SPECTROSCOPY of HIGH ENERGY NEUTRONS EMITTED AFTER MUON CAPTURE in 40Ca

SPECTROSCOPY OF HIGH ENERGY NEUTRONS EMITTED AFTER MUON CAPTURE IN 40Ca

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J. A.N. van der PLUIJM Stellingen.

1. De stootgolven die uitgezonden worden bij het ontstaan en de groei van scheuren in materialen ( z. g. akoestische emissie ) kunnen informatie verschaffen over de structurele integriteit van constructie- onderdelen. Het gebruik van akoestische emissie als niet-destructieve onderzoekstechniek kan evenwel eerst als volwaardige onderzoekstechniek worden beschouwd als de relatie tussen heersende of perio- diek optredende spanningen in een constructie, scheurvorming en groei van eventueel aanwezige defecten enerzijds en de aard en hoeveelheid van akoestische emissie anderzijds modelmatig is vast- gelegd.

2. De door Alaerts en Anders gebruikte "activatiecoefficienten" die dienen om het verlies van spoor elementen uit geologisch materiaal ten gevolge van verhitting te beschrijven suggereren ten onrechte dat hier één enkel fysisch proces werkzaam is.

Leo Alaerts and Edward Anders, Geochim. Cosmochim. Acta 43_ (1979), 547.

3. Het is slechts zinvol een zo hoog mogelijke onderdrukkingsfactor voor een anticompton spectrometer na te streven als experimenteel is gebleken dat de continue ondergrond in de fotonspectra veroor- zaakt wordt door comptonverstrooiing in de Ge-detector en niet door absorptie van andere straling met een continu energiespectrum.

4. De meest gebruikte tabellen voor de berekening van het energie- verlies van energetische geladen deeltjes in materie suggereren een veel grotere nauwkeurigheid dan ze in werkelijkheid bezitten.

5. De keuze van Ho als tref plaatkern voor een onderzoek aan hoogenergetische neutronen die uitgezonden worden na muonvangst in atoomkernen lijkt eerder het resultaat van geblinddoekt prikken op de nuclidenkaart dan van fysische overwegingen. i E. K. Mclntyre et. al., Phys. Lett. 137B(1984), 339. 6. Gezien het feit dat effecten van ioniserende straling vaak pas op langere termijn zichtbaar worden is het onbegrijpelijk, dat de nauwlettende medische controle, waaraan radiologisch werkzame personen onderworpen worden, volledig stopt zodra de radiologische werkzaamheden beëindigd zijn.

7. De benaming "electronisch brein" voor een computer geeft blijk van een grove onderschatting van het menselijk brein. VRIJE UNIVERSITEIT TE AMSTERDAM

SPECTROSCOPY OF HIGH ENERGY NEUTRONS EMITTED AFTER MUON CAPTURE IN 40Ca

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad van doctor in de wiskunde en natuurwetenschappen aan de Vrije Universiteit te Amsterdam, op gezag van de rector magnificus dr. P.J.D. Drenth, hoogleraar in de faculteit der sociale wetenschappen, in het openbaar te verdedigen op donderdag 25 October 1984 te 13.30 uur in het hoofdgebouw der universiteit, De Boelelaan 1105

door

JOHANNES ADRIANUS NORBERTUS VAN DER PLUIJM

geboren te Helvoirt

IDSIDIST Grootebroak Promotor : Prof. dr. H. Verheul Copromotor : Dr. W.H.A. Hesselink Referent : Dr. H.K. Walter Voorwoord.

Het onderzoek waarop dit proefschrift betrekking heeft werd uitgevoerd binnen een samenwerkingsverband van de Vrije Universiteit te Amsterdam, de Technische Hogeschool te Zurich en de Universiteit van Zurich. De experimenten die in dit proefschrift beschreven staan zijn voorbereid en uitgevoerd aan het Sahweizerisahe Institut für Nuclearforschung (S.I.N.) te Villigen. Het spreekt vanzelf dat dit promotieonderzoek slechts tot succes kon leiden dank zij de inspanningen van velen. Ik denk daarbij niet alleen aan de wetenschappelijke kant maar ook aan al de organisatie, administratie en technische ondersteuning die ervoor nodig waren. Ik wil graag in de eerste plaats al die mensen van de betrokken vier instituten bedanken die, door gewoon hun werk op kantoor, in de werkplaats of achter het instrumentenpaneel goed te doen, dit proefschrift mogelijk hebben gemaakt.

Van degenen die direct bij het onderzoek betrokken waren wil ik graag in de eerste plaats mijn promotor professor Verheul bedanken die me bij dit onderzoek betrokken heeft en die me met name gedurende de laatste twee jaren van mijn promotieperiode op een prettige wijze intensief begeleid heeft. Willem Hesselink dank ik voor het feit dat ik ondanks zijn zeer drukke, overige werkzaamheden toch steeds de portie aandaaht kreeg die ik nodig had en voor de belangrijke bijdrage die hij heeft geleverd aan de experimenten en aan de afronding van het proefschrift. I thank Hans Christian Walter for his careful reading of the manuscript of the thesis. I also thank him and Roland Engfer for the warm hospitality I enjoyed during the years I spent in their group at SIN. I will allways remember this period with warm feelings. Met Andries van der Schaaf heb ik tijdens mijn verblijf in Zwitserland het meest intensief samengewerkt. Ik denk dat dit project zonder zijn inzicht, zijn creativiteit en zijn inzet niet geslaagd zou zijn. Ik dank hem voor dit alles en ik dank ham en sijn vrouw Sherry voor de ki^m-jraudcoriai-pelijke wijze waavov zij mijn gezin en mij heblei, opgevangen. I thank Tadeusz Kozlowski for all the work he did as spokes- man for this project, for his superb work in the conception and implementation of the setup for the first experiment, for the theoretical guidance he provided and for the many fruitfull discussions concerning muons we had during his three months stay in Amsterdam. I thank yilli Bertl, Christovh Grab and Antek Zglinski for the m.iny shifts they took duriïig the runs and for the skill they displayed in keeping the experiments going. I thank Erwin Hermes and the crew of the workshop of the University of Zurich for all the hardware they provided and especially for all the pieces of equipment they produced at short notice with expert skill. I thank Fritz Schlepütz for a fine online program and a lot of help with its adaption to our needs. Jeroen van Goudoever dank ik voor vele maanden van prettige samenwerking tijdens de analyse, fase. I thank all members of the "Walter-Engfer Gruppe" for their friendliness and for the continuing support and interest they gave the muon program. I thank the staff of SIN. My special thanks goes to Claude Petitjean not only for providing us with the best muon channel in the world but also for showing us how to optimize it to our needs, to Nicolas Lordong and Johan Jansen, the wire chamber experts we heavily leaned upon, and to Wilfried Schoeps, who provided us with beautiful electronics. Ik wil graag de bevolking van het Natuurkundig Laboratorium van de Vrije Universiteit bedanken. Mijn speciale dank gaat naar de

J leden van de maandagochtendolub die altijd bereid waren in een aangename sfeer mijn problemen te bespreken en die me vele oplossingen aan de hand hebben gedaan, naar Hessel van Wijngaarden en Andries Pomper die de tekeningen voor dit proefschrift hebben gemaakt en naar de heer Van Sijpveld die het fotowerk heeft verzorgd. Mijn huidige -werkgevers, Vestvries Computer Consulting, wil ik graag danken voor het begrip dat ik in velerlei opzicht van hen ondervonden heb. Renske dank ik niet alleen voor het typen van het manuscript, maar vooral voor het vele geduld, dat ze de afgelopen jaren met me gehad heeft. CHAPTER I

INTRODUCTION

When a fast muon penetrates matter it is gradually slowed down to thermal velocities by electromagnetic interactions. A negatively charged muon is then captured by an atom. The muonic atom formed rapidly decays to its ground state, the muonic S state. This state is not stable. It can decay trough

U~ + (A,Z) •* (A,Z) + e~ + "ve + v , (1.1) with a partial decay rate of 45.10 s , which slightly depends on Z. It can also decay through

\T + (A,Z) •+ (R,Z) + e~ + v"e + v + Y, (1.2) with a partial decay rate of 600 ± 200 s [PAR 82] . Other decay processes in which electrons are created are extremely rare. A third decay channel is muon capture by the nucleus

U~ + (A,Z) -h (A,Z-1) + v . (1.3)

Like the electron capture process

e~ + (A,Z) •*• (A,Z-1) + v , (1.4) the muon capture process is due to semileptonic weak interactions. In both cases a charged lepton is transformed into a neutrino and the rest energy of the lepton is shared by the neutrino and the residual nucleus. However, due to the large difference in rest energy between the electron and the muon the energy- ana momentum transfer to the nucleus are in the average much larger in muon capture than in electron capture. In muon capture on a free ( i.e. not bound by a nucleus ) proton \T + p •+ n + v , (1.5) the energy transfer to the nucleon is 5 MeV, the momentum transfer is 100 MeV/c. In nuclei the 4-momentum transfer has a distribution that depends on the reaction mechanism which determines the momenta of the particles taking part in the interaction. Muon capture with energy transfer up to =30 MeV can be described as a quasi free process with nearly the same kinematics „as muon capture on a free proton. Here one can distinguish between processes in which the neutron is created in a bound state and processes in which the neutron is created in an unbound state. In the latter case muon capture is most likely followed by neutron emission. Two energy regions can be distinguished in the spectra of neutrons emitted after nuclear muon capture. The lower part of the neutron spectra corresponding to a nuclear excitation energy E =: 15 MeV shows pronounced structures, which are due to the excitation of the giant dipole resonance. The part of the spectra corresponding to an excitation energy E >15 MeV is associated with a direct reaction mechanism. A quasi free reaction mechanism cannot account for the emission of high energy neutrons ( E > 30 MeV ). In a quasi free process, assuming a proton momentum of 300 MeV/c the maximum neutron energy E is about 10 MeV. Neutrons with much higher energy have been reported [SUN 73, SCH 83] . As is discussed in more detail in chapter II, several mechanisms have been proposed which account for these high energy neutrons. The muon can be captured for example by a correlated nucleon pair. In this respect the role of meson exchange currents has been emphasized by several authors. In the approach of Bernabeu, Ericson and Jarlskog FBER 77J the muon generates a virtual pion field in the nucleus which is annihilated by a nucleon pair.

The aim of the present study was to obtain better experimental information about muon capture at large energy transfer. We have measured the neutron energy spectrum up to the kinematic limit of

1 maximum energy transfer. For this purpose a novel neutron detection system was developed. We measured the energy spectrum and the angular distribution of neutrons with respect to the muon spin direction and, to gain direct insight in the capture on nucleon pairs,the angular distribution of neutron-neutron coincidences. In chapter II some theoretical aspects of muon decay and muon capture are discussed. In chapter III the experimental techniques used in this study are described. Two different methods were applied to measure the neutron energy spectra. These methods are to some extend complementary to each other. In a first experiment the neutron spectra and the energy dependence of the angular distribution of the emitted neutrons with respect to the muon spin were deduced from the pulse height spectra generated by neutrons in an organic scintillator. This experiment is described in chapter IV. Significant results were obtained in the energy region 7.5 MeV

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CHAPTER II

THEORY'

2.1 Muon decay.

In our experiments electrons from muon decay are detected for a number of calibrations. Their energy spectrum and angular distribution with respect to the muon spin direction are discussed in this section. The standard theory of weak interactions [e.g. COM 73] describes the purely leptonic decay 1.1 to a high degree of accuracy. Assuming a purely vector-axial vector interaction and a two- component neutrino the effective decay amplitude for a free muon is

M 5 A 5 = 72 • "e Yx (1 + Y ) Vj. u2 Y (1 + y ) »y (2.1)

where G is the weak interaction coupling constant, u , u , v e \i 1 u are spinors representing electron, muon, e- neutrino and 2 y V- neutrino, respectively, and y and y, and "y are Dirac matrices. 5 A Neglecting the electron mass and radiative corrections the transition rate, integrated over electron spins, obtained from this amplitude is

(3 - 2e) (1 + ^-~ cos8) de • •• "" , (2.2)

Only the most important formulae are given in this survey. Derivations of the expressions can be found in the publications referred to, where the notations are also explained.

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p/p e e, max c.max

Flfj. 2.1. Spectrum shape (a) and angular distribution parameter (b) of electrons from free muoii decay without (a) and with (b) the finite electron mass and radiative corrections taken into account. where m is the muon mass,e the electron energy in units m /2 ( yielding 0 < E <1 because of 4- momentum conservation ) and 8 is the angle between the electron momentum and the muon spin direction. The normalized electron spectrum 2e ( 3 - 2e ) and the socalled "asymmetry parameter" 1 - 2e / 3 - 2e, which describes the angular distribution, are shown in fig. 2.1. For comparison the results of a calculation including radiative corrections and a finite electron mass and using the most general decay amplitudes with experimental values of the decay parameters [PAR 82] are also shown in fig. 2.1. When the decaying muon is bound to a nucleus in the S state

the calculation of the electron energy- and asymmetry spectra is much more complicated. The binding energy shows up in a reduction of the accessible phase space and thus in the decay rate ( =5% in case of "* °Ca ). The finite width of the momentum distribution in the laboratory frame increases the mean lifetime of the muon through time dilatation and thus reduces the decay rate further. It also shows in a Doppler broadening of the electron spectrum which for °Ca amounts to more than 15%. A third complication arises from the 12

Fig. 2..:. spuclrum shape la) and angul..r distribution parameter (b) of electrons from decay of muotis buund to a Ca'nuclou.*;.

Coulomb force acting on the outgoing electrons. This causes a larger overlap of the muon and electron wave functions than would be the case for plane wave electrons and thus increases the decay rate. It also shifts the electron energy spectrum towards lower energy. A last complication arises from the recoil of the nucleus. This has the largest influence on the spectrum above m /2; it is extended up to m , however with a very low intensity.

The above complications have been discussed by several authors [POR 51, UEB 60, GIL 60, HOF 61, HAE 74, HER 80, SHA 82]. Also for bound muons the transition rate can be factorized as ""

sin8d9 dW (2.3)

where Ng (e) is the electron spectrum and a (E) is the asymmetry parameter. To calculate the electron energy spectrum and the energy dependence of the asymmetry parameter shown in fig. 2.2 the results of Gilinski and Mattews [GIL 60] have been used. Other calculations lead to similar results. 13

2.2. The muon capture rate.

The process 1.3

\i~ + ( A,Z ) •*• ( A,Z-1 ) + V , (2.4) is the subject of this thesis. The rate for this process is well explained by the standard V - A theory of weak interactions. To derive an effective Hamiltonian for the process 1.3 Fujii and Primakoff started with the matrix element for the interaction

u~ + p,_ •* n, + V (2.5) *bare bare u,

and modified this to include the interactions with the pion field. This leads to renormalisation of the coupling constants, introduction of form factors and introduction of an induced pseudoscalar term. In the Hamiltonian finally found the interaction of the muon with an aggregate of A nucleons is expressed by [FOJ 59, PRI 59]

1 (+) •* - (—) •*••*• H — ~r T ( 1 — 0.V ) Z T ri G 1.1 + eff v 2 i V i

+ Gft O.a - Gp 0.V 0..V } 6 (r - rJ,

where X transforms the muon into a neutrino, 0 is the muon spin operator, V = VV is the neutrino momentum, T. transforms the i proton into a neutron, 1 and 1. are unit operators, O. is the i nucleon spin operator and

G «V, = gV„ ( 1 + v/2m p ) , where

gv = 0.972 g , and m the proton mass.

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GA = gA - gv (1 + up - un> V/2V Wh6re

(ö> g =0.999 g, » and y - un= 3.706,

Gp = { gp - gft - gv d + Pp - UR)1 v/2ny where

g = 7 g . Jp ^A

The 6- function describes the local character of the weak interaction. The above nonrelativistxc approximation of the weak interaction is called the Primakoff Hamiltonian. It describes muon capture as a quasifree process. Since the energy transfer in muon capture is usually small, it describes the total capture rate accurately. It leads to the total capture rate [FOL 64]

2G G A + (Gp " p A> Mp } + '< (2.7)

where is the muonic S wave function, M^, M and M are the Fermi, Gamow - Teller and induced pseudoscalar matrix elements and A is an -10% correction due to nuclear recoil. The total capture rate has been calculated by several authors, in the closure approximation IPRI 59"], in the independent particle shell model [SEN 58, LUY 63, ECK 66], in the Migdal theory [MIG 63 , BUN 66, NOV 66] and in the giant resonance model \FOL 64, CAN 7(f). Typical results of these calculations are shown in Table 2.1, together with experimental values. Excellent agreement with the experimental value of the total capture rate for various nuclei has been found by Bunyatan [BUN 66] , Novikov and Urin [NOV 66] and Cannata et. al. [CAN 7o]. All calculations show a variation of the total capture rate with nuclear charge:

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A = Z (2.8) 'eff' where Z is the nuclear charge, corrected for the overlap of the muon wave function and the proton density distribution. For large nuclei Z << Z, the nuclear charge, and Zeff /Z -»• 1 as

Z •*• 0.

Nucleus th

( 103 a"1 ( 103 s ' )

36.6 37.3 ( 1.1 ) 150 159 ( 14 ) 'A! 633 662 ( 3 ) 2E30 2444 t 23 ) 6160 5760 ( 170 ) 10900 11200 { 700 ) 'Pb 11900 12900 ( 1400 )

Table 2.1. Theoretical and experimental results for the muon capture rate. The data are a selection from the table in A. O. Weisenberg, Huons, pp 165. [HEI 67j.

