OQNF-9203164—1 DE92 016800
EXOTIC NUCLEAR SHAPES AND CONFIGURATIONS THAT CAN BE STUDIED AT HIGH SPIN USING RADIOACTIVE ION BEAMS
J. D. Garrett Physics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6371, USA
ABSTRACT
The variety of new research possibilities afforded by the culmination of the two frontier areas of nuclear structure: high spin and studies far from nuclear stability (utilizing intense radioactive ion beams) are discussed. Topics presented include: new regions of exotic nuclear shape (e.g. superdeformation, hyperdeformation, and reflection-asymmetric shapes); the population of and consequences of populating exotic nuclear configurations; and complete spectroscopy (i.e. the overlap of state of the art low- and high-spin studies in the same nucleus). Likewise, the various beams needed for proton- and neutron-rich high spin studies also are discussed.
DISCLAIMER
This report was prepared as an account of work sponsored by an agency of the United Slates Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, rccom- mendaiiun, or favoring by the United Stales Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily slate or reflect those of the United Stiles Government or any agency thereof.
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Probably today's two most exciting frontiers of nuclear structure are rapidly-rotating nuclei and nuclei far from stability. The current renaissance in both frontier areas is based on recent technical innovations: to wit, the advent of large Complon-suppressed germanium detector arrays (e,g. EUROGAM and GAMMASPHERE) based on the ability to grow large crystals of high-purity germanium'1, and new breakthroughs in producing and accelerating high-intensity beams of radioactive ions, the subject of the last day of this workshop. Therefore, it is imperative at such a gathering as this to consider the culmination of these two initiatives, high- spin research possibilities afforded by intense beams of radioactive ions.
The large angular momentum imparted to the residues of heavy-ion induced fusion-evaporation
reactions produces two major nuclear structure effects: (i) a stabilization of highly-deformed
nuclear shapes; and (ii) a major rearrangement of the nuclear single-particle states generated by
the Coriolis and centrifugal forces acting on the nucleons due to the rotation of the nucleus.
The increased stability of superdeformed nuclei, well known from microscopic calculations
2 3 (see e.g. - !), can be illustrated by plots of Ex(i) for the yrast states (i.e. the state of lowest energy for each angular momentum) of different deformations, see Figure 1. Though the rotational sequence based on the superdeformed intrinsic slate at low angular momentum occurs at a high excitation energy, it becomes the lowest decay sequence at the largest angular momentum. The superdeformed nucleus has a larger moment of inertia, hence a smaller slope on the EX(I) plot.
The modification of the single-particle spectrum of states by rotation is illustrated in Figure 2.
The Coriolis plus centrifugal term in the single-nucleon hamiltonian'°l (= -co ji. where a) is the angular frequency of rotation, and j] is the component of the intrinsic nucleonic angular momentum along the rotational axis) can produce perturbations as large as those resulting from nuclear deformation. Such rotationally-induced single-particle effects are the bases of a variety of high-spin phenomena as diverse as "backbending" (band crossings)1 '«l2l, loss of pair t 30-
> /
20- jf/ B if/ C Superdeformed c o band r S /' Low deformation , />' band 4, ^^l fl) it a 10- ,A" sp\ o X M UJ ^* ^—^ *Oblate states
0- *~™ -r~—: 1 0 10 20 30 40 50 60 Spin(ti)
152 Figure 1. Plot of EX(I) for yrast states of Dy (refs. 4,5) corresponding to shell-mode!, normally-deformed, and superdeformed configurations. This figure is taken from ref. 6 which is an adaptation of a similar figure in ref. 5.
14 9 correlations'3. ), ,ne nuciear shrinking paradox !, and an enhancement of residual interactions'5! based on an increased overlap of nucleonic states9-16'.
