. For protons, spin-1/2 particles, only P3 is protons in alcohols doped with free radicals. Burghini required to de-excite the state of polarization of the and Scheffler (Bo71) at CERN have.recently pub- beam; whereas for deuterons, spin-1 particles, both lished results for proton and deuteron polarizations at P.i and P3 3 are necessary. The actual polarizations are 25 kilogauss and temperatures of 0.5 to 1 K. They reduced by the quenchable fractions, also given in the used targets of 1-butanol and perdeuterated Table V-9-I. This factor is the fraction of the negative 1-butanol doped with porphyrexide t« achieve deu- ions in the beam produced by ionization of the teron polarizations of 22rS and proton polarizations metastable state as opposed to the ground state. of 70 to 80%. It is known that such targe is A 1-2 uA tensor polarized beam of 6 Li positive deteriorate as a result of radiation damage so that the ions has recently been reported (Ho70). The authors polarized material has to be changed on roughly a used an atomic-beam magnetic-state selection method daily basis. and produced the positive ions with surface ioni- Significant degrees of nuclear polarization and zation on a hot tungsten electrode. Attempts arr- alignment in many elements can be produced hy the -137- thermal equilibrium method using temperatures of scattering on polarized Ho (Uh71). A polarized 20-100 m°K and the large hyperfine fields which 59Co target has also been built using a '1He-4He occur in ferromagnetic materials (Sh66). 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Ferguson and J.S. Fraser, Atomic Energy of Canada Limited Report, AECL-3563 (1970). -139- Additional copies of this document may be obtained from Scientific Document Distribution Office Atomic Energy of Canada Limited Chalk River, Ontario, Canada KOJ 1J0 Price -$2.50 per copy 2059-73