2.3 Neutron emission.

The Hamiltonian 2.6 describes capture of the muon by a single proton in the nucleus, similar x.o electron capture. There are however large differences between muon capture and electron capture. In electron capture the energy- and momentum transfer to the nucleus is small, thus the interaction is dominated by L = o terns, which lead to "allowed transitions". In muon capture on the other hand the momentum transfer is typically = 100 HeV/c, and higher order terms are very important. Thus a substantial 16

part of the total capture rate is explained by "forbidden transitions". Several authors have stressed the importance of L = 1 transitions to GDR states jjJEB 74J . In nuclear muon capture the energy transfer to the nucleus can be large. An unbound final state is possible. In case of GDR excitations in light nuclei the energy transfer is about 15 MeV. The GDR often decays by the emission of neutrons with energy up to = 10 MeV. In the energy region above the giant resonance calculations of the neutron energy spectra are usually based on the impulse approximation using the Hamiltonian 2.6. The nuclear wave functions are in most cases taken from a shell model description of the nucleus. A serious problem in these calculations is imposed by the final state interaction of the outgoing neutrons with the residual nucleus. This can be described by using a distorted wave approximation for the neutron and an optical model for the neutron- nucleus interaction. The results of these calculations however are very sensitive to variations in the parameters of the optical model. Information on the capture process is obscured by these effects.

A common feature of all calculations based on the impulse approximation and shell model nuclear wave functions is under estimation of the number of neutrons emitted with energy > 30 MeV. The reason for this is that in a quasifree reaction mechanism extremely high proton momenta are needed to produce neutrons with energy larger than 30 MeV. For a 300 MeV/c proton the maximum neutron energy is only 10 MeV. Taking the protons on mass shell, in a quasifree reaction mechanism the neutron energy is restricted to

En < m_J2 - B, (2.9)

where B is the neutron binding energy. Proton emission, which is a secondary process in this picture, should have about the same energy limit. However, protons have been observed JVAI 70, BUD 71, BAL 78, KRA 79] with energy up to 70 MeV. Bertero, Passatore and 17

Viano [BER65] explained these protons as the result of muon capture by proton pairs through the pion exchange between the protons. Neutron energy spectra have been reported ranging up to 50 MeV [KRI 69, SUN 73] and, with less resolution, up to 90 MeV [SCH 83]. It follows that emission of high energy neutrons may be very sensitive to short range nuclear correlations, which can account for the high proton momenta needed. The effect of the short range correlations can either be included in the calculations by an "effective momentum distribution" or by assuming that the muon is captured by a correlated nucleon pair. Introduction of nuclear correlations in the reaction mechanism leads to a treatment of the muon capture reaction similar to that of photo- nuclear absorption at intermediate energy. In a recent description of this process the contribution of meson exchange current has been taken into account explicitly [GAR 8f]. A somewhat different approach to muon capture at large energy transfer has been made by Bernabeu, Ericson and Jarlskog [BER 77]. They showed that as a result of PCAC in the limit for momentum transfer •* 0 and energy transfer •+ m the muon capture process can be interpreted as due to an external pion source proportional to the muon probability: the muon generates a virtual pion field in the nucleus which is annihilated on a nucleon pair.

They predict that about 1% of the capture takes place with energy transfer larger than 80 MeV. Since the energy is shared by two nucleons and the nucleon binding energy has to be taken into account this leads to about 1% capture into states with unbound neutrons having more than 30 MeV kinetic energy. A first onsst to the calculation of the shape of the high energy neutron spectrum has been undertaken by Kozlowski [koz 83] . He calculated the phase space for a pair of neutrons emitted after muon capture on a pair of nucleons according to the predictions of 18

80 MeV

Fig. 2.3. ShapjjgOf the spectrum of neutrons emitted after capture of muons by pairs of nucleons in Ca.

Bernabeu, Ericson and Jarlskog. The nuclear model chosen for this calculation is a degenerate Fermi gas. The spectrum obtained is shown in fig. 2.3. Besides the inclusive energy spectra two other distributions were measured in our experiments. The first one is the distribution of the opening angles of neutron - neutron pairs emitted after nuclear muon capture as a test for capture on nucleon pairs. This measurement is discussed in chapter VI. The second one is the angular distribution of neutrons with respect to the muon polarisation. This angular distribution is usually written as:

F (6,E ) « 1 + P a (E ) case, (2.10) n u n n

where 8 is the angle between the momentum of the-neutron and the 19

polarization direction of the muon, P is the degree of muon polarization and a is the asymmetry parameter. After integration over all nuclear excitations Primakoff arrives at the following expression for the asymmetry:

Gv - Gi + Gp - 2GP GA a = , (2.11) n G2 2 2 V + 3Gft + Gp - 2Gp GA where G , G and G are the effective weak interaction coupling constants introduced in 2.6. From the values of G , G and G it follows a. = - 0.4. n The energy dependence of the neutxon asymmetry parameter a has been calculated by several authors within the framework of the impulse approximation using shell model nuclear wave functions. In some cases relativistic terms have been included in the hadronic part of the Hamiltonian. These higher order terms are found to contribute significantly to the asymmetry in particular for high energy. The calculated asymmetry is very sensitive to details in the nuclear structure. This is due to interfering partial wa*~es with different parity. This interference of the various partial waves is changed by the interaction of the neutron and the residual nucleus This interaction is usually described as a distorted wave for the neutron interacting with an optical potential. Calculations performed thus far indicate that the prediction for the energy dependence of the asymmetry is strongly determined by the choice of the optical model parameters. The asymmetry parameter is thus a complicated function of many variables and it is therefore not such a direct tool for a study of the neutron capture process as e.g. the neutron spectrum or the angular distribution of neutron - neutron coincidences.

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2.4 The target.

This work is part of a larger project [EIC 78] in which for a number of nuclei the inclusive neutron energy and asymmetry spectra were measured up to about 40 MeV neutron energy and a statistical error of = 10%. The nucleus 16O has been selected for the measurement of exclusive neutron energy and asymmetry spectra [sCH 83], The nucleus '*°Ca has been selected for a measurement of the neutron energy spectrum and the neutron asymmetry up to the highest energy kinematically possible, and for a measurement of the angular distribution of neutron - neutron coincidences* The latter work is described in this thesis.

''"ca was chosen for this in - depth study because on the one hand the yield of neutrons is much higher than the yield for light nuclei like 160 ( cf. Table 2.1 ) while on the other hand it is a relatively light nucleus, doubly - magic, and well understood from the theoretical point of view. Furthermore, for lt0Ca an overlap exists with other experimental work, thus comparison is possible. 21

CHAPTER III

EXPERIMENTAL METHOD

3.1 General considerations.

The probability of emission of high energy neutrons ( E 2: 15 MeV ) is below 10~ [SUN 73] . The neutron yield decreases rapidly with increasing energy by about a factor 100 in the energy region 15 MeV < E < 50 MeV. A major problem is caused by neutrons produced in the pion production target and in the muon channel. The intensity of these background neutrons shows much less variation with energy. The background can be suppressed and precisely estimated by measuring the time delay between neutron detection and the preceding muon stop ( time differential method, see section 3.2 ). Due to the long lifetime of the muon in the muonic * S state C for '•"Ca : 340 ns ) the time of flight method which is commonly used in neutron spectroscopy can be applied only under special circumstances to measure the neutron energy spectrum LSCH 83]. For this work the interaction of neutrons with organic scintillators has been used to obtcin the neutron energy spectrum. In these scintillators the neutrons are detected through nuclear interactions in which part of their energy is transferred to charged particles. The main process is the elastic scattering of neutrons by free protons in the scintillator, for which the following relationship between the proton energy ( E ) and the neutron energy ( E ) exists:

4m m -2 E = —2- ( 1+ -2- ) E cos2 9 = E cos2 6 , (3.1) p m m n r n r n n

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where m m and 6 are the proton mass, the neutron mass and the p n r proton recoil angle, respectively. Heavier charged particles are produced as well. In a first series of experiments the pulse height spectrum of the charged particles has been measured from which the neutron energy spectrum has been deduced. As will be shown in section J.3 this method is characterized by a high neutron efficiency (= 20% if high energy resolution is not required or if the detectors are used as treshold counters ) and a small effect to background ratio ( in our experiments decreasing with energy down to 0.02 at 45 MeV ) , which makes it suitable only to the energy region below 45 MeV. In a second experiment only the protons produced in a hydrogenrich organic scintillator in the forward direction have been selected. A detector has been developed which measured both the energy and the recoil angle of the protons from which the neutron energy could be obtained directly using relation 3.1. As will be shown in section 3.4 this method is characterized by a small neutron efficiency ( increasing with energy from 0% at 10 MeV to less than 1% at 100 MeV ) and a large effect to background ratio ( = 10 in the relevant energy region ), which makes it especially suitable to the energy region above 30 MeV.

3.2 The time differential method.

The setups for both experiments which will be separately discussed in chapters IV and V, are merely adaptations of the basic setup shown in fig. 3.1. Negative muons are stopped in a 40Ca target and captured in the muonic S state. After some time they either decay into an electron and two neutrinos or they are captured by the nucleus, during which process neutrons can be emitted. Decay electrons and neutrons are detected by the same detectors.

Besides information on the energy of the particle detected and its nature also the time delay between the muon stop, monitored by

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Fig. 3.1. Principle of the setups for both experiments. Huons emerge from the left, are detected by the plastic scintillators SI, S2 and S3 and stop in the target T. Helmholtzcoils H provide a magnetic field which causes the muon spin rotation. Neutrons and electrons are detected by the detector D. the beam telescope ( SI, S2, S3 and S4 in fig. 3.1 ), and the detection of the particle has been recorded. From the time spectra the exponential If0Ca component and the constant random background component can be resolved by a fitting procedure. In comparison with the integral method -where particles detected are not correlated with' definite muon stops- this differential method strongly suppresses the background. In our experiments, where a stoprate of 105 Hz has been used, we permitted a maximum time delay of 800 ns between muon stop and particle detection leading to a background suppression factor of 12.5. The stoprate has to be below 10 Hz to achieve a low probability that a particle detected can be correlated with several stopped muons, i.e. to avoid ambiguities in the time information, at 105 Hz 20 % of the events were rejected because of this ambiguity. The time differential method also provides an elegant means to measure the angular distribution of the neutrons with respect

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to the muon spin direction. For muons with polarisation P^ the intensity of the neutrons emitted after muon capture varies with the angle 0 between neutron momentum direction and muon polarisation direction like

N (6) K 1 + a P cos 0 , (3.2) n n p where a is the asymmetry parameter, which depends on the neutron energy ( cf. section 2.3 ). If P is known a can be measured using detectors at various angles 9 with respect to the polarisation direction, a can also be measured using one detector and uniform rotation of the muon polarisation direction in an external magnetic field. Then the neutron intensity measured varies with the time t the muons spend in the external magnetic field like

N It) = ( 1 + a P cos ( list + <(> )) e~ r (3.3) n n vi where w is the Larmor frequency, § a phase angle equal to the angle between the initial polarisation direction and the neutron momentum direction and T is the mean life time of the muon in the *S orbit. To a constant time the time delay between muon stop and neutron detection is a good approximation for t if u is chosen such that neutron time of flight differences are negligeable. Thus a can be deduced from the aforementioned time spectra. If however relation 3.3 is applied to an experimental situation it has to be amended. The first modification reflects the finite size of the space distribution of stopped muons and the detectors, which cause a smearing of in relation 3.3. Integration over all values of ( with the proper weight function ) leads to a less pronounced shape of the time spectrum:

(t) °= ( 1 + a P C cos ( uit + $ )) e ~^X, (3.4)

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where C, a factor between 0 and 1, and ^ , a mean phase angle, depend on the geometry of the experiment. The second modification reflects the inhomogeneity of the magnetic field in combination with the finite size of the muon stopdistribution, which causes a variation in u . If the product of the measured number of periods and the inhomogeneity AB/B is small compared to unity 3.4 may be approximated by

N (t) = ( 1 + a P Ccos [iü,t+i )) e-t , (3.5) n n vi 11 where u , is the ( weighted ) mean Larmor frequency. The third modification reflects the fact that muons are generally not only captured by target atoms but also by other atoms in the neighbourhood of the target, and that there exists a random background. The total time spectrum is

N (t) = Z A. ( 1 + a3" P1 C1 cos ( i/ t + fj" )) e"t/Ti + B , nil nu 11 n (3.6) where i denotes the various isotopes present, A. are weighting factors and B is the random background. In our experiments the conditions? have been chosen such that the neutron time spectra can completely be explained by a calcium component and a random background component:

a a Ca a a t/T Nn It) - ( 1 + a^ P^ C cos ( o^ t + +j )) e" Ca + Bn. (3.7) Relation 3.7 has been fitted to the time spectra measured ( see sections 4.5 and 5.5 ). The factor a a P a C00 has been n u treated as one parameter in these fits. The factor P a CCa has been obtained from a fit of the time spectra of electrons from muon decay in orbit. Here the asymmetry parameter a is well known from experiment and theoretically well understood. For the electron time spectra and the neutron time spectra 3.6 the same arguments are valid, thus: 26

N (t) = I h'. ( 1 + a1 P1 CX cos ( ui1 t + $\ )) e Ti + B , e . i. e y * e 1 (3.8) where the weight factors A.' differ from the weight factors A. in 3.6 since the nuclear capture rate varies strongly with the nuclear charge. In our experiments three contributions to N (t) axe important: a contribution from calcium, a contribution from carbon due to stopping of muons in the detectors surrounding the target ( CH ) and CH foil in which the target is wrapped to prevent oxidation, and a random background component. Thus:

N (t) - A' ( 1 + aCa PCa CCa cos ( u,f t + *

• , , c c ^c , c . ,c -t/i„ + A' ( 1 + a P C cos ( u) t + ) ) e C c e u 1 1

+ B, (3.9)

The ratio A' / A' found in the various experiments is of the C Ca order of a few percent.

3.3 The NE213 neutron detectors.

In the first experiment the neutron energy spectrum and the neutron asymmetry have been deduced from the energy- and the asymmetry distributions of charged particles produced by neutrons in NE213 ' liquid organic scintillation detectors. The unfolding procedure is described in section 4.5.2. The present section describes the detector characteristics. NE213 has been chosen for the detection of neutral particles because of its good n-y pulse shape discrimination, which is needed to cope with a very high background of bremstrahlungsphotons produced by decay electrons ( cf. section 4.5.2 ).

Nuclear Enterprisesp Edinburgr Scotland. 27

JJ4 Mf f ff \ rf *^^TÉCJ^lüJLlllSHfiS!üf **'** y f """""'üüf*üjlÉi BËS8

— >1 10 cm Fig. 3.2. The NE213 detector. 1- scintillator volume, 2- overflow to neutralize pressure variations, 3- optical interface, 4- photomultiplier, 5- g-metal shield, 6- springs, 7- housing for electronics t courtesy E. A. Hermes ).

The NE213 is contained in aluminum cells, 127 mm 0 and 102 mm thick, with quarz windows at the backside for the optical coupling to 127 mm 0 XP2031 photomultipliers. The photomultipliers have p-metal shields. Each cell and its photomultiplier is held in a nickel-plated soft iron container for easy mechanical handling and additional magnetic shielding ( fig. 3.2 ). NE213 mainly consists of carbon and hydrogen ( CH. „., ). 12 1'zlji i2 The most probable interactions with neutrons are C ( n,n' ) c. 9 1 112 12*12 1212 n,a ) Be, H ( n,n' ) H, C n,n' ) C , C { n,p ) B, C 12 and C ( n,n'3a ). The energetic charged particles thus produced ( C, C*, B, B,a,p) excite the molecules along their track and are gradually brought to rest. The excited molecules decay to their ground states in which process light is produced by rather complicated processes [BIR 64^ . In organic scintillators the efficiency of the conversion of energy deposit into light intensity depends on the ionisation density along the track ( quenching ) and thus on the energy and mass of the 12 ionizing particle. For example, a C nucleus produces much less light than a proton of the same kinetic energy. Since in addition the mean energy of the charged particles produced decreases with increasing mass of these particles, the upper part of the pulse height spectrum produced by monoenergetic neutrons in the 28 scintillator is dominated by protons from the H ( n,n' ) H interaction. t The response function of the NE213 detectors to neutrons has been measured in an experiment with stopped negative pions. Emission of high energy neutrons is the main decay channel after pion capture. Since negative pions are captured by nuclei immediately after the atomic capture the neutron energy can be calculated from the time of flight. For a series of neutron energy windows the pulse height spectra of the NE213 detectors have been accumulated. The upper half of these spectra is rather flat, showing a sharp endpcint at the selected neutron energy. The positions of the endpoints have been used to obtain the response function of the detectors to high energy protons. Due to the quenching effect the light output of the detectors for protons is a non-linear function of the energy. For electrons with energy above 5 MeV the stopping power is nearly constant, about 2 MeV per g/cm , thus the conversion efficiency mentioned above is also constant. The spectrum of electrons from the muon channel, scattered in the target, shows a pronounced peak at 17.2 MeV [POW 80, fig. 3.3], which is caused by electrons with higher energy which pass through the detector ( Landau spectrum ). The position of this peak establishes an absolute calibration. From the absolute calibrations and the edge positions a relation could be obtained which relates the energy of electrons E and protons E for which the intensity of light in NE213 is the same ( E in MeV ):

E = - 6.42 ( 1 - exp ( - 0.1 E0-9 )) + 0.91 E (3.10) e PP A similar empirical relation was obtained by Verbinski et. al. [VER 68]. In the main experiment ( ch. IV ) relation 3.10 was used together with the position of the electron peak to calculate te recoil proton energy from the pulse height. The efficiency of the NE213 detectors has been calculated by H. P. Isaak et. al. [iSA 82] using a Monte Carlo code which is

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250

Fig. 3.3. Calculated energy loss distribution of high energy electrons in the NE213 detectors. 20 30 • AE ( McV) based on a code by Del Guerra et. al. [J3UE 76J . The reliability of the program has been checked for several detector geometries with measured efficiency curves. An optimal energy resolution of the NE213 detectors is not extremely important for the measurement of smooth energy spectra ( cf. section 1.1 ). A rough estimate can be made using the shape of the Landau peak ( cf. 4.7 ). The FWHM of this peak is about 18% for all six detectors. The low energy edge of the peak, which is very steep in theory, rises from 10% of the maximum value to 90% over 1.2 MeV, which indicates an energy resolution of about 8% FWHM at 15 MeV. If the resolution is dominated by statistical fluctuations, the maximum energy resolution in the relevant energy region is better than 3 MeV FWHM.