Radioactive ion beams will provide experimental access to a variety of even more exotic shapes and combinations of single-particle orbitals in nuclei far from stability. Some examples are described in Sections 2 and 3, respectively. Likewise, the possibility and consequences of comprehensive high spin studies of nuclei, whose low angular momentum properties also are well known, are discussed in Section 4. Whereas the neutron-rich portion of this research will require large ISOL facilities, for example, the proposed IsoSpin Laboratory30), nearly all of the proton-rich studies also can be made using "first generation" facilities, such as the Oak Ridge RIB Facility3U. DEFORMED
Jg3v
odd
Figure 2. Comparison of the spectra of single-particle states from spherical, deformed, and rotating deformed nuclear potentials taken from refs. 7,8 and 9, respectively (see also figures 7 and 9). Because of the greater complexity of the single-particle states with increasingly- complex approximations to the nuclear potentials, only the subset of states indicated in the figure is shown for the deformed and rotational cases. 2. Kxotic Nuclear Shapes Accessible with Radioactive Ion Beams
The observations of high-spin superdeformed stales (2:1 ratio of the major to minor axes) in A = 150 and 190 nuclei (refs. 5,17 and 18.19, respectively) and deformations intermediate between normal and superdeformed in A = 130 and 186 (refs. 17,20 and 21, respectively) have focused an intense interest on highly-deformed nuclear shapes. Such states correspond to secondary minima in the nuclear potential energy at large deformations resulting from major gaps in the single-particle levels22^*]. This striking illustration of the interpluy of single-particle
CO 0 1
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Figure 3. Predicted shell-energy corrections for a 2:1 ratio of the major to minor axes (i.e. prolate superdeformed nuclei) as a function of particle number and rotational frequency, to, for protons (top) and neutrons (bottom). Note that the proton calculations28' predate the discovery of high-spin superdeformed states. Though similar calculations for neutrons also exist predating high-spin superdeformed states, see e.g.28', later calculations6' are shown because of the availability of u superior figure. and collective degrees of freedom was developed-*! 10 describe isomerie fission of actinide nuclei25 26l Already in 1968 it was realized that such secondary minima should also exist in lighter nuclei; indeed the proton and neutron numbers of the occurrence of such shell corrections were predicted27!. However, it wasn't until 1986 that the technique of populating superdeformed minima at high spin and observing the gamma-ray cascade based on the rotating superdeformed intrinsic stale succeeded5' in establishing additional superdeformed states at high spin.
Figure 3 shows calculations6'28' of the proton and neutron shell energy as a function of Z and
N respectfully, and of the rotational frequency. The high-spin superdefonned states near A =
150 and 190 and the actinide fission isomers all occur at or near predicted minima in both the
proton and neutron shell energy, see Figure 4. Other regions of the table of isotopes where the
proton and neutron shell energies arc predicted to act coherently to produce additional minima
in the potential energy at superdeformed deformations, also are indicated in this figure, as are
the projected "new" nuclei •hat can be studied29' using the radioactive ion beams planned for
the isoSptn Laboratory^'. Though a large number cf "new" neutron-rich nuclides become
accessible to study with radioactive beams, these cannot be populated by heavy-ion fusion-
evaporation reactions, the traditional technique for studying high-spin superdeformed states17).
Therefore, new techniques are necessary to populate high-spin superdeformed states to the
right of the valley of beta stable nuclei. For example. Coulomb excitation of neutron-rich
radioactive beams can provide some high spin information, but this process has a vanishingly-
smalt probability of populating superdefonned states. On the other hand, Coulomb excitation
plus few-particle transfer may offer some chance of studying superdeformation in these
neutron-rich nuclei; however, the associated cross sections also are small at very high spin32'.
So far, the probability of populating superdeformed states has not been demonstrated by these
mechanisms.
Indeed, the known A = 150 and 190 high-spin superdeformed nuclei"-19! are on the proton- rich side of stable nuclei, see Figure 4. Although some of the best candidates33,34) of (j,e jjghj NWtt UN ftltVCIIfSa i P.M *NB
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Figure 4. Comparison of regions of nuclei in which the proton and neutron shell energy corrections act coherently at high spins producing stable prolate superdeformed shapes and the "new" nuclei which can be produced with high intensity radioactive ion beams. The proton and neutron numbers of the minimum shell energy corrections arc taken from Figure 3 at« = 0. Itoo = 4. I/A"•*, and the regions of overlapping proton and neutron shell energy minima are indicated by diagonal shading. The lower Z boundary of the heaviest regions has been decreased to include Hg, Tl, and Pb, since superdeformed states have been identified for isotopes of these elements'9'. The predicted "new" nuclei that can be studied with radioactive ion beams, but which cannot be studied with stable beams and stable targets are estimated29) using the projected beams of the isoSpin Laboratory^!. Smaller "first generation" facilities, such as the Oak Ridge RIB Facility31! could produce most of the proton-rich nuclei indicated with Z £ 82, see ref. 29. superdeformed nuclei, Z - 33-35 and 38-42 and N *= 29-47 are accessible with stable beams and targets and have been investigated, no discrete transitions attributed to superdeformed states have been observed35!. This lack of success may be the result of the large Doppler shift and low photopsak efficiency associated with the high-energy gamma-ray transitions between supenieformed states of light nuclei (due to the smaller moment of inertia). It also may be that the nuclei with the most stable supenMormed minimum at the lowest excitation energy (i.e. the best candidates for superdefonnation) in this mass region are too proton-rich to be populated with stable beams and targets36!.
Two unstudied proton-rich regions of superdeformation that should become accessible to
experiments with radioactive ion beams are indicated by Figure 4. These are the light (N = 63-
67) isotopes of Gd - Tm nuclei (Z = 64-69) and the light (N = 86-92) isotopes of Hg - Np (Z =
80-93). The lower Z boundary of the heavy region has been decreased relative to the predictions shown in Figure 3 to include the mercury, thallium, and lead isotopes, since superdeformed states have been identified for the heavier isotopes of these elements1^'.
Indeed, the proton and neutron numbers for the very proton-rich mercury - lead nuclei suggested to be superdeformed are the combination of the proton number of the known superdeformed mercury - lead nuclei and the neutron number of the known superdefonncd europium - dysprosium nuclei. However, the larger ratio of protons to neutrons will lead to increased fission especially at high angular momentum for these very proton-rich heavy nuclei.
Thus, the lighter region of veiy proton-rich Gd - Tm (Z = 64-69) isotopes perhaps is the favored new rejon for superdefonnation studies with proton-rich radioactive ion beams.
The preceding discussion of possible new regions of superdeformation accessible to radioactive ion beams is primitive; such a discussion could have been given nearly a quarter century ago27l The complete potential energy surface, minimized with respect to a variety of deformations, must be calculated systematically for the new nuclei that can be popuk'ed at high spin using radioactive ion beams. The first results of a systematic program of such state-of- the-art calculations for the mercury isotopes37' are shown in Figures 5 and 6. Indeed, these 0? 0 0 04 on o« to i?o? PO o? a* o 6 QH IO
Figure 5, Calculated zero rotational frequency potential energy surfaces*7' for l7<)Hg<)o, l8t'llglD(), l
MASS 170 180 190 200 1 , . , . —T—i—r 1 • • ' 1 .. f . , r i | • .
10 - Hg - ^=0.8. |i3=0 | 2 p2=0.8,P3=0.15 5 - — z 5
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P2=0.25. P3=0 > . I . i i i + * T 7 i i 1 , 1 , • 90 100 110 120 NEUTRON NUMBER
Figure 6. Calculated excitation energies of selected secondary minima in the poteniial energy surface for mercury isotopes37'. The approximate P2 and P3 values are given for each set of minima, and the complete potential energy surfaces for 170,lSo.l90,2CX)j.|g are snown jn flg 5 •% •01 00 01 0.1 03 04 -0 2 -€1 0 0
Figure 7. Plot of predicted single-proton (left) and single-neutron (right) energies for Nilsson configurations as a function of the quadrupole deformation (P2)- These single-particle levels, calculated using Woods-Saxon potential39' and assuming P4 = y = 0, are taken from ref. 41. calculations correctly predict the minima associated with the known low-lying normally- detbrmed prolate states (P2 = 0.25) in 180-190^ (ref 33) an(j tne known superdeformed states19' in 189-l94j-jg (P2 « 0.47) that coexist with the oblate ground-state configuration.