Using the NE213 detectors the neutron is identified by a corresponding pulse from a single detector. Thus the detectors are equally sensitive for neutrons from all directions.

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High energy neutrons penetrate matter quite easily, which implies that the detectors cannot be shielded completely against neutrons coming from the side. In fact, in our experiments shielding is disadvantageous since neutrons from inuon capture may be scattered from the shielding into the detectors, thus distorting the spectra. Since strong sources of high energy neutrons exist in the vicinity of the setup ( muon channel, pion production target and proton beam dump ), the isotropic sensitivity of the NE213 detectors leads to an effect to background ratio which is very small at high neutron energy ( cf. section 3.5 ).

3.4 The neutron telescopes.

To measure the high energy part of the neutron spectrum a new neutron detection system was developed. It consists of 4 different particle detectors and 4 wire chamber planes. All parts were designed especially for this purpose. The subsequent sections give the design considerations and describe the extensive tests of the performance of the telescope and its parts.

3.4.1 Gent.ral principles of the neutron telescopes.

Wher"' er a neutron with energy E is scattered on a proton at rest, the recoiling proton will have an energy ( see 3.1 )

E = E cos2 8 , 13.11) p n r where 9 is the proton recoil angle. Thus a simultanous measurement of the proton energy and -recoil angle yields the neutron energy:

2 En= Ep cos" 9r , (3.12)

This is the basic principle of the proton recoil telescope.

.1 31

Fig. 3.4. Top view of the inain parts of the neutron telescopes. 1- radiator window ( 100 urn Al ) + wire chamber window ( 35 um mylar ), 2- wire chamber cathode planes ( 20 um Al ), 3- vertical wire planes, 4- horizontal wire planes, S- two wire chamber windows, 6- wire chamber exit window, 7- stopdetector window ( 20 um Al ), 8- AE detector ( 3.2 ram NE102A ), 9- anticounter ( 10 mm NE102A ), 10- active radiator ( 70 mm NE235 ), 11- Nal(Tl) crystal, 12- radiator housing < 10 mm perspex ), 13- jJal(Tl) housing t Al ), 14- optical window of the stopdetector.

Telescopes have been developed, in which recoiling protons are produced in a scintillating radiator. If a proton escapes from the backside of the radiator its direction is measured by two pairs of wire chambers. The proton is subsequently stopped in a Nal(Tl) crystal. To enable discrimination of charged and neutral particles a plastic scintillator is added in front of the radiator. Neutron - gamma discrimination is achieved by taking advantage of the different stopping powers for electrons ( from Y ) and protons ( from n ) in a thin plastic scintillator, mounted in front of the Nal(Tl) crystal ( fig. 3.4 ). 32

3.4.2 The radiator.

The efficiency of the proton recoil telescope is mainly determined by the radiator escape efficiency, i.e. the probability that a neutron produces a proton in the radiator that escapes from it. Therefore the choice of the scintillator is motivated by the highest possible number of hydrogen atoms per unit mass. Although the best scintillator in this respect is NE228 ( CH_ ) , the scintillator NE235 ( CH ) has been chosen since it is much easier to handle: NE228 is agressive and very sensitive to oxygen, NE235 can be used in plastic tanks which are filled under atmospheric conditions.

The other important design parameter is the radiator thickness. The escape efficiency is the product of the probability for creation of an energetic proton and the probability the proton escapes from the radiator. The first probability obviously increases with increasing thickness of the radiator. The second probability depends on the range of the protons and the distance from the point where they are created to the backside of the radiator. This limits the effective thickness for a definite neutron energy. Another factor which limits the thickness of the radiator is multiple scattering. Here one has to distinguish between multiple Coulomb scattering of the proton by electrons along its track and scattering of the neutron by nuclei. The first causes an error in the recoil angle measured of the order of a few degrees or less and may thus be neglected [PAR 82] . The second occurs

occasionally, the probability for it increases with increasing thickness of the radiator- If it occurs the induced error in the recoil angle can be large. This effect tends to cause an overestimation of the neutron energy.

In order to optimize the radiator thickness a series of Monte Carlo simulations of the performance of the combination of a

Nuclear Enterprises, Edinburg, Scotland.

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radiator and a 5 cm thick, 5" 0 Nal(Tl) crystal has been carried out. In these simulations the six main neutron reactions mentioned in section 3.3 have been taken into account. The neutrons could also interact in a 2 cm thick NE102A scintillator in front of the radiator, which approximated the effect of matter between target and the radiator. The gap between radiator and Nal(Tl) crystal was 60 mm. Protons were selected which left the radiator with at least 10 MeV kinetic energy and which stopped in the Nal(Tl) crystal. The finite energy resolution of the various detectors, the position resolution of the wire chambers and the size of the beamspot have been taken into account.

The thickness of the radiator has been varied from 30 mm ( the range of 45 MeV protons ) to 120 mm { the range of 95 MeV protons ) in the simulations. P. thickness of 70 mm I the range of 70 MeV protons ) gives the optimal combination of high efficiency and low multiple scattering probability over the relevant energy region. The results of the simulation for 70 mm thickness are shown in fig. 3.5 and 3.6. Fig. 3.5 shows the recoil proton energy spectrum for monochromatic neutrons of 70 MeV. t g. 3.6 shows the neutron energy spectrum calculated from the proton energy and the angular information. The events with a

largely underestimated neutron energy are mainly due to protons 12 12 from the C ( n,p ) B interaction. The events with an over- estimated neutron energy are mainly due to scattering of neutrons. Fig. 3.7 shows the efficiency of the neutron telescopes as a function of neutron energy together with the scattering probability 12 11 and the probability of occurrence of the C ( n,p ) B interaction. The systematic error due to scattering of neutroné can be limited quite well by limitation of the proton recoil angle in the off-line analyses as will be shown in section 5.5. This limitation also reduces the effective efficiency of the neutron'telescopes.

J 34

J20 40 60 80 Fig. 3.5. Simulated spectrum of recoil protons generated by 70 HeV neutrons in the radiator and detected in the Nal(Tl) crystal.

120

Fig. 3.6. Simulated response of the'neutron telescopes to 70 MeV neutrons. To obtain the upper histogram no restriction was applied to the recoil angle; in the lower histogram the recoil angle is restricted to values for which cos 9 >0.85.

\ 35

50 75 100 En(McV)

Fig. 3.7. Calculated efficiency of the neutron telescopes as function of the neutron energy. Curve a: total efficiency; b: contribution of the 12C ( n, n' ) 12B reaction; c: contribution of neutrons which are scattered before the proton is generated.

However, to measure the high energy neutron spectrum with the same accuracy as was achieved in the experiment with the NE213 detectors, an efficiency of only 4.10 is needed ( cf. section 3.5 ). Fig. 3.8 gives the efficiency for the detection of neutrons as a function of the incident neutron direction with respect to the detector axis for 70 MeV neutrons and the mean neutron energy calculated for these neutrons if it is assumed that they originate in the target. From this figure the anisotropic sensitivity of the detectors can be seen and the behaviour of the detector with respect to the random background can be understood.

3.4.2.1 The radiator response function.

The light output of the radiator depends on the energy of the created proton, its energy loss in the radiator and of the coordinates of its track, which are known from the wire chamber 36

Fig. 3.8. Calculated efficiency of the neutron telescopes as a function of the incident angle. Dots ( left scale Ï represent the efficiency, crosses ( right scale ) represent the energy calculated for these events if it is assumed that 6. = 0. 10 20 30 £0 50 60 70 80 90 'incident -

information. The geometrical variation is caused by the position dependent light collection efficiency. The amount of light AL produced by a proton along a trackelement with length Ar is given by [BIR 64]:

1 g (r) af (r))" Ar, (3.13)

where — (r) is the stopping power as a function of the range ( and thus of the energy ) of the proton and a is the quenching parameter, which depends on the scintillator material. Only a fraction of this light reaches the photomultiplier.

j 37

This fraction f generally depends on the coordinates of the track element ( x,yfz )

AL = AL f ( x,y,z ) (3.14) m P where AL is the intensity of the light reaching the m photomultiplier. Before carrying out the integration a few remarks should be made. From the simulations discussed in section 3.4.2 it became clear that most of the protons which contribute to the efficiency move roughly in z-direction, i.e. with cos 6 « 1, and that their tracklength in the radiator is of the order of a few cm or less, i.e. small compared to the detector dimensions. The ( x,y ) dependence of f ( x,y,z ) was measured with a monoenergetic proton beam, incident perpendicular to the back plane of the radiator. The variations are smooth and within 20%. Secondly, the shape of the response functions at these points as a function of energy ( and thus, through the range, also of z ) does not vary significantly. From these calibrations it turned out that the function

f { x,y,z ) can be approximated by fj ( x,y ) f2 (z). A further simplification is the replacement of the coordinates x and y by the center of gravity of the track x and y . This is g g permitted since the variation along the track is much smaller than the expected detector resolution ( = 1% FWHM ). Thus: V v

L =f l ' If(r ) Cl cx-(r)) m g Og r + P

where r and r, are the range of the proton when it is created and when it leaves the radiator, respectively, z is a function of r ,r P 38 and the angle between proton momentum and the back plane of the radiator. The function f ( x ,y ) has been measured using the decay electrons emitted during the experiment. Using the wire chamber information the windows of the radiators have been divided into 8x8 ram2 bins. For each bin [IX,IY) energy loss spectra of electrons with directions ( in the wire chambers ) nearly parallel to the detector axis have been accumulated and the mean value of the energy loss peak ( Landau peak ) E has been calculated. -LA. ( IX The outher bins ( IX = 1 or 16 or IY = 1 or 16 ) show large variations in E which can be explained by the assumption XX, XX that part of the track of the electrons was outside the scintillator. These bins have not been taken into account in the calculation of the correction factor of each bin: 15 15 _

IX-2 IY-2 El IX~2 IY-2 (3.17) fIX,IY IX'IY 196

The correction factors C have been fitted assuming a 6 - parameter polynomial ( up to 1 order in y, up to 2 order in x; y was the direction towards the photomultiplier ). Fig. 3.9 shows results of the fits. The variations of the response function of the radiator with the proton energy and with the z - coordinate could not be measured independently since the range of the proton is itself a function of the energy. The variation with energy has been measured using the continuous spectrum of protons emitted after nuclear pion capture. The protons entered the radiators through the backplane windows. The position and direction of the protons were measured using two wire chambers directly in front of the radiators. The proton ti.->rgy has been calculated from the time of flight over a distance of 3.28 m, corrected for energy loss in air, wire chambers and radiator windows. Since the photomultiplier 39

1.1

0.8 :

50 100 50 100 x(mm)—> x(mm)—^ Fig. 3.9. The position dependent correction factors to the radiator response functions for both radiators anfl f or y = 20 mm ( upper ), y = 65 mm ( middle ) and y = 110 mm ( lower curve ). The negative y direction is the direction to the photomultiplier.

of the radiator is placed at the side a finite size correction was applied to compensate for the velocity of light in the radiator ( 204 """/ns ). The spectrum of the radiator was fitted using the energy calculated from the t.o.f to the formula

L C M = 1 '# (r) ( l+ «ïï£(r) ) (3.18)

dE dr and a are defined as in 3.13, r is the proton range when it enters the radiatotor and C is the ccalibratioa n constant. The fit parameters are C^ and a .

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Fig. 3.10. The energy dependent part of the radiator response function for protons. 10 20 30 40 50 60 70 80 90 MeV Proton energy—»

2O-4O MeV

0.8 1.0 1.2 0.8 1.0 1.2 0.8 1.0 1.2 • Erad/Etof

Ind'eo'-'êo to protons of 20 - 40 MeV ( a ), 40 - 60 MeV ( b )

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With statistical errors of the order of 0.1% the value a = ( 7.8 + 0.6 ). 10 g/MeVcm2 has been obtained with x2 c 1-8. The low x2 indicates no strong z - dependence ( fig. 3.10 ). During the above experiment also energetic electrons have been detected. These electrons, originating from the pion production target, are transported through the channel and scattered in the target. They pass through the radiator and deposit an energy in it which only slightly varies with their energy, thus the spectrum contains the Landau peak ( c.f. section 3.3 ). This peak can be used to calibrate the equipment, since the mean energy loss can be calculated using the Sternheimer formula [~STE 7lj . The energy loss can also be calculated using the calibration constant C. and the value -r— = 2 MeVcm /g for the electron stopping power in formula 3.18. The mean energy loss found was 11.96 (5) MeV, consistent with theory.

Fig. 3.11 shows the response of the radiator ( with the response function taken into account ) to protons in the energy region 20 - 40 MeV, 40 - 60 MeV and 60 - 80 MeV, as measured in the T.O.F. experiment on protons emitted after pion capture.

3.4.3 The hE - E detector.

For the large area AE detector a slice of standard plastic scintillator ( NE102A +) has been chosen. To obtain a good electron - proton separation even for high energy protons, for which the energy loss is of the same order of magnitude as the energy loss of electrons, a rather thick ( 3.2 mm ) AE detector has bean chosen. Herein a proton may lose a considerable part of its energy ( 18.2 MeV protons are completely stopped ). 42

p - l'JO MeV/c ; E = l'J MeV p = 195 MeV/c ; E =20 MeV

scales 5 mV/div ; 2Ü ns/div scales 5 mV/div ; 20 ns/cliv

" p = 209 MeV/c 7 £~ 7= ~23~ MeV --" p = 239 MeV/c ,- E ~= -30 HeV P

scales 5 mV/div ; 20 ns/div scales 10 mV/div ; 50 ns/div

p = 277 MeV/c ; E = 40 MeV p = 421 MeV/c .- E =90 MeV P

scales 10 mV/div ; 50 ns/div scales 20 mV/div ; 50 ns/div

Fig. 3.12. Typical pulse shapes of the stopdetector. J 43

Its energy resolution is therefore an important contribution to the total resolution of the proton recoil telescope. To minimize the amount of light lost by reflections, the detector is not read out from the side but through the Nal(Tl) crystal. The light of both scintillators is detected by the same photomultiplier. Both contributions can be separated because of the very different pulse shapes. Pulse shapes of this charged particle AE - E telescope measured with monoenergetic protons are shown in fig. 3.12.

During data taking the signal of the AE - E detector is fed into three different ADC's , one with a gate over the first 8 ns of the pulse ( "AE" ), one with a gate over the first 30 ns of the pulse ( "2ndAE" ) and one with a 200 ns long gate starting 30 ns after the beginning of the pulse ( "Nal" ). Then the responses of the ADC's "AE", "2ndAE" and "Nal" are related with the light produced in the AE detector and the Nal(Tl) detector through

"AE"

"2ndAE" = a2 L^ + B2

L + L " = "3 AE h NaI

These relations can be inverted to give

LAE " Yl "AE" + 61 "NaI"

L = Y 2ndAE + S NaI AE 2 " " 2 " "

LNaI = Y3 "AE" + 63 "NaI" ' etC" (3.20)

The ratios Y^/S,/ Yn^2 an<^ Y3^3 are stained from the measured

J 44

distributions of the response "AE" resp. "2ndAE" versus the response "Nal". The first two ratio's can be obtained from these distributions for energetic electrons, which have L = const./cos0, A E 9 being the incident angle. The latter ratio can be obtained from the distributions of protons which are stopped in the AE detector and thus have L = 0. To obtain the value of the constants y and 6 a calibration is needed which will be discussed in section 3.4.3.2. "2ndAE" is used to calculate L if L is small; in chi" case it has a better resolution than "AE". The energy resolution of "AE" for 15 MeV protons is 8%, that of "2ndAE" is 5%.

3.4.3.1 The response functions of the LE and Nal(Tl) detectors.

As is shown for the radiator in section 3.4.2.1 the response function of the AE and the Nal(Tl) detectors can be separated into a part which depends on the energy and nature of the particle and its penetration depth and a part which depends on the coordinates of the point where it enters the detector, (x,y). Both parts have been measured using the considerable proton component of the SIN TTM3 pion beam, which is present if the channel is tuned for positive pions and no degrader is used. Each detector in turn was carefully positioned at the exit window of the channel. In front of the detector two wire chambers measured the position of the beam particles. The channel was tuned to a range of momenta from 174 to 445 MeV/c, corresponding to proton energies ranging from 16 to 100 MeV. The total current never exceeded 1000 Hz to avoid saturation of the photomultipliers. Each detector was first expos3d to a focussed and collimated beam with an energy spread much smaller than the detector resolution. From the wire chamber information the crossection of this beam could be obtained. It was about 2 . 2 mm (FWHM). Later a series of measurements has been done with a beam crossection as large as the detector size ( 5"0 ) . To obtain this beam crossection the channel

J 45

had to be mistuned strongly, which resulted in non-uniform energy distributions of the protons over the surface of the detectors. To obtain the (x,y) dependency of the response function these energy distributions have to be known. They have been found using the function

_ response "AE" , (3.21) response "Nal"

for protons, which strongly depends on the proton energy in the region between 20 MeV, where protons just penetrate the NaT(Tl) crystal, to about 40 MeV. If the (x,y) dependency of the AE detector does not vary strongly from the (x,y) dependency in the first few mm of the Nal(Tl) crystal, this function does not vary strongly with x and y. The function f has been measured using the well-defined focussed beam. Using the function f the energy distributions were calculated. Smooth distributions were obtained which show variations of about 4%.

Since the proton energy found was the proton energy in the channel, it has been corrected for the energy loss in the channel window ( 190 um mylar ), the wire chambers ( 70 um mylar + 90 um Al ) and the entrance window of the AE - E telescope. Then the energy loss in the AE detector has been calculated from the relation used by Gooding and Pugh for NE102A [GOO 60]:

f = 17.91 x - °"448 MeV cm^ (3"22)

x being the range of the protons,'from (3.22)

x = 1.827.10 "3 E 1#812 g/cm2 (3.23)

The remaining energy is the energy deposit in the Nal(Tl) detector, an energy-independent fraction of which is converted into light. The amount of light produced in the AE detector has been calculated using

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----- 5.5 4.8 5.4 5.2 5.0 5.8

- , 2.7 4.4 4.0 4.3 4.5 4.4 4.6 5.0 5.5 5.6 - - -

2.1 3.2 3.3 3.3 3.0 2.8 3.4 3.5 3.8 4.4 4.8 4.8

1.2 1.5 1.6 2.1 1.8 1.5 1.3 1.8 1.6 1.7 2.6 3.6 3.3 3.8

0.0 0.4 0.4 0.3 0.0 0.6 1.2 1.4 0.8 0.5 0.6 1.6 2.6 3.0

- -0.4 -0.5 -0.8 -0.8 -0.2 1.1 2.3 2.5 1.8 0.5 -0.5 -0.2 0.9 2.0 2.6

-0.8 -1.1 -1.3 -1.6 -1.9 -0.3 1.1 2.1 2.5 2.3 0.9 -1.5 -1.5 -0.5 0.9 1.9

-2.7 -2.7 -2.5 -3.3 -2.5 -0.6 0.6 1.6 1.8 1.9 0.8 -1.8 -3.1 -1.8 -0.6 0.0

-4.0 -3.9 -4.2 -4.4 -4.0 -1.7 -0.4 0.7 0.8 0.9 -0.9 -3.2 -3.9 -2.B -1.4 -0.4

-4.0 -4.8 -4.9 -5.4 -5.3 -3.8 -1.9 -0.7 -0.2 -0.6 -2.6 -4.6 -4.6 -3.3 -2.0 -0.9

- -5.0 -S.3 -6.3 -6.1 -5.7 -4.5 -3.3 -2.9 -3.7 -5.6 -5.6 -4.9 -3.7 -2.4 -1.8

- -4.9 -5.9 -6.2 -6.4 -6.7 -6.5 -6.4 -6.3 -6.3 -6.5 -6.2 -5.0 -4.0 -3.5

- -5.6 -6.1 -6.0 -6.7 -7.1 -7.2 -7.1 -6.7 -5.5 -4.9 -4.1 -3.5 -3.0

- -4.5 -5.2 -5.5 -6.4 -6.5 -6.8 -6.9 -6.5 -5.7 -5.3 -4.5 -3.7

- -3.C -4.9 -5.5 -5.5 -5.9 -5.9 -5.5 -4.8 -4.9 -

- - - - -2.5 -4.9 -5.2 -5.7 -5.4 -4.9 -----

Tjbli- 3.1 Variation with x I horizontal direction ) and y ( vertical direction ) of the

stopdetector response functions.

^-i «•••i>-1 with a = 1.31 - 10~ c /g found by Craun and Smith [cRA 70] . From the response thus calculated and the measured response the variation of the response function with x and y has been obtained for 9 measurements with central proton energy in between 22 and 40 MeV. Although the energy distribution over the surface of the detectors varied considerably in these measurements , the response functions obtained are proportional to each other, which confirms the hypothesis of equal x-y dependence for AE response and the first few mm of the Nal (Tl) crystal. The mean XY dependence is tabulated in Table 3.1.

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Eo- 80 MeV Eo=40MeV

A 0.8 1.0 12 0.8 1.0 1.2 0.8 1.0 1.2

Fig. 3.13. The response of the stopdetector to protons of 24, 40 and 80 MeV.

Measurements have also been done for proton energy 60, 80 90 and 100 MeV. Although the proton energy distribution over the surface of the detector could not be calculated with sufficient accuracy to be comparable with the 22 to 40 MeV measurements, the results show no large deviations of the results of these measurements. Since AE is a thin detector no z-dependency was assumed for the AE response function. The Nal(Tl) z-dependency has been obtained by comparing the response measured for the focussed beam with the calculated response. The variation in the z-dependency is proportional to the range of the protons. The variation is 1655 for one of the detectors and 11% for the other one over the energy interval 0 < E„ < 80 MeV, where E , is the calculated Na Tl Nai energy deposit in the Nal(Tl) crystal. Fig. 3.13 shows the response of the AE + Nal(Tl) detector ( with the response function taken into account ) to the protons in the calibration experiment for three different measurements. A resolution of 5 to 6% FWHM is observed. The events in the low energy tails of the peaks are not due to position dependency. 48

"AE" response

Fig. 3.14. " iE " response vs. Nal " response.

3.4.3.2. The energy calibration of AE and Nal.

In the main experiment there was no possibility for a direct energy calibration of the Nal spectra which was reliable also at high energy ( > 30 MeV ). Therefore the energy calibrations were derived from the "AE" respectively "2ndAE" versus "Nal" plots of which an example is shown in fig. 3.14. In these plots three regions can be distinguished which are of interest for the calibrations: the region containing particles that stopped in the AE - detector (I), the region containing minimum ionizing particles mainly electrons produced by high energy gammas (II), and the

j 49

Fig. 3.15. Central curves in the "ÜE " vs " Nal " plot.

region that contains protons stopping in the Nal(Tl) crystal (III). In each region a central curve, connecting the points of highest density can be drawn ( fig. 3.15 ). The central curves of the regions I and II are straight lines in the plots, the central curves of I describing ( cf. section 3.4.3 )

L »Na, Tl = Y3a "AE" + S$, "Nal" = 0

LNaI = Y< (3.25) and those of region II

LAE = Yl "AE" + 6 "NaI" = 680 keVee

LAE = yz "2naAE" + s "NaI" = 680 (3.26) 50

where 680 keVee is the light produced by a relativistic ( E > 5 MeV ) electron which loses 680 keV of energy in the A E detector. The ratios y. /& ( i = 1 4 ) follow immediately from i i the slopes of these lines. can The calibrations y-, and Y2 be obtained from the distance between the intersection point of curve I and curve II, which is the point L., = O, L _ = 680 kevee, and the intersection point Na Tl A E of curve I and curve III, which is the point for which L = 0 and L takes the value for protons just stopped in the AE detector. From ( 3.22 ) the energy of these protons is 18.2 MeV and from ( 3.24 ) the light produced by these protons is 10.40 MeVee. Thus the projection of this distance on the 11 AE" axis resp. "2ndAE" axis is 9.72 MeVee long. The calibrations for the "Nal", y and 6 , have been deduced from a comparison of the "AE" vs "Nal" plots obtained in the main experiment and that obtained in the measurement of the response function using the focussed proton beam. In these plots the ratio of the distances between the central curves of the regions II and III for a given value of L and that for

L = 0 is a function of LN only. The accuracy of these calibrations is of the order of 3% FUHM. Errors are introduced mainly through the uncertainties in the positions of the intersection points.

3.4.4. The wive chambers.

In the neutron telescopes the proton recoil angle is measured by two MWPC's. The MWPC's have been designed by U. Weidman [wEI 78]. Each MWPC ( cf. fig. 3.1 ) contains two anode planes oriented 90 with respect to each other and three aluminum foils which act as cathodes. The wire planes contain 64 51

active wires with a thickness of 20 van and a separation of 2 mm. The distance between the wire planes and the cathodes is 5 mm. Ee:h chamber has an entrance- and exit vjindow of 35 ym thick mylar. The total thickness of one chamber including the HT connectors, the gas connectors and the signal connectors is only 2 26 mm. The mass in the active area is 34 mg/cm . During the experiment the chambers operated on a 50-50 Argon - Ethane gas mixture and a H.T. of 3800 - 3850 V. The wire chamber pulses were processed by the SIN wire chamber readout system WCRS. From the wire chambers the signals were transported by 1 m long shielded flat cables to amplifiers ( voltage gain in 50SÏ: 10 ) ,coupled to differential cable drivers. From the cable drivers the signals were transported by 50 m long twisted pair cables to discriminators (threshold adjustable from 20 mV to 80 mV) which were coupled to coincidence registers. The discriminators and the registers of each detector are packed into one modified CAMAC crate together with electronics for diagnostics. Each crate

is provided with a "Wire Chamber Subcontroiler" , trough which the discriminators can be enabled by a gate pulse and through which the registers can be cleared by an external pulse. The subcontroller also serves to connect the registers with the "Wire Chamber Master Controller" , which provides the link with the CAMAC system crate. In each neutron detector the wire chambers are mounted as close together as mechanically possible in order to maximize the efficiency of the neutron detectors. The justification for this can be seen in fig. 3.16. The recoil angle e is the angle between the proton and the neutron directions. The coordinates of the interaction point P can be calculated from the track in the wira chambers and the energy loss of the proton in the radiator ( cf. section 5.5 ). However, the point in the target where the neutron originates from is unknown. In the geometry chosen this leads to an error in the neutron direction of about 6% FWHM. 52

•

ÏARöET- >__ —-è ^^^r^ P RADIATOR

Fig. i.16. Components of the error in the recoil angle 0 .

The error in a , the proton direction, can be calculated from the wire chamber resolution using

6 = arctan { (- -) } , (3.27) P

where x , x„, y. and y_ are the coordinates measured in the wire chamber planes and d is the distance between equally oriented wire planes. All wire planes have equal position resolutions (a ) . we thus, from 3.27

/2 y2 -yi } (3.28) d

Using a =2ram, th e wire distance, a (9 ) is smaller than the we p error in the neutron direction if d is larger than 27 mm. In the most compact setup d is 26 mm. The propagation of the error a(ö ) to the error in the neutron energy a (E } can be obtained using relation 3.12. Thus, 53

2 2 6 2 2 h a (En) = { cos "* 9r o (Ep) + E 4 cos" 8r sin 8r a (8^ } (3.29)

The contribution of a(8 ) can, using 3.12, be written as r

2 E tg 6 a(8 ), (3.30) n r r which, for 8 =0 and A8 = 0-1 rad ( FWHM > can be approximated by

4 h 0.2 E tg 8 ( 1 + cos 6r ) (FWHM) (3.31)

where the term cos1* 8 stems from 3.29. Values of this contribution to AE / E are given in Table 3.2. n n From Table 3.2, fig. 3.12 and fig. 3.14 it can be concluded

that the neutron detector resolution is dominated by a (E ) if 8r is

small ( S 10° ) and by a (8^ if 6r is large. 9r can be restricted in the off-line analysis in order to improve the energy resolution.

e AEn 1E n 1 AE - 0 r P % FWHM 0° 0 10° 5 20° 10 30° 14 40° 19 50° 26 60° 36

Table 3.2. 54

5 10 20 30 £0 50 60 70 80 90 100

Fig. 3.17. Measured efficiency of the neutron telescopes if in the off-line analysis cos 6 is restricted to values larger than 0.85.

3.4.5 The y and resolution of the n&utron telescope.

The efficiency of the neutron detectors as a function of the neutron energy has been obtained from a measurement of a known neutron spectrum. The mechanical setup used for this calibration experiment and the electronics are the same as in the experiment discussed in chapter V and the calibration experiment has been analyzed with the same program, thus there can only be a slight difference due to different detector tresholds, different wire chamber efficiency and different off-line cutoffs. The neutron spectrum chosen for the calibration was the spectrum of high energy neutrons emitted after nuclear pion 55

Fig. 3.18. Distribution of the sum of the energy of coincident neutrons emitted after pion capture in 6Li, measured with the neutron telescopes. 200

capture in Li measured by Isaak et. al.fjcSA 82] . The neutron yield of this reaction varies about a factor 1.5 in the energy region 15 MeV 0.85 (9 <26°) are shown in fig. 3.17. The shape of the curve agrees well with the shape expected from the Monte Carlo simulation. An estimate for the energy resolution of the neutron telescopes was obtained from the neutron - neutron coincidences. Isaak et. al.found that the sum of the energies of both neutrons for 180 coincidences centers around two peaks at 105 and 135 MeV. These are explained by capture on two d-shell nucleons ( 135 MeV ) and by capture on an s-shell nucleon and a d-shell nucleon ( 105 MeV ) , the residual nucleus acting as a spectator- In fig. 3.18 the spectrum of the sum of the energies obtained in

J 56

the calibration run is shown. From this spectrun. an upper limit of the resolution at 70 MeV of 12% FWHM can be deduced.

3.5 Concluding remarks.

A comparison of the efficiency of the NE213 neutron detectors and that of the telescopes at first glance leads to the conclusion that the neutron telescopes are much less efficient than the NE213 detectors. However, as will be shown in section 4.5, the spectra obtained using the NE213 detectors have to be unfolded to obtain the neutron '.nergy spectra. Since the proton spectrum from the H (n,n) H interaction is flat and the intensity of neutrons emitted after nuclear muon capture strongly decreases with increasing neutron energy most of the information on high energy neutrons is hidden under information on low energy neutrons. This leads to a low effective efficiency for high energy neutrons. The effective efficiency is also influenced by the isotropic sensitivity of the NE213 detectors, which causes a small effect to background ratio. For instance, as is shown in chapter IV, using six NE213 detectors the value — = (7.6 ±3.8). 10 neutrons per MeV and per stopped muon is obtained for the energy interval between 45 and 50 MeV. (Table 4.1). If the error is purely statistical, this indicates that 4 neutrons were measured in this energy interval. The total yield N is n dN Nn = di 'A E ' V fi' neff ' (3'32)

where AE is the width of the energy interval, N the number of stopped muons (4.10 ), n the detector opening angle ( 6*1% )

and neff the effective efficiency. Thus n = 4 . 10 between 45 and 50 MeV, which is more than a factor 10 lower than the efficiency of the neutron telescopes, even if only protons with

6r >0.85 are selected. 57

In experiments where time of flight spectroscopy of high energy neutrons is possible, like for instance in spectroscopy of high energy neutrons emitted after pion capture, the use of the neutron telescopes instead should be considered. In its present form its performance ( for 100 MeV neutrons ) in terms of resolution and solid angle efficiency is comparable with that of a time of flight measurement using a detector of the same size, three meters flight distance and 1 ns time resolution. In many cases the performance of the neutron telescopes can be improved by a smaller beamspot, a better resolution of the recoil angle measurement and probably also by a better energy resolution of the radiator and the stopdetector. 58

CHAPTER IV

EXPERIMENT I: EMISSION OF NEUTRONS WITH ENERGY BETWEEN 7.5 AND 45 MeV.

The energy- and asymmetry distributions of neutrons emitted after nuclear muon capture have been measured using six detectors as described in section 3.3. To suppress the background which is not correlated with muons stopped in the target the time differential method described in section 3.2 has been used. The abundant high energy gamma background which is caused by electrons from muon decay interacting with nuclei in the target ( bremstrahlung ) has been suppressed using an efficient pulse shape discrimination technique. The combination of techniques used leads to reliable results in the energy region between 7.5 and 45 MeV.

4.1 Mechanical setup.

The experiment has been done at SIN using a polarized u beam from the uE4 channel with a momentum of 70 MeV/c, a small contamination of ir ( 10 ) and about 10% contamination of e . A top view of the setup is shown in fig. 4.1. The muon beam was collimated by active collimators Cl, C2 and C3. The collimators are 20 mm thick. The holes in the collimators 2 2 are ellipsoidal with sizes 150 x 100 mm , 100 x 80 mm and 2 60 x 60 mm . They followed the 90% beam envelope as measured with wire chambers. The muon beam passed the plastic scintillators Si ( 10 mm thick ), S2 ( 5 mm thick ) and S3 ( 1 mm thick ) before it reached the target. To maximize the fraction of the beam stopping

in the target a CH2 degrader was installed between S2 and S3. A tartargee t of natural Ca with dimensions 6 cm x 6 cm x 1 g/cm was used.

J 59

Fig. 4.1. Schematic top view of the setup. Details are explained in the text.

It was positioned in the scintillator S4 which has the shape of an open box ( S3 forms the lid of the box ). S4 is 2 mm thick. Stopping muons were identified as SI. S2. S3. S4~ events; the box - shape of S4 has been chosen to reduce the number of false stop signals due to large angle scattering of the muon. The magnetic field needed for the muon spin rotation was generated by Helmholtz coils. The coils, with an inner diameter of 350 mm, an outer diameter of 556 mm, a thickness of 64 mm and a separation of 276 mm, consist of 4 subcoils with 450 windings of 1.18 mm thick cylindrical Cu - wires each. Each subcoil is cooled separately ( water cooling ). Both coils are mounted in a magnetic shield of 1 mm thick soft iron to provide a return path for the magnetic flux. A current of 4 A was applied; the field strength at the center was 0.0305 + 0.0001 T. The inhomogeneity of the field

AB B Z/ Z was =: 0.3% over a volume of 8*8*8 cm at the center of the field.

Six neutron detectors as described in section 3.3 were arranged in a circle at a distance of 30 cm from the target centre and at 60

Dump

590 MeV protons

S*K Concrete shielding =CH, shielding

Fig. 4.2. Layout of the SIN UE4 channel.

angles of ± 45°, ± 90° and ± 135° with respect to the beam axis. To be able to distinguish between neutral particles and the electrons originating from muon decay in orbit 1 mm thick plastic scintillators A , A„ A,- were positioned in front of each neutron detector. Charged particles from other sources, e.g. electrons from muon decay in the collimators or electrons from the muon channel, which entered the neutron detectors from the side and thus did not pass the scintillators A., caused the same detector signature as neutral particles. To recognize part of these events two large area veto counters PI and P2 were installed between the muon channel and the neutron detectors.

4.2 The muon beam.

A top view of the layout of the SIN \iE4 area is shown in fig. 4.2. Pions are produced by the 590 MeV, lOOjiA primary proton

J 61

beam in a 9.5 cm thick pyrolithic C target. Negative pions are analyzed and focussed by an injection system into a 5 m long superconducting solenoid with a field strength of 5 T. The pions can decay in flight. In this process negative muons with helicity ( projection of the spin on the direction of motion ) + 1 are produced isotropically in the rest frame of the pion. An extraction system serves to analyze the muon beam thus formed and to focus it on the experimental target. The muon channel was tuned using the general beam optimum found by C. Petitjean [PET 80] . In this setting the injection system of the channel was tuned to 134.5 MeV/c ( pions ) and the extraction system to 70 MeV/c ( muons ). Thus the muon velocity was smaller than the pion velocity and the muon beam had a negative helicity, the polarisation being = 80%. The fine tuning of the beam comprised a check on the position of the beam with respect to the holes in the active collimators, a check on the position of the focus with respect to the experimental target and an optimization of the thickness of the degrader. The checks have been carried out by slight variation of the currents in the analyzing magnet and the last quadrupoies of the extraction system and observation of the rates in the collimators and the various scintillators of the beam telescope ( SI, S2, S3 and S4 ). only minor corrections on the general beam optimum were necessary.