These superdeformed stales, predicted to occur at an excitation energy of between 3 and 4 McV for l88,l90[-ig in tne absence of rotation (co = 0), should become yrast at I = 30-40. An unobserved high-lying hyperdeformed (3:1 ratio of the major to minor axis) configuration (p2
= 0.8, P3 = 0) also is predicted for !88,l90Hg Another superdeformed configuration ($2 =
0.56, (J3 = 0, but "soft" with respect to the refiection-assymetric, P3, degree of freedom, see the calculation for 170Hg in Figure 5) is predicted to occur quite low in excitation energy for some of the light mercury isotopes that are on the verge of experimental study at high spin with stable beams and targets and which should be easily accessible with radioactive beams. This superdelormed configuration can be associated with the shell corrections shown in Figures 3 and 4, and described in the preceding paragraphs of (his section. Likewise, a hyperdeformed (|i2 ~ 0.8, P3 ra 0.15) configuration is predicted at an ever lower excitation energy for
178-I84j jg man for ^g |ieavicr mercury isotopes, see Figure 6.
Both the superdeformed and hyperdeformed minima predicted for the lightest mercury isotopes, see the calculations for 170Hg and 180Hg shown in Figure 5, are "soft" with respect to the octupole degree of freedom. This "softness" can probably be attributed to the occurrence of both proton and neutron 1 i ] 3/2 — 2^7/2 A/ = 3 pairs near the Fermi level for these lightest mercury isotopes at large deformation, see Figure 7. The lowest fission barrier of these nuclei
is associated with a large octupnle deformation. lndeed: the predicted decrease in the fission barrier associated with the octupole degree of freedom could lead to isomeric fission for the light mercury isotopes!
3. Hxotic Nuclear Configurations Accessible with Radioactive Beams
The major rearrangement of the spectrum of single-particle stales associated both with a prolate
quadnipole deformation of the mean nuclear field (most deformed nuclei are prolate) and with
nuclear rotation (see Figure 2) have a common feature. Both favor (i.e. decrease the energy of) the high-j, low-ft configurations, (il, the projection of j on the nuclear symmetry axis, = 1/2,
3/2,..., j.) These are the states whose wave functions are most highly localized. The spacial localization of the high-j Nilsson states is a result of the quantization of axially-deformed nuclei
(nonrotating) with respect to Q. Plots of the probability distribution of wave functions as a function of the intrinsic angular momentum and the angles of the orbital median plane, shown in Figure 8, help to demonstrate the concept of quanial localization. The localization is enhanced for large j, since a large number of states (reflecting the large number of ii values) must be accommodated in the same phase space, i.e. angular range. Likewise, for a specific j the localization is further enhanced for small values of Q, see refs. (9,30). CXD Pigure 8, Pedagogical depiction of the concept of quantul / varying localization. (Top) Probability fflo( distributions relative to the potar axis for the m~i component as a function of the orbital angular momentum (t) and for the / = 3 <* 3, (Ds *3 / » 4, m » tA tstata g stnto (f state) as a function of the magnetic quanutm number (m) Adapted from ref. 40; see also refs. 9 and 30. (Bottom) Semiclassical depiction of the median angles of the orbital planes for different Q states of a Ik 17/2 orbit in a deformed <• = 3 (t state) nucleus. Note the extreme m varying localization for the lowest li, <*3, 3. m»i3 equatorial orbits. Adapted from ref. 30.