The degrader thickness has been optimized by maximization of the ratio SI. S2. S3. S4 / Si. S2 as a function of degrader thickness ( fig. 4.3 ).

4.3 Electronics.

A simplified block diagram of the electronics is shown in fig. 4.4. The simplification consists of removal of delays, 62

Degrader thickness—>

Fig. 4.3. The stopratio S1.S2.S3.S4 / S1.S2 as a function of the degrader thickness. The curve Is drawn to guide the eye.

5 of the 6 neutron detectors and some subsystems from the complete blockdiagram. The master trigger ( LflM ) is defined as a neutral or charged particle detected in one of the neutron detectors in a time interval ranging from 150 ns before to 850 ns after a muon stop signal SI. S2. S3. S? is received ( "y-gate" ), or as a light emitting diode ( LED ) event. The LAM is restricted by a few conditions. It is inhibited if ( SI + PI + P2 + cl + C2 + C3 ) fire in a time interval of + 10 ns with respect to the particle detection, since these events are mainly due to accidental beam electrons, electrons from muon decay in the collimator or particles emitted after pion capture in the target.

J 10

=J 2ND STOP

.IEAB TIME SCALE!

> Tl ME SCAUR

H -fÖS] II > AOC TOTAL ———^~ puütoeiT) 1HZ LED "BEAM" LCD DRiVCRS

Fig. 4.4. Simplified block diagram of the electronics. Details are explained in the text. 64

The LAM is inhibited in case S3 or S4 fire within 10 ns of the detection of a neutral particle since these events are mainly due to bremstrahlungsphotons produced somewhere in the setup by electrons escaping from the target box. If a charged particle is detected S3 or S4 is required to ensure that these particles emerge from the target box. Charged particles have been measured for calibration purposes ( cf. section 4.5 ) ; since not all charged particles detected are needed in the analysis the charged particle rate is reduced electronically by a factor 10 using a blockpulse called suppressor in order to reduce the trigger rate. The LAM is furthermore inhibited in case a muon stops in the target within 1 \xs from another muon stop ( 2 stop ) since these events give rise to ambiguities in the time information ( cf. 3.2 ).

Four types of events have been recorded during the experiment, i.e. neutral singles, charged singles, twofold coincidences of neutral particles and LED events. The event types are distinguished using the bit pattern recorded by a coincidence register ( pattern unit, p.u. ). Besides the pattern unit word the total charge in the detector pulse ( energy ) has been recorded for each detector firing, the time between muon stop and particle detection has been recorded for neutral and charged particles, and the charge in the tail of the detector pulse has been recorded for neutral particles in order to enable pulse shape discrimination ( cf. section 4.5.2 ) The time delay has been measured using a 100 MHz quartz clock. A train of clockpulses, started by the V - gate and stopped by the detector signal is fed into a CAMAC sealer. If no detector signal is received the end of the u- gate cleares the sealer. The detector signal is delayed by 150 ns with respect to the muon stop signal; thus during the first 150 ns of the U- gate only accidental background is measured. 65

4.4 The ONLINE program.

The experiment has been controlled using a PDF 11-34 computer provided with disc drivers, tape units, 128 k memory, keyboard, printer and a CAMAC coupler. A display was coupled to it via CAMAC. The software used is the program ONLINE, developed by F. Schlepütz LSCH 8l] from an older program, written by H.K. Walter. ONLINE is mainly written in assembler code. It is loaded under the DOS-Batch operating system, which is overwritten during execution to increase the memory space available for a display buffer.

ONLINE is quite a flexible program due to the use of an externally generated data file. In this data file a number of event types is defined, which are adressed by an appropriate code in the pattern unit readout. Furthermore the CAMAC stations in use are defined, as well as a number of tape buffers and a number of histograms. For each event type it is defined which CAMAC stations have to be read, in which tape buffer the information obtained has to be stored, which routine in the program has to be called for special calculations and which histograms have to be incremented. In this experiment 28 event types are specified: for each of the six neutron detectors a neutral or a charged single particle, the fifteen twofold coincidences possible and LED events. The events are temporarily stored in 4 tape buffers, one for neutral singles, one for charged singles, one for coincidences and one for LED events. For each of these classes of events a special routine is used. For charged singles and LED events the special routines only check if the parameters measured are in a predefined range to ensure that they are suitable for display. For the neutral singles and the coincidences however also a rough n-Y pulse shape discrimination is carried out to enable the observation of neutron spectra on line. A total of 128 one- or twodimensional spectra can be displayed to monitor the experiment. DECODE CAMAC CONFI- GURATION DECODE EVENT LIST DECODE DISPLAY LIST DEKINE TAPE BUFFERS DEFINE DISPLAY BUFFER

PRINT IMPORTANT ADRESSES OF BUFFERS ETC

KEYBOARD INTERRUPT

Fig. 4.5. Flow diagram of the ONLINE program.

During data taking the computer spends most of the time in a display routine, displaying histograms. If a master trigger ( LAM ) is received the pattern unit word is read which points at a location in the list of event types. If no existing adress is read the program returns control to the electronics ( end of busy ) and continues displaying; otherwise the program reads the CAMAC stations and copies the information to one of the tape buffers. If the tape buffer is full it is dumped to tape. Hereafter control is returned to the electronics. Meanwhile the program carries out the special routine and increments the histograms, which processes may be interrupted by a new event. If it is not interrupted, it continues displaying.

i 67

4.5 Data reduction and analysis.

During one week of beam time 4.10 valid muon stops SI. S2. _ 7 S3. S4. B. 2nd have been registered. 7.10 events have been stored on tape, flbout half of the data concerns electrons, mainly from muon decay in orbit, 80% of the rest of the data concerns gammas from decay electron bremstrahlung und nuclear excitations. The rest of the data concerns neutrons, mainly of low energy. The data have been analyzed using the program MTSORT, written by A. Zglinski TzGL 8l| .

4.5.1 Electrons.

The charged particles measured are nearly all electrons emitted after muon capture in the target or in the scintillators S3 and S4. The energy spectrum of these electrons is a distorted Michel spectrum ( cf. section 2.2 ). Their angular distribution with respect to the muon spin direction is well known both from theory and experiment. The electrons have been used for three purposes: to obtain the polarisation of the muons in orbit, to stabilize the neutron detector response and to calibrate the neutron detectors. The polarization of the muons in orbit has been obtained from the electron time spectra ( fig. 4.6 ) and the theoretical value for the integrated electron asymmetry a = - - cf. section 2.1. The expression 3.12

Ca Ca Ca t/T N (t) = N„ ( 1 + a p c cos ( uP t + ^ ) e~ Ca

c c/T + Nc ( 1 + a^ p cos ( w^ t + C ) e~ c

+ B, (4.1)

J 68

Fig. 4.6. Time spectrum of electrons in detector 1.

where NG ( resp N ) is the intensity of electrons from muon decay in calcium ( resp carbon ), has been fitted to the electron time spectrum in the interval denoted by "a" in fig. 4.6. The random background B has been obtained from the region detected by "b". The mean life x for muons in calcium and T *-a C for muons in carbon have been obtained from literature ( for references: see [ERA 72]). The value for the experimental

a a a asymmetry ag p c found from the time spectra is -0.034 (2) from which value it follows

= - O. 102 (7) , (4.2)

in good agreement with the results of other experiments [EVS 67j , if C =1. The correction of instabilities in the response of the NE213 detectors proceeded in two steps. Short term ( =12 hrs ) instabilities have been corrected using the response cf the detectors to LED pulses. The LED's fired each second during the 69

20 40 —• DETECTOR RESPONSE ( arb.units)

Fig. 4.7. Pulse hight spectrum of electrons in detector 1. run, and every 165 seconds an LED record has been written to tape. In ths analysis pulse height spectra have been accumulated for each LED record. These spectra consist of a single peak with a width of about 2.5% FWHM, thus the positions of the peaks can be obtained with an accuracy of 0.2% FWHM. Between LED records all data containing pulse height information are divided by the position of the corresponding LED peak obtained from the subsequent LED record. The pulses of an LED are normally not stable over a period of a week. Therefore the long term ( =12 hrs ) instabilities are corrected using the position of the peak in the pulse height spectrum of charged particles, which is produced by high energy electrons (>17 MeV ), the Landau peak ( fig. 4.7 ). To calculate the correction factors the total runtime was divided in 12 hrs long periods and for each period pulse height spectra have been 70

60 70 80 9C 100 Oiscr parameter—>

Fig. 4.8. Distribution of the discrimination parameter. The smallest dots represent 2 or 3 counts per channel. The size of the dots increases in steps representing a factor 2. The largest dots represent 4O')6 to 8191 counts per channel. The curves bound the region of particles that are assumed to be protons. The cluster of events to the right is due to electrons generated by photons. The arrows indicate the position of the cuts shown in fig. 4.0.

accumulated for charged particles. The position of the Landau peak in these spectra could be obtained with an accuracy of about 0.1%- The correction is applied by division of all data containing pulse height information by the position of the corresponding Landau peak. These positions varied smoothly during the run over a range of 5%.

The calibration of the NE213 detectors for electrons is obtained from the position of the Landau peak. The calibration for protons is connected with this calibration through 3.1G. A small error is made in this connection since the energy distribution of the electrons which led to 3.10 is different from the distorted Michel spectrum measured in the muon experiment. As the stopping power for electrons in NE213 varies only 4% between 15 MeV and 100 MeV £STE 7l] this error has been neglected. 71

CHANNEL CONTENTS ÏARB. UNITS)

PROTONS

DISCRIMINATION PARAMETER

Pig. 4.9. Distribution of the discrimination parameter for low C left ) and high ( right ) detector response.

4.5.2 Neutrons.

The raw neutral spectra contain a large gamma contribution which is mainly due to electron bremstrahlung. This component has been removed by pulse shape discrimination in the off-line analysis. For each event a discrimination parameter has been calculated which is a function of the total charge in the detector pulse and the charge in the tail. Fig. 4.8 shows the distribution of this parameter for all values of the total charge. Fig. 4.9 shows the distribution for two values of the total charge. The contour shown in fig. 4.8 encloses the region of particles that are assumed to be protons; this region contains less than 1% gammas at low energy and less than 0.1% at high energy. 72

The neutron energy spectrum and the neutron asymmetry distribution a ( E ) ( cf. section 2.3 ) are obtained in two n n steps. First the recoil proton energy spectrum and the experimental asymmetry parameter a as a function of the recoil proton energy are obtained; subsequently these functions are unfolded. To obtain the recoil proton energy spectrum and -asymmetry the recoil proton energy range is divided in 5 MeV wide intervals and for each interval a time spectrum is accumulated. These time spectra are fitted using relation 3.7

N (t) = N ( 1 + aCa PCa cCa cos ( oof* t + ^a )) e"t/TCa + B p o P v l (4.3)

Ca where N and a are the recoil proton yield and -asymmetry P P parameter respectively. The transition from 3.7 to 4.3 is allowed since 4.3 is a sum of time spectra of neutrons with energy in the energy interval concerned or in higher energy intervals. In the fitting of 4.3 the parameters us., the Larmor frequency and $., the phase angle have been taken from the results of the fit of 4.1 to the electron data, since there they are determined much more precisely than can be done using neutron data, T , the mean life time of negative muons in calcium has been obtained from literature ( for references, see PEFA 721). The parameters N , a P C and B J P P are free parameters in the fits. The result of two of the fits is Ca shown in fig. 4.1C, a has been obtained using 4.2. From the fitting procedure isotropic ( N (E) ) and anisotropic .( N (E). a (E) ) recoil proton spectra have been obtained. The spectra have been converted into neutron spectra N (E) and N (E). a (E) using a matrix technique. The recoil proton spectra measured and the neutron spectra sought can be represented by vectors

P= (Np (Eo), 73

6x10

_1 LÜ 1 400 T X TP*Ut.^^ • i * u f 1T f, 1 rt 1/1 ••••• § 200 - 8 4 t o 0.2 Q4 0.6 0.8 1.0

Pig. 4.10. Time spectra of recoil protons with about 15 ( upper spectrum ) and 35 (lower spectrum ) HeV kinetic energy.

and

(Bo>, (4.4)

where EQ, E., represent energy intervals. The response of a neutron detector to a neutron spectrum can be represented by a matrix M:

P = MN {4-5, 74

M has been calculated using known crossections for neutrons interacting with hydrogen and carbon in the NE213 scintillator TcEC 79J . The calculations have been compared with the results of the calibration experiment described in section 3.3 and good agreement was found. The neutron spectra have been found from 4.5 using a generalized version of Cooks least square method [cOO 63J . In this method the neutron spectrum is sought ( by iteration ) which leads through 4.5 to a recoil proton spectrum which corresponds with the experimental spectrum in the X^ sense. In addition the deviations of the counters of all triplets of successive bins of the neutron spectrum from a straight line are minimized. Cooks method is especially suitable for smooth spectra which do not show strong fluctuations. The method is generalized in this work in the sense that the weights of each bin have been taken into account, whereas they are assumed to be constant in [COO 63]. To obtain the final neutron spectrum shown in Table 4.1 the spectra of the six neutron detectors were added to improve statistics. The total spectrum has been divided by the number of captured muons, the solid angle of the six detectors and the width of the energy intervals. The anisotropic part N (E).a (E) of the recoil proton spectra has been treated identically. The spectrum N (E).a (E) thus obtained represents the anisotropic part of the neutron spectrum. By division of this spectrum by N (E), the isotropic neutron spectrum, the energy dependent asymmetry parameter a (E) was found, which is presented in Table 4.2

4.5.3 Neutron - neutron ooincidenaes.

Neutron - neutron coincidences are selected from the experimental data in a similar way as the single neutron events. A real coincidence is defined as an event with |t -t_|< 20 ns,

tj and t2 being the time delay between the muon stop and the 1 75

E neutrons per MeV per E a n n n (MeV) captured muon (MeV)

7.5-10 ( 1.9 ± 0.5 ) . IQ"2 7.5-10 t 21 * 11 ) . IQ"3 10 - 12.5 ( 8.4 i 3.0 ) . 10"3 10 - 12.5 ( 48 1 22 ) . IQ"3 12.5-15 ( 8.1 1 1.4 ) . IQ"3 12.5-15 l 65 t 15 ) . IQ"3 15 - 20 ( 6.0 ± 0.6 ) . IQ"3 15 - 20 ( 140 1 30 ) . IQ"3 20 - 25 ( 3.7 t 0.2 ) . .O"3 20 - 25 ( 227 t 20 ) . lO"3 25 - 30 l 2.0 t 0.2 ) . IQ"3 25 - 30 ( 283 t 20 ) . IQ"3 10 - 35 ( i.3 i 0.1 ). 10"3 30 - 35 ( 29 ± 4 ) . IQ"2 35 - 40 ( 7.4 ± 1.0 ) . io"4 35 - 40 ( 27 ± 9 ) . IQ"2 40 - 45 ( 3.3 ± 0.8 ) . io"4 40 - 45 ( 27 ± 17 ) . IQ"2 45 - 50 ( 7.6 + 3.8 ) . io-5 45 - 50 ( 26 ± 24 ) . io-2 50 - 60 l 2.5 ± 1.8 ) . lo"5 6 60 - 90 ( 5.2 ± 3.6 ) . 10"

Table 4.1 Neutron energy spectrum. Table 4.2 Neutron asymmetry sptctru

detection of the first and the second neutron, respectively. 10 ns is the shortest time interval which can be measured in the experiment ( cf. section 4.3 ). This 10 ns represents 1 clockpulse. A better time resolution was not needed, since the accidental background is small compared to the real coincidences, fin accidental coincidence is defined as an event with |t -t |> 20 ns. One can distinguish between events which occur before the muon stops and thus are not correlated with it and events which occur after the muon stops and which may be correlated with it. Two major sources of background to the real coincidences which are correlated with a stopped muon exist: real coincidences which are not correlated with the stopped muon and accidental coincidences. The first has been obtained from the density of events in the real non-stop correlated region of the ^ vs. t., plane ( fig. 4.11 ) after subtraction of the density of events in the accidental non-stop correlated region. The latter has been found from the density of events in the accidental stop correlated region.

j 76

800

It2, 600 m ^

400 jn m 200

-J empty regions (antiprpmpt) , fa O 200 400 600800ns

Fig. 4.11. The definition of the various classes of coincidence events. I: real stopcorrelated region; II: real non-stopcorrelated region; III: accidental stopcorrelated region; IV: accidental non-stopcorreljted region.

The small number of coincidences does not permit a calculation of the en-argy spectra of the coincident neutrons. The results are therefore given as a function of a threshold energy for both recoil protons. The number of coincidences produced per captured muon has been calculated from the number N of coincidences measured P using the relation

dH _1_ 1_ (4.6) dcos9 4 n

where n is the number of detector combinations with the same angle 9 between the neutron directions,fl i s the detector solid angle, Nc is tne total number of captured muons and e is the mean efficiency of the neutron detectors. In the calculation of e it has been assumed that the neutron spectra for coincidences have the same shape as the neutron spectra for singles. In Table 4.3 the number of n-n events produced with proton recoil energies above 10, 15 and 20 MeV are given for 9 =100° and 9 = 135°. The 77

Recoil proton events .10 / muon capture neutron coincidences energy threshold neutron singles (MeV) t S ) 180° 135° 180° 135°

10 1.21 i 0.09 0.73 ± 0.06 1.08 t U. 16 0.6S 1 0.10 15 0.75 t 0.11 0.46 t 0.08 1.06 ± 0.19 0.65 ± 0.12 20 0.36 ± 0.13 0.17 ± 0.0B 0.88 t 0.32 0.42 ± 0.23

Table 4.3 Neutron-neutron coincidences with each neutron having a higher energy than the thresholds given.

data for opening angles of 45 and 90 are unreliable because of cross talk between nearby neutron detectors. Events with proton recoil energies above 25 MeV are probably all accidental background. The last columns in Table 4.3 gives the ratio of coincidences to singles. These ratios do not vary strongly with energy, which supports the way the mean efficiency has been calculated. 78

CHAPTER V

EXPERIMENT II: THE ENERGY REGION ABOVE 45 MeV.

The experiment discussed in chapter IV yields a neutron spectrum up to 45 MeV and an indication that the spectrum continues beyond that energy. This is very interesting since the energy transfer in the interaction 2.6 is limited to half 40 the muon mass, and as the neutron binding energy in Ca is 7.8 MeV no neutron should escape with more than 45 MeV kinetic energy. Our experience with the experiment described in chapter IV leads us to the conclusion that the spectrum beyond 45 MeV cannot be measured much more accurately using the muon beams presently existing, the method described in section 3.2 and the neutron detectors described in section 3.3. The main reasons for this are the intense neutron background in comparison with the low yield of high energy neutrons from muon capture and the tremendous loss in effective efficiency of the NE213 detectors due to the unfolding procedure. The neutron telescopes discussed in section 3.4 have a much higher effective efficiency. If the neutron yield between 60 and 90 MeV is indeed 5. 10 per MeV and per stopped muon, as is indicated in table 4.1, a neutron detector with 0.4% solid angle and the efficiency shown in fig. 3.7 will detect 360 neutrons in this energy region during three weeks of beam time (-10 stopped muons ), which is an important improvement. Furthermore, as can be seen from fig. 3.8 the sensitivity of the neutron detectors varies strongly with the incident angle of the neutrons. This feature can be used to suppress background by having the telescope axis at right angles to the beam axis since 79 the background originates mainly from the muon channel. The spectrum has been measured using two proton recoil telescopes. To suppress the accidental neutron background further the time differential method discussed in section 3.2 has been applied. An attempt has been made to measure the neutron asymmetry parameter by the muon spin rotatie -thod. Electrons from muon decay in orbit have been meas^ed for calibration purposes. The large background of photons generated by these electrons ( bremsstrahlung ) has been removed in the off-line analysis using the different pulse shapes of the secondary particles of photons and neutrons in the AE-E telescope discussed in section 3.4.3.

5.1 Mechanical layout.

A schematic drawing of the setup is shown in fig. 5.1. It is similar to the setup discussed in s-ection 4.1. A 66 MeV/c muon beam with a polarisation of about 80% stops at the center of the 2 target ( 60* 60* 15 mm ). The beam is collimated by active collimaters C1,C2,C3, each of which is 20 mm thick. The holes in 2 the collimators are ellipsoidal with sizes 150* 100 mm , 2 2 100* 80 mm and 60* 60 mm . They follow the 90% beam envelope as measured with wire chambers. The plastic scintillators S2 ( 5 mm thick ), S3 ( 1 mm thick ) and S4 ( 2 mm thick ) serve, in the combination S2.S3.S4, as a monitor for the stopped muons. The target is contained in the box formed by S4 and S3 at the center of the magnetic field of the Helmholz coils ( cf. section 4.1 ). Two proton recoil telescopes N and N_, as described in section 3.4, are positioned at ± 90 with respect to the beam axis at a distance of 30 cm from the target. All detectors were aligned using a laser beam, the estimated accuracy being 2 mm. The target is positioned by hand within the counter S4, the estimated accuracy with respect to this detector being 2 mm. The accuracy of the direction of the wire chambers in the neutron telescopes is 2°. 80

Fig. 5.1. Schematic top view of the setup. Details are explained in the text. The insert is a front view of the counter S4 holding the target.

5.2 Beam handling.

The SIN E4 channel has been tuned to a rauon momentum of 66 MeV/c. As initial settings of the injection- and extraction magnets the values found by C. Petitjean [PET 82] have been used. By fine tuning of the extraction system the beam profile has been adjusted so that a maximum ratio of the count rates S2.S3 and { Ci+C2+C3 ' was obtained. In this procedure the signals of electrons in all counters were suppressed electronically and the slits were fully opened. In a second step the stoprate S2.S3.S4 was reduced to 10 s by closing the slits partly. Finally the ratio of the countrates S2.S3.S4 and S2.S3 was optimized by ( slightly ) readjusting the positions of the slits. The rates measured for the final settings are given in Table 5.1. 81

Signal Rate ( s~ )

Cl + C2 + C3 93.7 . 103 S2 . S3 159.4 . 1O3 S2 . S3 . SÏ 100.0 . 103

Table 5.1. Signal rates at the end of the setup procedure.

5.3 Electronics.

a simplified block diagram of the electronics is shown in fig. 5.2. As in the scheme discussed in section 4.3 the master trigger ( LAM ) is defined as a charged or neutral particle or an LED event detected in the time interval ranging from 250 ns before to 750 ns after the muon stop. The LAM is inhibited in case C1,C2,C3 or S2 fires in coincidence with the particle detection, in order to avoid registration of events induced bv -4 pions ( 10 per muon ) or by beam electrons ( 0.1 per muon ) and events induced by muons previously stopped in one of the collimators. In case a neutral particle is detected the LAM is inhibited if S4 fires in order to suppress bremstrahlung events. In case a charged particle is detected S4 is required to ensure that the particle emerged from the target box. The charged particle event rate is suppressed by a factor 5 using a blockpulse called suppressor ( supp. in fig. 5.2 ) in order to reduce the trigger rate. The LAM is further inhibited in case a second muon stops within 1 JIS of the muon stop under consideration. This is done since for part of these events ( i.e. if the 2nd muon arrives before the particle is detected ) it is not clear which muon generates the event and thus the time information is ambiguous; the rest of these events is discarded to obtain a fixed inhibition time of ljis ( if this time is not fixed the

J 00 10

—U-p*—QSMSJiJ •ae

föTT-

h» ADC AE

|-> ADC2U0ÖC 'O > PU GATE HI—^ ADC NA1 —föm— DELAV F.LECSON jUPPee ^L-^ ABC RAD 0>' DELAY TBIGGEB ,Nt£.R FAN Oüf LED DRIVERS B,N SIGNAL 5HAPEB

VETO LED 3CALERS VErOLED &CALERS O 5 CAM AC SCALE» LOGICAL FAN-OUT ^ajrrru n I tlAWAi ai-A. tk LEO SCALED . j la-LTT-ü-l—»LXC bl.ALE8 ,«IAM! Ok PU -0= LCD"BEAM' \—| ——>nr. hi AI£> —TÖT— DISCRININAroR -^CAMACSCAILH ->LED SCALER I'lili» ••LEL- 5CALEB

Pig. 5.2. Simplified block diagram of the electronics. Details jre explained in tr,^ text. 83

shape of the time spectra varies with the countrate ). 10% of the LAM signals were inhibited due to the 2nd stop signal. In these cases the stop signal of the second rauon is not accepted because of a 1 ys long dead time in the S2.S3.S4 signal, thus the effective countrate is reduceü by 20% by this feature. Special care is given to the analog pulses, in particular to the signals of the stopdetectors (AE+Nal(Tl)). The reason for this is the shape of the stopdetector signal ( fig. 3.12 ). The front of this signal contains information on the AE signal, which is superimposed on the Nal(Tl) signal. If a long delay line is used for this signal the resolution of the AE signal is reduced. Thus the ADC's are set immediately after a coincidence between radiator and stopdetector is registered and cleared if the LAM is inhibited ( up to 2us later ). A fast busy signal spans the clearing time of the devices. The pulse of the stopdetector is fed into an LRS2249SG 12-fold ADC with separate gates. Three ADC's are used for each stopdetector. Each ADC is gated by a separate gate pulse. One of these gate pulses, called the "AE gate" overlaps the first 8 ns of the stopdetector pulse, a second one, called "2ndAE gate" overlaps the first 30 ns of the stopdetector pulse and the third one, called the "Nal gate" starts 30 ns after the beginning of the stopdetector pulse and lasts for 200 ns, which is the maximum gating time permitted for these ADC's. The "AE" response is used in the off-line analysis to deduce the energy loss in the AE detector in case there is a large Nal siqnal, the "2ndAE"' is used for that purpose in case there is a small Nal signal ( then it has a much better resolution than the "AE" response ) and the "Nal" is used to deduce the energy loss in the Nal(Tl) detector.

The radiator signal is also fed into the LES2249SG. The corresponding gate pulse is 30 ns long and it is timed by the radiator signal. The electronics needed for the wire chambers, which is not 84

Signal ,1 Rate ( B ' )

LKD ( trigger ) 100 j 15') . 10* i LED . 4 'J'i.S 2 . 1 . 4 102 . lu LED . 4 . Busy OS.l 2 . 3 . 4 Bus.1/ BB.2. lu' J LED . 4 . Busy. 2nd 'J.'j 2 . 1 . 4 Busy. 2nd 9.1. io Rl . Nl MJ.4 Rl . Nl 267 R2 . N2 93. .'• V2 . N2 260 Rl . Nl . AÏ 'M.4 Rl . N.! . AT 23.Ü R2 . N2 . A2 'H.-1 R2 . N2 . A2~ lb.o LAM 1 14.1 Tota.1 efficiency 75.(. LAM 2 13.6

Table S.2. Electronic efficiency Table S .3. Signal rate during the during the run. run.

shown in fig. 5.2, is discussed in section 3.4.4. Both radiators and both stopdetectors are provided with light emitting diodes. During the experiment the LED's are pulsed with a frequency of 1 Hz. The LED signals are not only used to monitor the stability of the detectors, but also to monitor the electronic efficiency. For this purpose the LED trigger simulates a stopped muon, thus an LED event is treated electronically as a valid neutral event. At 10 different points in the setup I in fig. 5.2 denoted by "I" ) a sealer, gated by the LED trigger counts the number of signals. Division by the number of LED triggers gives the electronic efficiency, tabulated in table 5.2.

A second sealer at each point "I" can run for a predefined time and thus measures the signal rates at these points, ft typical readout is tabulated in Table 5.3. A third sealer is a CAMAC sealer which counts continuously. It is copied to tape regularly. Six different types of events are processed during the experiment, i.e. neutral particles and charged particles in

J 85

detector 1 and detector 2 ( 4 types ), coincidences between detector 1 and detector 2 and LED events. Information concerning the event type is stored bitwise in a Lecroy 2341A coincidence register ( pattern unit ).

5.4 The ONLINE program.

The experiment is controlled using che ONLINE program, described in section 4.4. For this experiment the ONLINE program is extended with a wire chamber readout routine, which is necessary since the SIN WCRS system is not a standard CAMAC device. Instead it generates an internal LAM as long as any register is set, and only the highest adress of the registers set can be read. Thus wire chamber readout consists of a series of command sequences " TEST LAM ; READ AND CLEAR REGISTER ; CLEAR LAM ". The wire chamber readout routine transforms the information thus obtained into the sizes and the positions of all groups of adjacent wires ( clusters ) which are set. If however any wire plane contains more than two clusters the routine drops the event and returns control to the electronics ( end of busy ).

After an event interrupt ( LAM ) is received the program reads the pattern unit word. This word is compared with a predefined list of event type codes. If no matching code is found the program returns control to the electronics. Otherwise the appropriate CAMAC stations ( up to 2 "time" sealers, up to 8 ADC's) are read and, if necessary, the wire chamber routine is called. Then the information is copied to the appropriate tape buffer. Four tape buffers are available, one for neutral singles, one for charged singles, one for coincidences and one for LED events. Hereafter the program checks if room is left for events in the tape buffer. If not, the CAMAC sealers containing information on the signal rates are read and copied to the tape buffer, which is then dumped on tape. Hereafter control is returned to the electronics. 86

Then the calculations needed to update the software monitor are carried out, which process can be interrupted by the next LAM. The software monitor consists of a buffer containing data for 128 different spectra, scatter plots, wire chamber profiles etc. Two onedimensxonal spectra or one twodimensional spectrum can be selected for display. After updating the display buffer the ONLINE program continues displaying until it is interrupted by the next LAM.

5.5 Data reduction and analysis.

After three weeks of beam time the total number of events stored on tape was 2.5 . 10 . The event description is 23 ( 16-bit ) words long for singles, 46 words long for coincidences and 10 for an LED event. About half of the data concerns electrons, mainly from muon decay in orbit. 99.1Z of the rest of the data concerns photons from decay - electron bremstrahlung and nuclear excitations. About 0.15% of the events are neutrons. The data have been analyzed using the CEBN subroutine package HBOOK.

5.5.1 Electrons.

The charged events measured have been used to check the alignment of the proton recoil telescopes, to calibrate the radiators, to monitor the stability of the radiator- and stopdetector response in the long run and they have been used to obtain the polarisation of the muons in orbit. The alignment of the recoil telescope has been checked by extrapolation of the tracks of the electrons in the wire chambers to the backside of the radiators, the frontside of the stopdetectors and the position of the target. Scatter plots have been accumulated of the coordinates of the tracks in these planes 87 from which the position of the target, the radiators and the stopdetectors with respect to the wire chambers can be deduced The scatter plots for backside radiators and frontside stopdetectors show misalignment less than 1 mm; no correction has been applied for this. The scatter plots at the position of the target show deviations between 2 mm and 11ram, whic h may be caused by an error in the target position, the position of the beam or the wire chamber direction. This misalignment has been taken into account in the final analysis by the assumption that the neutrons originate from the center of gravity of the electron distribution.

The correction for gain instability of the photomultipliers of the radiators and the stopdetectors has been applied in two steps. For the short term (-12 hrs ) the LED signals have been used. During the run every 100 seconds an LED record has been written to tape. In the off-line analysis spectra of the LED pulses have been accumulated for each LED record separately; the centroids of the peaks can be calculated with an accuracy of = 0.2% FWHM for the stopdetectors ("Nal") and of = 0.5% for the radiators. The numbers thus found show smooth variations over up to 4% during a 12 hrs long period. In between LED records all data containing pulse height information are divided by the centroid of the LED peak of the corresponding detector obtained from the subsequent LED record in order to correct for these variations. The "AE" response and the "2ndAE" response are corrected using the centroids of the "Nal11 LED peaks.

For the long term the electron pulse height spectra are used to correct for gain instability of the photomultipliers. This has been done because the LED light output can be unstable over a period of several weeks. For this correction the run has been divided into 12 hrs long periods and for each period spectra have been accumulated of the response of the radiators and the stopdetectors ("Nal") to charged particles with the LED correction taken into account. The radiator spectra thus obtained show a

J 88

100 200 300 «00 500 Radiator response (Channel number)

5.3. Response of radiator 1 to charged particles.

strong peak due to relativistic electrons losing part of their energy in the radiator, the Landau peak ( fig. 5.3 ). The "Nal" response has a triangular spectrum ( fig. 5.4 ). The centroids of these spectra can be calculated with an accuracy of 0.1% FWHM ( radiators } and 1.0% ( stopdetectors ). For two of the detectors the variation of the centroids is insignificant, which indicates that the LED correction is sufficient. For one of the radiators and one of the stopdetectors the centroids show smooth variations over 4% and 8% respectively, which means that the LED's were unstable. These variations are compensated in the final analysis.

The energy calibration of the radiators is described in section 3.4.2.1. The muon polarisation in orbit has been deduced from the time spectra of charged particles, of which fig.5.5 shows an example. The expression 3.9 was fitted to the data in the interval marked "a" in fig. 5.5: 89

Fig. 5.4. "Nal" response of stopdetector 1 to charged particles. 100 200 300 .Nal" response (Channel number)

GCa cos e"t/TCa

C ""t/x + Nc ( 1+ a| PC CC cos ( oi, t + $^ )e c

+ B, (5.1) where N ( resp N ) is the intensity of electrons from muon decay in calcium ( resp carbon ). The random background B was obtained from the region marked "b" in fig. 5.5. The mean lives

TC for muons in calcium and T„ for muons in carbon were obtained from literature ( for references: see QERA 72] ). The value found for aCapCacCa is 0.047(1), which is different from the value 0.034(2) found in section 4.4 mainly because the energy thresholds for the detection of electrons is different in both cases ( cf. fig. 2.2) In experiment I the electronic energy treshold is 200 keV, whereas in experiment II the electrons have tp pass through 9.5 g/cm of matter ( target, detector S4, return yoke of the Helmholz coils, anticounter, radiator and wire chambers ) in 90

200 £00 600 ,_^ 800 1000 (ns)

Fig. 5.5. Time spectrum of charged particleb in detector 1.

order to be detected. The electron energy treshold is 19 MeV. To compensate for this effect the theoretical asymmetry has been calculated from

a . = ƒ a (E) N (E) dE , (5.2) th 19 MeV th th

where a , (E) and N (E) were taken from [GIL 6Ö1. From the Ca Ca Ca ^- Ca-' experimental value of a p c and a , = a it follows e y th e

Ca Ca P C = - .105 (8) (5.3)

5.5.2 Neutrons.

To distinguish between neutrons and photons scatter plots have been accumulated of the "Nal" - vs "AE" response and of the "Nal" - vs "2nd AE" response to neutral particles ( fig. 5.6 ). 91

"AE"( arb.units)

Fig. 5.6. Correlations between the "AE" response and the "Nal" response of stopdetector 1 for neutral primary particles. The curves bound the region of particles that are assumed to be protons.