I « 3, m - 0
In a rotating system the Coriolis interaction destroys13' the nudear pair correlations by
decreasing the energy of the state corresponding to the highly-localized, Iow-12 components of
the wave function that orbit the nucleus in the direction of the nuclear rotation and increasing
the energy of those orbiting in the opposite direction, see Figure 9. Indeed, this interaction not only enhances the spatial localizaion, but in the limiting case it also restricts the valence nucleons (i.e. those of non-filled shells) to equatorial orbitals in the direction of nuclear No Rol, Large Rot. •• • "•' \ i -r
-13/2
+ '*§/$,
WWBIIIH 9/2 "1/2" i/sr 5/2
*""""--" "~-->-~_
4 -' 5/2-
- 9/2
13/2
,-....-, L-^,^. ^^.L L. M_
Figaro 9. Calculated spectrum of single-panicle states for a single-j shell in a rotating axially- deformed nucleus (£2 - 0.25) in the absence of pair correlations. Solid and dashed curves correspond to starts of signature (a) 1/2 and -1/2. respectively. Though the details of the calculation correspond to 113/2 neutrons, this spectrum of states is typical of any high-j shell. Values of
rotation, see Figure 10. The large overlap of such orbits is a necessary, though not sufficient, condition for new types of roiationally-induced correlations9!-
Such quanta] localization effects (which will produce, e.g. coexisting nuclear shapes, large residual interactions9'15'16], and perhaps even new types of nuclear correlations9!) become increasingly important for heavy nuclei, where many of the intrinsic (i.e. shell-model) configurations occupied have large angular momentum, j, see e.g. Figures 2 and 7. Even larger enhancements are expected in regions where the Jow-ii states of the nuclear wave functions and/or the same neutron and proton configurations are selectively occupied. Indeed, Figure 10. Idealized figure depicting the valence nucleunic motion in a very rapidly-rotating deformed nucleus.
all these conditions are met for the "new" proton-rich isotopes of xenon - neodymium (Z = N =
54 - 60) which can be studied with proton-rich radioactive beams, see Figure 4 and ref. 29.
Even more dramatic examples of quantal localization perhaps can be studied in the "new" very
proion-rich isotopes of platinum to lead41! (Z = 78 - 82). For the prolate deformations,
associated with the occupation of down-sloping orbitals on the Nilsson diagram, (he low-Q
components of the intruding i 13/2. "9/2. and f7/2 proton orbitals have nearly maximal overlap
with each other and even more importantly with the same neutron orbitals which are occupied just above the N = 82 neutron shell, see Figure 7.
4. Complete Spectroscopy - Overlapping High- and Low-Spin Data in the Same Nucleus
A dream of nuclear structure physicists (see e.g. refs. [ 10 and 42]) since the advent of heavy- ion beams — obtaining state of the art low- and high-spin data in the same nucleus - can be realized for tne first time utilizing beams of heavy neutron-rich radioactive nuclei. The combination of the increased neutron excess in heavy stable nuclei (to counteract the repulsive
Coulomb interaction), the emission of neutrons from highiy-excited nearly-stable and neutron- rich compound nuclei, and the necessity of heavy ions for imparting angular momentum to the system (in heavy-ion induced fusion evaporation reactions), has confined previous high spin studies to proton-rich nuclei. For example, nuclei such as I68Erioo. which are studied4^.44] in great detail at low spin in (n,y) studies and transfer reactions (see the level scheme shown in K-3',4' 5"3\4'4J' 3' 6, X JL £. T'€3'"7 — '-£~~ ' JL -£l — 6" ™ ^ - 8' 1 ill
5 6- — 3; I
s* T °* 168 6Bcr100 -81 T
Figure 11. l^evel scheme for J68Rr, the best studied erbium JL isotope at low spin. The data was taken from refs. 43 and 44.