The position of an event in these plots strongly depends en the nature of the particle produced in the radiator. One can easily distinguish between electrons ( mainly produced by photons ) and protons ( mainly produced by neutrons ). Events within the boundaries drawn in fig. 5.6 are assumed to be protons. This is not strictly true for the low energy particles stopping in the AE detector; a fraction ( =10% ) of these particles are deuterons and alphas. Since the "2nd AE" response has a better resolution for low energy protons than the "AE" response, it is used for the identification whenever this is possible. If overflow occurs for the "2nd AE" the "AE" response is used. For protons the next step in the analysis consists of the calculation of the recoil angle using the coordinates in the 92

Cluster center \ •!• > 4-Sensitj I | area wire I i^Wires

Expected cluster size Cathode planes

^Cluster centre 4 I I I I I I I I I I i l .|.|.|.|.|.|.|.|.|u|\ I I I I I I I I I I I I I I I I I I I I I I I I I

"\ Particle track

Fig. 5.7. Tho relation between cluster size and cluster positions.

four wire planes. The coordinates are also used to calculate the correction for the position dependence of the stopdetector response and the radiator response. To calculate any of these parameters accurately the track of the proton in the wire chamber has to be defined well, i.e. one and only one group of adjacent wires (clusters) per plane has to .a set. Events for which the wire chamber signal in one of the planes was missing ( =9% per plane ) are not taken into account. Events with more than one cluster in any plane (^ 7% per plane ) can in most cases still be used. The latter events are partly due to crosstalk ( not necessarily to an adjacent wire because of the geometrical and electronical configuration of the preamplifiers etc. ). to large clusters in which one or more wires produce a signal below the discriminator level and to delta rays induced by protons in the radiator. The events with two clusters in any plane were analyzed using the size and separation of the clusters. As is shown in fig. 5.7 the size of a cluster can be calculated from the positions of the clusters

J 93 in the planes with the same wire orientation. Moreover, the sizes of the clusters in both planes are about equal. For the majority of events with two clusters in one plane the cluster separation is only one wire, the size of both clusters is smaller than the calculated cluster size and the size of the combination of both clusters agrees with the calculated cluster size ( - 1 wire ). In these cases it is assumed that the signal of one wire in a large cluster is not observed. The two clusters are replaced by the combined cluster.

Another type of double cluster event has a larger cluster separation and the size of one of the clusters of the pair and the size of the cluster in the corresponding wire plane agrees with the calculated cluster size ( ± 1 wire ), while the size of the other cluster of the pair does not agree. For those events the second cluster of the pair is removed. A third type of double cluster event shows a variety of cluster configurations, but the neutron energy that can be calculated using any combination of clusters varies over less than 10%. In these cases that combination of clusters is used which leads to the neutron energy closest to the mean value. The above three types of double cluster events comprise 70% of all double cluster events. The tracks in the wire chambers are extrapolated to the front side of the stopdetector and the backside of the radiator and the coordinates of the intersection points are calculated. From the energy information ( see next paragraphs ) the ranges of the proton in the detectors are roughly calculated and using these ranges the coordinates of the point where the neutron interacted with the proton in the radiator and the point where the proton stopped in the stopdetector are calculated. Then the coordinates of the centers of gravity of the light production in both detectors are calculated and for these points the correction factors for the position dependences of the response. Using the response of the stopdetectors for protons, 10

Energy spectrum of recoil protons

I/)

Fig. 5.a. Energy spectrum of recoil protons. corrected for gain instability of the photomultipliers and the position dependence, the stopdetectors have been calibrated following the method described in section 3.4.3.2. From the calibrations found and the response of the stopdetector the energy deposit in the Nal(Tl) crystal is calculated and, using that and the response function of the ^E detector ( section 3.4.3.1 ) the energy deposition in the AE detector. To calculate the energy in the layers of matter in between the active parts of the radiator and the stopdetector these layers are approximated by a single layer of aluminum, which is a good approximation since most of this matter is aluminum, some of it is lighter ( H,C,O ) and some heavier ( Ar,W,Au ), and the energy loss is usually less than 1 MeV. The calculation is done using an emperial range-energy relation from [GOO 60] adapted to data for aluminum by £RIC 54]:

J 95

E = E - E „ = 24.71 (At/cos9 + R ) °-552_ Al tot stopdet. p Al E stopdet (5.4)

where E and E , are the energy deposit in the absorbers and Al stopdet the stopdetector, respectively, E is the proton energy when it leaves the active part of the radiator, At = 95 rag/cm , the absorber thickness, 9 the incident angle of the proton and the range of protons with energy E in aluminum.

„-3 „1.812 R = 2.99 . 10 . E_:!*:_ (5.5) A1 "stopdet

which is also obtained from [GOO 60] . From E , the response of the radiator and the response function of the radiator ( section 3.4.2.1 ) the energy deposition in the radiator is calculated. The proton energy E is found by addition of all energy deposits ( fig. 5.8 ). The proton recoil angle 8 is calculated from the position of the centre of gravity of the target distrii.--y.tion found in the alignment check ( x , y ) and the distance between target and detector z , the coordinates of the point where the neutron interacted with the proton ( x ,y ,z ) , which is calculated using the coordinates of the P P P track in the wire chamber and the range of the proton in the radiator, and the coordinates of the track in one of the wire chamber planes ( x ,y ,z ). The neutron energy E is calculated using ( c.f. 3.4.1 )

E = E / cos2e n p r (5-6)

The energy spectrum of all neutrons measured is shown in fig. 5.9. The target-correlated component of the neutron energy spectrum is obtained by fitting of the time spectra. To do this the neutron energy range of 0-100 MeV has been divided into intervals of 2.5 96

50 60 70 80 90 100 En(MeV|

Fig. 5.9. Energy spectrum of all neutrons. The detector efficiency is not taken into account. The last channel contains all overflow.

MeV wide and for each of these intervals and for all neutrons with E > 100 MeV time spectra are accumulated. These time spectra are accumulated for three intervals in cos28 ranging from 0.55 to 1.0, each interval having a width of 0.15. In this way the effects of multiple scattering of neutrons and of the bad energy resolution ( cf. table 3.4 ) for small values of cosz6 can be inspected. Examples of the time spectra are shown in fig. 5.10. The time spectra are fitted using the relation 3.8:

Ca Ca t/T Nn(t) = (E) P C cos Ca e- Ca (5.7) + B,

where NCa is the intensity of the target-correlated component of

the energy spectrum. NCa(E) and B(E) for the three intervals in 2 cos 8r are shown in fig. 5.11. The values of a (E) , found from

J 97

50-

60MeV«En<70MeV

100H

50- T Ê 200- Counts/Channel

100-

.*•.•*.•••.«.,* 0.2 aï oü 0.8

Fig. 5.10. Time spectra of neutrons in detector I for three intervals in E

2 Ca Ca cCa and 53 fQr all intervals in cos e together and for n r various combinations of energy intervals are shown in fig. 5.12. The neutron energy spectra thus found have been corrected for the detector efficiency employing the results of the efficiency calibration experiment discussed in section 3.4. The spectra found are given in Table 5.4. They will be discussed in chapter 6. 98

300

Fig. 5.11. Neutron background ( open circle* ) and yield corrected for background for three intervals in cos 0 .

50 100

En(MeV)

Pig. 5.12. The neutron asymmetry parameter. 99

Energy interval Detector 1 Detector 2 Sum

12.5 - 15 17 ( 4) . IQ"3 22 5) . to"3 19 ( 3) . ID"3 15 - 17.5 87 (12) . io-4 134 (22) . io~4 110 (13) . lo"4 17.5 - 20 bO ( 6) . io-4 75 (10) . IQ"4 68 I 6) . IQ"4 20 - 22.5 41 ( 3) . !0"4 43 ( 4) . to"4 422 (28) . 10"5 22.5 - 25 221 (17) . IQ"5 249 (22) . IQ"5 235 (14) . io~5 25 - 27.5 161 (11) . IQ"5 165 (14) . IQ"5 163 ( 9) . 10"5 27.5 - 30 115 ( 8) . 10"5 93 I 9) . ID"5 104 ( 6) . IQ"5 30 - 32.5 78 ( 6) . io"5 82 ( 8) . ID"5 80 ( 5) . ID"5 32.5 - 35 61 ( 5) . io-5 56 ( 6) . IQ"5 58 ( 4) . io"5 35 - 37.5 43 ( 4) . io-5 42 ( 4) . ID"5 427 (28) . io-6 37.5 - 40 36 < 3) . io-5 37 ! 4) . lO"5 362 (25) . io'6 40 - 42.5 301 (28) . io-6 31 ( 4) . io-5 303 (22) . io-6 42.5 - 45 211 (24) . to"6 28 ( 3) . IQ"5 247 (21) . ID'6 45 - 47.5 192 (20) . to"6 108 (21) . ID"6 150 (14) . IQ"6 47.5 - 50 136 (16) . io-6 139 (18) . IQ"6 137 (12) . ID"6 50 - 52.5 112 (16) . to"6 102 (16) . ID"6 107 (11) - IQ"6 52.5 - 55 91 (14) . io-6 99 (16) . IO-6 95 (11) . ID"6 55 - 57.5 76 (12) . IQ"6 68 (14) . to"6 72 ( 9) . 10"6 57.5 - 60 67 (12) . ID'6 50 (11) . IQ"6 59 I 8) . 10"6 60 - 62.5 44 ( 8) . io"6 20 ( 6) . 10"6 32 1 5) . ID"6 62.5 - 65 45 ( 8) . IQ"6 36 ( 9) - ID"6 40 ( 6) . lO'6 65 - 67.5 12 ( 7) . to"6 32 ( 8) . IQ"6 22 ( 5) . IQ"6 67.5 - 70 13 ( 6) . ID"6 15 ( 6) . ID"6 14 ( 4) . io-6 70 - 72.5 0 ( 3) . 10"6 12 ( 7) . to"6 6 ( 4) . lO"6 72.5 - 75 84 (28) . io-7 6 ( 3) . IQ"6 75 (22) . ID"7 75 - 77.5 3 ( 4) . lO"6 8 ( 3) . ID"6 53 (26) . ID"7 77.5 - 80 13 (13) . lo"7 6 ( 3) . ID"6 37 (17) . IQ"7 80 - 82.5 40 (26) . 10"7 88 (29) . IQ"7 64 (20) . io~7 82.5 - 85 56 (28) . 10"7 15 (15) . ID"7 35 (16) . IQ"7 85 - 87.5 27 (13) . IQ"7 0 13 ( 7) . io"7 87.5 - 90 12 ( 9) . io-7 27 (14) . ID"7 19 (19) . io"7 90 - 92.5 0 0 0 92.5 - 95 0 12 (12) . ID"7 6 ( 6) . io"7 95 - 97.5 26 (13) . io-7 0 13 ( 7) . ID'7 97.5 - 100 0 0 0

Table 5.4a. Energy spectrum of neutrons emitted after muon capture in ""ca. Cut in cos28 at 0.85.

J 100

ïïnergyinterval Detector 1 Dtitectur 2 Sum

12.5 - 15 18 l 4) . 10~3 20 l 4) . io-3 19 ( 3) . 10"i 15 - 17.5 104 112) . io-4 157 (21)) . io-4 130 (14) . • .;-' 17.5 - 20 69 l 6) . !0-4 7U l 7) . to"4 70 ( 5) . !0-4 4 5 20 - 22.5 46 l 3) . io-" 42 ( !) • IQ" 440 (23) . IQ" 22.5 - 25 259 (17) . ïcf ' 1!U5 (21) . IQ'5 272 (14) . IQ"5 25 - 27.5 101 (10) . ID'5 207 113) . IQ'5 194 l 8) . io-5 5 27.5 - 30 125 ( b) . • o" 114 ( 9) . io-5 120 l 6) . IQ"5 30 - 32.5 91 ( 5) . io-5 94 ( 7) . io-5 93 ( 4) . io-5 32.5 - 35 71 ( 5) . io-5 69 ( 5) . ID"5 70 ( 3) . IQ"5 35 - 37.5 50 ( 3) . IQ"5 •17 l 4) . IQ"5 486 (26) . io-6 37.5 - 40 43 ( 3) . IQ"5 42 ( 3) . IQ"5 426 (23) . IQ"6 fc 40 - 42.5 3H1 (26) . i.r 46 ( 3) . IQ'5 371 (20) . IQ"6 42.5 - 45 270 (23 . io-6 J44 (2B) . IQ'6 307 (18) . io-6 6 45 - 47.5 199 (17) . IQ"6 164 (16) . .o' 182 (12) . 10"6 47.5 - 50 175 (16) . IQ"" 169 (16) . 10"6 172 (11) . IQ"6 50 - 52.5 119 (14) . ID"6 132 (14) . 10"6 125 (10) . io-6 52.5 - 55 102 112) . IQ"6 127 114) . io-6 114 l 9) . IQ"6 55 - 57.5 94 (11) - io-6 ')6 (12) . IQ"6 95 ( 8) . IQ"6 57.5 - 60 82 (10) . 10"6 75 ( 9) . io-6 7B l 7) . IQ"6 60 - 62.5 64 ( 9) . IQ'6 46 ( 8) . lO"6 55 l 6) . io-6 62.5 - 65 59 ( 9) . io"6 53 (10) . lO'6 56 l 6) . IQ"6 6 65 - 67.5 22 ( 7) . ,o" 27 ( 6) . IQ"6 24 l 5) . io"6 6 6 6 67.5 - 70 26 ( 7) . I0" 22 ( 6) . 10' 24 l 5) . IQ' 70 - 72.5 8 ( 5) . • o"6 23 ( 5) . io-6 15 l 4) . 10'6 72.5 - 75 16 ( 4) . .O"6 9 ( 4) . 10'6 125 (27) . io-7 75 - 77.5 2 ( 3) . io-6 8 ( 4) . IQ'6 50 (25) . 10"7 77.5 - 80 81 (24J . io-7 12 ( 3) . 10"6 100 (20) . IQ"7 80 - 82.5 7 ( 3) . IQ"6 93 (23) . lo"7 71 (19) . 10"7 6 82.5 - 85 ') ( 3) . ,o" 22 115) . io-7 56 (17) . IQ"7 7 7 7 85 - 87.5 29 (15) . 10- 42 (14) . IQ" 35 (10) . io- 87.5 - 90 0 ( 3) . I0"6 24 (12) . IQ"7 12 ( 6) . 10"7 90 - 92.5 -32 (19) . IQ"7 6 ( 6) . !0"7 -12 (10) . IQ"7 92.5 - 95 12 (IS) . io-7 6 ( 6) . !0~7 9 ( 9) . io-7 95 - 97.5 -6 (12) . io-7 0 -3 ( 6) . IQ"7 97.5 - 100 11 l 5) . to"7 0 53 (25) . !0-8

Table 5.4b. Energy spectrum of neutrons emitted after rauon capture in Ca. Cut in cos20 at 0.70.

J 101

Energy interval Detector 1 Detector 2 Sum

12.5 -• 15 18 ( 4) . ID"3 20 I 4) . lO"3 19 ( 3) . !0"3 4 4 15 • 17.5 104 (12) . to'4 155 (26) . lO" 130 (14) . 10" 17.5 -- 20 71 ( 6) . io"4 70 ( 7) . IQ"4 71 ( 5) . lo"4 20 • 22.5 48 ( 3) . IQ"4 47 ( 3) . IQ"4 474 (23) . 10"5 22.5 -- 25 299 (16) . IQ"5 319 (20) . io"5 309 (13) . JO"5 25 - 27.5 209 (10) . ID"5 228 (13) . io"5 219 ( 8) . lO"5 27.5 -- 30 143 ( 7) . io"5 148 I 9) . io"5 145 I 6) . io"5 30 - 32.5 105 ( 5) . io"5 113 ( 6) . IQ"5 109 ( 4) . io"5 32.5 •- 35 87 ( 4) . io"5 82 I 5) . 10"5 85 I 3) . IQ"5 35 - 37.5 59 ( 3) . IQ"5 56 I 4) . 10"5 579 (24) . 10"6 6 37.5 •- 40 503 (28) . xo" 48 ( 3) . IQ"5 493 (21) . io"6 40 - 42.5 448 (25) . ie"6 434 (28) . ID"6 441 (19) . ID"6 42.5 - 45 346 (21) . ID"6 359 (24) . ie"6 352 (16) . JO"6 45 - 47.5 258 (17) . IQ"6 223 (18) . IQ"6 240 (12) . IQ"6 47.5 - 50 219 (16) . ID"6 199 (15) . ID"6 209 (11) . io"6 50 - 52.5 165.(15) . IQ'6 166 (14) . to"6 166 (10) . ID"6 52.5 - 55 132 (13) . IQ"6 146 (13) . io'6 139 ( 9) . 10'6 55 - 57.5 129 (12) . ID"6 119 (12) . ID"6 124 ( 8) . ID"6 57.5 - 60 99 (11) . 10"6 111 (11) . IQ"6 105 ( 8) . io-6 60 - 62.5 73 ( 8) . 10"6 68 ( 9) . 10"6 71 ( 6) . 10"6 62.5 - 65 68 ( 8) . IQ'6 59 ( 9) . 10"6 64 I 7) . ID"6 65 - 67.5 53 ( 8) . IQ"6 42 ( 7) . io"6 47 I 5) . IQ"6 67.5 - 70 40 ( 7) . IQ"6 29 ( 7) . IQ"6 35 ( 5) . to"6 70 - 72.5 22 ( 6) . IQ"6 32 ( 6) . 10"6 27 ( 4) . io-6 72.5 - 75 17 ( 5) . 10'6 22 ( 5) . IQ"6 19 ( 3) . ID"6 75 - 77.5 11 ( 4) . io-6 12 ( 4) . 10"6 118 (28) . 10"7 77.5 - 80 11 ( 5) . io"6 6 ( 3) ,. ID"6 70 (28) . io"7 80 - 82.5 9 ( 3) . IQ"6 9 ( 3) . io"6 89 (22) . IQ"7 82.5 - 85 5 ( 4) . IQ"6 51 (17) .. io"7 5 ( 3) . io"6 85 - 87.5 51 (22) . io"7 88 (21) .. lO"7 65 (16) . IQ"7 87.5 - 90 4 (20) . IQ"7 35 ( 3) . IQ"7 20 (11) . lO'7 90 - 92.5 -23 (18) . IQ"7 42 (12) . IQ"7 10 (11) . ID"7 92.5 - 95 31 (18) . IQ"7 4 (10) . IQ'6 43 ( 5) . io"6 95 - 97.5 16 (12) . IQ"7 0 8 ( 6) . io"7 97.5 - 100 24 (11) . io"7 8 ( 5) . io'7 16 ( 7) . io-7

Table 5.4c. Energy spectrum of neutrons emitted after muon capLure in l>oca Cut in cos 9 at 0.55.

J 102

CHAPTER VI

RESULTS AND DISCUSSION

6.1 The neutron energy spectrum.

The inclusive neutron energy spectra measured in both experiments are shown in fig. 6.1. The results of Sundelin and Edelstein [SUN 7Ï\ are included for comparison. In view of the large difficulties encountered in the experiments the agreement is reasonable. The differences can be explained by systematic errors in the various measurements, which are not included in the error bars. With respect to the systematic errors the methods applied are to some extend complementary. The experiment discussed in chapter IV has yielded most accurate results for the energy spectra as

well as for the neutron asymmetry in the energy region 7.5 MeV 30 MeV. In both experiments there are three main sources of systematic errors in the measured neutron energy spectra. The first source is the efficiency calibration of the neutron detectors. This has in both experiments been done by means of a Monte Carlo calculation. The calculated efficiency curves have been checked in separate calibration experiments using high energy neutrons emitted after nuclear pion capture. Although the agreement is quite reasonable, systematic errors in the Monte Carlo calculations as large as 10% cannot be excluded. For the spectrum of neutrons emitted after nuclear pion capture the authors claim an over all error of 15% |_ISA 82j . The statistical errors are much smaller. A second source of systematic errors is the energy calibration of the detectors. Due to the steep spectrum an error of 5% in the

j 103

1Ö2 Lff*

-3 10

Q. O U

10 t

io"6

10 2O 30 40 50 6O 70 80 9O 100 • En(MaV)

Fig. 6.1. The measured inclusive neutron energy spectrum. Full circles represent the results of the experiment discussed in chapter IV. Open circles and crosses represent the results of the experiment discussed in chapter V with cos28 > 0.85 ( 0 ), with cosz8 > 0.70 ( x ) and with cos29 > 0.55 ( + ). The trianglesrrepresent the results of Sundelin and Edelstein [SUN 73]* 104

energy calibration causes a 25$ error in the yield at 25 MeV and a 40% error in the yield at 50 MeV. The error in the calibration of the detectors used in the experiments discussed in chapter IV is of the order of 5%; the error in the calibration of the neutron telescopes is smaller. The latter was checked using the peak in the spectrum of the total energy of two neutrons emitted back to back after nuclear pion capture in Li. The mean value found is 137 MeV, whereas 136 MeV is to be expected (fig. 3.18). A third source of systematic errors is the finite energy resolution of the neutron detectors. Due to the steep spectrum this tends to cause an overestimate of the yield in the spectrum. The error is of the same order of magnitude in both spectra, about 10%. For the experiment discussed in chapter IV there is still another important source of systematic errors, i.e. the unfolding procedure. The matrix M in equation 4.5 is calculated using a Monte Carlo code. This code depends on a number of crossections and angular distributions of which only part has been measured. The rest is based on calculations which in some cases are no more than educated guesses. This may lead to a wrong response function ( see also ^SUN 73], fig. 13; in our calculations similar deviations occur ). This, together with large statistical fluctuations due to the high random background may lead to large systematic errors especially above 30 MeV, where the background is relatively largest. For the experiment discussed in chapter V an important source of systematic errors is the neutron multiple scattering. As is discussed in chapter V this error can be minimized by selecting only recoil protons with a small recoil angle. In Table 5.4 the results are presented for three ranges of recoil angles: 0.55 _ 2 2 2

cos 6r £ 1.0, 0.70 < cos 6 £ 1.0 and 0.85 < cos 9 1 1.0. From the above considerations and an inspection of fig. 6.1 it can be concluded that the latter spectrum is the most accurate result currently available. It is presented in fig. 6.2. 105

10 30 50 70 90 • En(MeV)

Fig. 6.2. The measured inclusive neutron energy spectrum in comparison with the calculations of Madurga and of Kozlowski.

For a comparison with calculations of the inclusive neutron spectrum the energy range has to be divided into two regions C cf. chapter II ). In the region between 10 and 30 MeV the capture process is dominated by capture on a single proton. Here the results of our experiments are in agreement with the results obtained by Sundelin and Edelstein as well as with calculations using the impulse approximation in the independent particle shell model. In fig. 6.2 the rate in this region is compared with the calculations of Madurga, who used a simple statistical model [MAD 72]. To produce neutrons of higher energy at least 2 nucleons have to participate in the reaction. The rate in this region is compared with the result of calculations of Kozlowski [koz 83] . In these calculations the shape of the spectrum is calculated under the assumption that the muon is effectively captured by a correlated n-p pair. Here also a simple statistical model is used for the nucleus. 106

-0.8 -

100

Fig. 6.3. The measured neutron asymmetry parameter. Full circles represent the result! of the experiment discussed in chapter IV, open circles represent the results of the experiment discussed in chapter V,«represent the results of Sundelin and Edelstein [SUN 73] . The curve is the result of a calculation by Bouyssy and Vinh Hau [sou 73].

6.2 Neutron asymmetry.

The results of the neutron asymmetry measurements are shown in fig. 6.3. For comparison the results of Sundelin and Edelstein are added. The agreement is reasonable. The results are in disagreement with those of Evseev et. al. [EVS 6l] and those of Anderson et. al. [AND 65], who report on large negative values for the neutron asymmetry in accordance with predictions based on the simple closure approximation. Calculations in the impulse approximation predict a positive asymmetry far E > 20 MeV as a consequence of the momentum dependent terms in the weak interaction Hamiltonian. The energy dependence of the asymmetry parameter is however very sensitive to variations in the optical model parameters needed to describe the outgoing neutron, which 107

E^.E,, »10M*

O. a u "o

Fig. 6.4. Integral energy spectrum Fig. 6.5. Opening angle distribution of coincident neutrons for the opening of coincident neutrons. The curves angles 180° ( upper ), 135° and 90° show the shape of the opening angle ( lower }. The results for 90° are distribution of neutrons emitted not reliable because of crosstalk after pion capture in 59Co. between nearby neutron detectors.

makes it very difficult to extract information on the interactira. mechanism from the experimental data. One of the results obtained by Bouyssy and Vinh Mau [BOU 73] is included in fig. 6.3.

6.3 Neutron - neutron coincidences.

In the experiment discussed in chapter IV neutron - neutron coincidences have been observed. The number of neutrons measured

I 108

is insufficient to unfold the neutron energy spectra. Therefore the results are presented in fig. 6.4 as integral recoil proton energy spectra, i.e. only events with both protons having higher energy

than a certain threshold contribute to the spectra. The opening angle distributions of the neutron - neutron coincidences are shown in fig. 6.5. It is remarkable that the angular distribution is peaked at 180 . This indicates a capture mechanism in which a muon is captured on a pair of nucleons as is the case for pions.

To illustrate this similarity the shape of the angular 59 distribution of neutron pairs emitted after pion capture in Co 40 ( data for Ca are not available ) is also shown in fig. 6.5. If one of the neutrons would have been a secondary particle, the angular distribution would be peaked forward. A further indication that the n - n coincidences are the result of a direct process is the ratio of the number of coincidences to the ratio of single neutrons measured. This ratio hardly varies with energy ( cf. Table 4.3 ) , whereas preequilibrium calculations [koz 78] show that the slopes for secondary particle energy spectra are much steeper than those of directly emitted particles.

It may be concluded that a pion-like capture mechanism as proposed by Bernabeu, Ericson and Jarlskog explains the surprisingly high yield of high energy neutrons emitted after nuclear muon capture.

J 109

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J Ill

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SAMENVATTING.

In dit proefschrift zijn twee experimenten beschreven waarin het energiespectrum en het asymmetriespectrum van neutronen, die worden uitgezonden na vangst van muonen in 40Ca, zijn gemeten. In het eerste experiment lag de nadruk op het meten van deze spectra in het energiegebied 10 < E < 40 MeV. Emissie van neutronen in dit energiegebied kan worden verklaard met behulp van een directe reactie, waarbij het muon wisselwerkt met een enkel proton in de kern volgens de reactie u + p ->• n + v. Dit proces kan worden beschreven met behulp van de stootbenadering. In het tweede experiment is het neutron energiespectrum gemeten tot 94 MeV, de limiet die wordt op- gelegd door de wetten van energie- en impulsbehoud. Het is van bijzonder belang om het energiespectrum te meten tot de hoogste energie die kinematisch mogelijk is omdat met behulp van dergelijke metingen kan worden nagegaan of muonabsorp*~ie ook door middel van andere processen, zoals absorptie aan een gecorreleerd nucleonpaar, plaatsvindt. In de beide experimenten werden verschillende technieken gebruikt om de energie van de neutronen te bepalen. In beide gevallen werden de neutronen gedetecteerd met behulp van vloeibare scintillatoren. In deze scintillatoren verliezen neutronen hun energie hoofdzakelijk door de *H ( n,n' ) p reactie. Bij deze wisselwerking wordt een deel van de energie van het neutron overgedragen aan het proton. In het eerste experiment werd het spectrum van de terugstootprotonen gemeten. Het spectrum van de neutronen werd daaruit verkregen door ontvouwen. Voor het tweede experiment werd een dunne vloeibare scintillator gebruikt, zodat een groot deel van de protonen aan de achterzijde ontsnapte. De hoek tussen de bewegingsrichting van deze protonen en de detectoras werd gemeten met behulp van MWPC's. De terugstootprotonen werden vervolgens gestopt in een AE-E telescoop die bestaat uit een dunne plastic scintillator er. een Nal(Tl) kristal. De energie van de terugstootprotonen kon zodoende worden 114

bepaald uit de hoeveelheid licht die in de vloeistofscintillator, de plasticscintillator en het Nal(Tl) kristal werd geproduceerd. De energie van de neutronen werd daarna berekend uit de energie van de terugstootprotonen en uit de hoekinformatie. De diverse onderdelen van de neutronentelescopen waren zodanig gedimensi- oneerd, dat de combinatie van de efficiency voor 70 MeV neutronen en de resolutie optimaal was. De neutronen telescoop heeft een aantal voordelen in verhouding tot een enkele vloeibare scintillator. Het belangrijkste voordeel is het vermogen om van een enkel neutron de energie te meten, zodat de noodzaak tot ontvouwen verdwijnt. De ontvouwingsprocedure is een bron van grote systematische fouten, in het bijzonder als er een steil aflopend neutronenspectrum gereten wordt, zoals het geval is voor onze experimenten. Een tweede voordeel is de reductie van de toevallige achtergrond, die het gevolg is van de eis dat het terug- stootproton de AE-E telescoop bereikt. Aan deze eis wordt vaker voldaan voor neutronen die uit de richting van het target afkomstig zijn dan voor neutronen uit andere richtingen, zodat de detector een anisotrope gevoeligheid heeft. Als een gevolg van het niet behouden zijn van de pariteit in zwakke wisselwerkingen worden de neutronen niet isotroop uitgezonden met betrekking tot de polarisatie van de muonen. De intensiteit van de neutronen als functie van de hoek 9 tussen de richting van de impuls van de muonen en de richting van de polarisatie kan worden geschreven als

N ( 6,E ) = N1 ( E ).( 1 + a ( E ).P .cos ( 9 ) ),

waarin P de polarisatie van de muonen is. De asymmetrie parameter a is energieafhankelijk. Deze parameter werd gemeten met behulp van een sterk gepolariseerde muonenbundel. Deze metingen werden tegelijk met de metingen van de neutron energiespectra gedaan met behulp van de muon spin rotatie methode. 115

In het eerste experiment werden gebeurtenissen geregistreerd waarbij twee neutronen gelijktijdig werden gedetecteerd. De hoek- verdeling van deze neutronen onderling is achterwaarts gepiekt, hetgeen niet het geval zou zijn als deze gebeurtenissen te wijten zouden zijn aan wisselwerking van een primair hoogenergetisch neutron met de kern. In die gebieden die reeds eerder zijn onderzocht stemmen de resultaten overeen. In gebieden die niet eerder zijn onderzocht, met name bij de hoogenergetische neutronen en bij de coincidenties geven de resultaten aanleiding tot de veronderstelling dat er naast het guasivrije reactiemechanisme een tweede mechanisme werkzaam is, waarbij het muon effectief wordt ingevangen op een aantal nucleonen. Het mechanisme dat wordt voorgesteld door Bernabeu, Ericson en Jarlskog, waarbij het muon een pionveld induceert in de kern dat vervolgens wordt geannihileerd op een nucleonenpaar, is een goede kandidaat voor een dergelijk mechanisme.

I 116

SUMMARY.

In this thesis two experiments are described in which the energy spectrum and the asymmetry spectrum of neutrons, emitted after muon capture in l*°Ca, have been measured. In the first experiment the measurement of these spectra in the energy region 10 < E < 40 MeV has been emphasized. Emission of neutrons in this energy region can be explained by a direct reaction mechanism, in which the muon interacts with a single proton in the nucleus according to the interaction u + p •*• n * \>. This process can be described using the impulse approximation. In the second experiment the neutron spectra have been measured up to 94 MeV, which is the highest energy permitted by the laws of energy- and momentum conservation. Measurements of the spectra up to the highest energy kinematically possible are of special interest since from such measurements it can be deduced if muon capture also proceeds through other channels, like capture by correlated nucleon pairs.

In the experiments different techniques have been used to measure the energy of the emitted neutrons. In both cases the neutrons were detected using liquid scintillators. In these scintillators neutrons mainly lose their energy by the interaction 1H ( n, n' ) p. In this interaction part of the energy of the neutron is transferred to the proton. In the first experiment the energy spectrum of the recoiling protons has been measured. The energy spectrum of the neutrons was deduced from this by unfolding. In the second experiment a thin liquid scintillator has been used, which enabled the escape of recoil protons with sufficient energy. The angle between the track of these protons and the detector axis has been measured using MWPC's. The recoil protons were finally stopped in a AE-E telescope consisting of a thin plastic scintillator and a Nal(Tl) chrystal. The energy of the recoil protons could thus be calculated from the light produced in the liquid scintillator, the plastic scintillator and the Nal(Tl) chrystal and the energy of the 117 neutrons could be calculated from the energy of the recoil protons and the angular information. The dimensions of the parts of the neutron telescopes were chosen so, that an optimum for the combination of the efficiency and the resolution was met for 70 MeV neutrons. The neutron telescope has several advantages in comparison with a single liquid scintillator. The most important advantage is the capability to measure the energy of a single neutron, thereby avoiding the need to unfold a recoil proton spectrum. The unfolding procedure is a source of large systematic errors, especially when a steep neutron energy spectrum is measured, as is the case for our experiments. A second advantage is the reduction in random background which is the result of demanding that the recoil proton reaches the AE-E telescope. This demand is easier met for neutrons from the vicinity of the target than for neutrons from other directions, thus the detector has an anisotropic sensitivity. As a consequence of the non-conservation of parity in weak interactions the neutrons are not emitted isotropically with respect to the muon polarisation diraction. The neutron intensity as a function of the angle 9 between the muon momentum direction and the polarisation direction can be written as

N ( 8,E ) = N'( E ).( 1 + a ( E ).P .cos ( 9 ) ), u

where P is the muon polarisation. The asymmetry parameter a is energy dependent. This asymmetry was measured employing a highly polarized muon beam. These measurements were done simultaneously with the measurements of the neutron energy spectrum using the spin rotation method. In the first experiment events were recorded in which two neutrons were detected simultaneously. Proof was obtained that these events are not due to final state interactions of a primary high energy neutron with the nucleus. In those regions where a comparison with earlier experiments is 118

possible the results agree. In regions which were not explored earlier, especially for energies above 50 MeV-and-for-the coincidences, the results give rise to the assumtion that besides the well known quasifree reaction mechanism, in which the muon interacts with a single proton in the nucleus, there exists another reaction mechanism, in which the muon is effectively captured by a number of nucleons. The mechanism which is proposed by Bernabeu, Ericson and Jarlskog, in which a muon generates a pionfield which is subsequently annihilated on a pair of nucleons is a good candidate for such a mechanism. 119

CONTENTS

Voorv/oord •*

I INTRODUCTION 7

II THEORY 10 2.1 Muon decay i^ 2.2 The suon capture rate 13 2.3 Neutron emission 15 2.4 The target 20

III EXPERIMENTAL METHOD 21 3.1 General considerations ' 21 3.2 The time differential method 22 3.3 The NE213 neutron detectors 26 3.4 The neutron telescopes 30 3.4.1 General principles of the neutron telescopes 30 3.4.2 The radiator 32 3.4.2.1 The radiator response function 35 3.4.3 The AE-S detector 41 3.4.3.1 The response functions of the a£ and Nal(Tl) detectors 44 3.4.3.2 The energy calibration of bE and Nal 48 3.4.4 The wire chambers 50 3.4.5 The efficiency and resolution of the neutron telescope 54 3.5 Concluding remarks 56

IV EXFERIMEOT I: EMISSION OF NEUTRONS WITH ENERGY BETWEEN 7.5 flND 45 MeV 58

J 120

4.1 Mechanical setup 53 4.2 The muon beam 60 4.3 Electronics 61 4.4 The ONLINE program 65 4.5 Data reduction and analysis 67 4.5.1 Electrons 67 4.5.2 Neutrons 71 4.5.3 Neutron - neutron aoina-la&naeo 74

V EXPERIMENT II: THE ENERGY REGION ABOVE 45 MEV 78 5.1 Mechanical layout 79 5.2 Beam handling 30 5.3 Electronics 81 5.4 The ONLINE program 85 5.5 Data reduction and analysis 86 5.5.1 Electrons 86

5.5.2 Neutrons go

VI RESULTS AND DISCUSSION 102 6.1 The neutron energy spectrum 102 6.2 Neutron asymmetry 106 6.3 Neutron - neutron coincidences 107

References 109

Samenvatting 113

Summary 116