49 19560 50' 20114 160ctrr 1376 6B 92 1306 48" 16761 47" 16184 48' — 18806 1316 1283 1309 46" 17483 46* — 17525 1264 45 — 16875 1240 44" — 16199 1256 44*- — 16285 1203 43"— — 15619 1187 42" — 14996 1169 42*- — 1509B 1141 41"— — 14430 1135 40" — 13855 1120 1083 40*- — 13963 39"— — 13310 1088 38" — — 12772 1055 38*- — 12875 102E 37"— — 12255 1045 36" — — 11?«8 997 36*- — 11830 974 11258 35"— 34*- 10912 1011 34" — — 10772 948 34*- 965 — 10618 932 33"— 10310 32*- 9947 984 32" — 9840 919 32*- I 9835 Figure 12. 914 31"— I— 9391 904 30" — 8928 906 30*- — !9043 30*- 961 6874 Level scheme for 894 29"— 6485 859> l62 28" — — 8032 675 28*- 6184 26*- 937 Er, the best 7937 848 27"— — 7610 843) 902 studied erbium 26" — 7184 620 26*- 7341 26*- 785 25"— — 6790 826> 7035 isotope at high spin. 24" — 6399 758 24*- 6515 24*- 653 718 — 6033 The data was taken 22" — 23"— BOO) 6182 705 22*- — 5714 22*- 793 from refs. 45 and 46. 20" — —95022 21"— ii53M 739) 5389 20*- 4975 20*- 723 18" — 1^4407 19"— — 4667 — 4666 !? 3834 17"— 4050 641 16" — Isa 18*- .4025 — 3487 14" F&3317 15"— 12" 3? 2877 13"— |25M82 14* 10" 17"—I 12 8" 1 Population of Erbium Nuclei
NEW HIGH SPIN DATA RIBS
NEW NUCLEI RADIOACTIVE BEAMS
(H.l.(2ai6),xn)
170
Figure 13. Comparison of the population of erbium isotopes by a variety of nuclear reactions using both stable and radioactive ion beams (RIBS). The stable erbium isotopes are shown by filled squares, and the best studied cases at both low and high spin are indicated.
Figure 11), cannot be populated at high spin using heavy-ion induced fusion, evaporation reactions with stable beams and targets. For comparison, the level scheme of 16OEr92, the best studied erbium isotope at high spin45'46! is shown in Figure 12. By coincidence, 78 levels are known in both isotopes; however, they are distributed over 4 bands in 160Er and in 20 bands for 168Er.
Figure 13 illustrates the population of erbium isotopes by a variety of reactions utilzing both stable and radioactive ions. All of the stable erbium isotopes can be studied at high, as well as at low spin, using the neutron-rich radioactive beams planned for the IsoSpin Laboratory30^ (and other simitar second-generation ISOL facilities). Likewise, the predicted47) best cases for hyperdefomnation, l66l68Er, also can be populated at high spin with these radioactive beams. uBEAMS 0 BEAMS S & Cl BEAMS Figure 14. (Top) Partial cross section, 0|, us a function of Ca BEAMS angular momentum. 1, for compound nuclei populated in typical fusion reactions with u, oxygen, sulfur, chlorine, and calcium beams. (Bottom) Pedagodical depiction of the population of the near yrasl states after particle and gamma-ray cooling of compound nuclei populated with a variety of angular momenta, such as indicated in the upper portion of the figure. A more complete discussion of the population of high spin states in fusion- evaporations reactions is given in refs. 10 and 54.
Indeed, for complete spectroscopic studies a variety of light-, intermediate-, and heavy-ion induced fusion-evaporation reactions are needed to populate the nucleus with the complete range of angular momenta, see Figure 14. The measurement of gamma-ray multiplicities and the total gamma-ray cascade energy can alleviate the use of some of the measurements with intermediate-mass ions (see e.g. ref. 10); however, then the energy of the incident beam must be varied to populate the evaporation residue of interest with the full range of angular momenta.
Of course, this nucleus also must be studied at low spin with (n,y), (e,e'), and transfer reactions and Coulomb excited.
Besides the obvious use of "complete spectroscopic studies" for more stringent tests of nuclear models, several other interesting nuclear structure questions can be addressed by "complete" data. For example, statistical analyses of level spacing distributions (see Figure 15), often associated with the order or chaos of the nuclear system48-5 ll, can be studied as a function of angular momentum50). Likewise, detailed studies of strongly-correlated nuclear states, such as the y-, P-, and octapole-vibrations, at larger angular momentum, will be greatly facilitated by the use of radioactive ion beams 10 overlap low- and high-spin studies in the same nucleus. Such dnia cun provide information on the spin dependence of the microscopic basis of such correlations, see e.g. refs, 142,521.
12 S/d • NORMALIZED LEVEL SPACING
Figure 15. Comparison of experimental level-spacing distributions (histograms) for nuclear states with identical spins and parities (top) at the neutron and proton threshold48', (middle) 116 49 levels of Sn below Ex = 4.4 MeV l, and (bottom) a variety of "cold" deformed rare-earth nuclei50'. Curves corresponding to Poisson and Wigner distributions (often associated with "ordered" and "chaotic" behavior, respectively48'51') are shown for comparison with each distribution of experimental level spactngs. The inset indicates the excitation energy and angular momentum ranges associated with each data set. Although the ensemble of nuclear levels considered for the various distributions is very different, a progression from "ordered" to "chaotic" behavior seems to occur with increasing excitation energy. Adapted from refs. 30 and SO. 5. Beams for Proton and Neutron-rich Studies in Rapidly-rotating Nuclei
The present forum seems most appropriate for discussing the radioactive beams needed for high-spin studies. The traditional technique for populating nuclei with the maximum allowed angular momentum is heavy-ion-induced fusion-evaporation reactions using projectiles of A = 30-50, see e.g. refs. 10 and 54. Lighter projectiles do not impart the maximum angular momentum to the fused system; the highest spin partial waves mostly produce "massive transfer" reactions-'*4!. Though heavier projectiles can provide the maximum allowed angular momentum, they apparently also produce a somewhat larger gamma-ray background54-55!.
For radioactive ions the ability to populate proton- or neutron-rich nuclear species also must be
considered. Due to the increased neutron to proton ratio of stable nuclei (available for targets
and beams) with increasing nuclear mass, proton-rich nuclei are produced most efficiently
using targets and beams that arc nearly equal in mass. Therefore, even when the flexibility of
populating the same fused system using different beam-target combinations is taken into
account, a variety of proton-rich radioactive beams are needed for a comprehensive program of
high-spin studies in proton-rich nuclei encompassing all mass regions. For example, proton-
rich radioactive beams for one even- and one odd-Z isotopic chain for each Z decade up to Z =
50 would be desirable.
In contrast, the most efficient method of producing neutron-rich nuclei (actually only near the
most neutron-rich stable isotopes, see the preceding section) in compound reactions is with
heavy targets and light projectiles (or vice versa). Therefore, the best means for studying
neutron-rich high-spin states are neutron-rich radioactive beams with A = 30-50 and the full
variety of neutron-rich stable targets. Heavy isotopes of argon and potassium (even- and odd-
Z respectively), which are easily diffused from ISOL targets and are relatively free from
surface sticking problems, would be excellent beams for studying neutron-rich high spin states. In certain cases, e.g. cesium or rubidium ions, where very neutron-rich heavy radioactive beams arc feasible30', it may be more efficient lo use inverse reactions with A « 30- 50 targets for populating the most neutron-rich rapid)y 6. Conclusion The purpose of this report is to present a flavor of the rich and exciting nuclear structure studies of rapidly-rotating exotic nuclei afforded by radioactive ion beams. It is not intended to be a comprehensive review of this frontier field. Indeed, the possibilities for studies on the limits of both angular momentum and isospin are just starting to be seriously considered. Additional information is contained in refs. 30,31,41, and 53. Acknowledgments Discussions with C. Baktash, R. Casten, l.Y. Lee, W. Nazarewicz, D. Winchel!, R. Wyss, and C.H. Yu are acknowledged. The author also would like to thank W. 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