Scattering of polarized protons by yttrium, iron and nickel nuclei

Scattering of polarized protons by yttrium, iron and nickel

nuclei

Citation for published version (APA):

Melssen, J. P. M. G. (1978). Scattering of polarized protons by yttrium, iron and nickel nuclei. Technische

Hogeschool Eindhoven. https://doi.org/10.6100/IR134242

DOI:

10.6100/IR134242

Document status and date:

Published: 01/01/1978

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SCATTERING OF POLARIZED PROTONS BY

YTTRIUM, IRON AND

NICKEL NUCLEI

PR[]Ef'SCHRIFT

TER VERKRlJGING VAN DE GFAAD VAN DOCTOR IN OF TECHNISCHE WETENSCHAPPEN AAN DE TECHNISCHE HOGESCHOOL EINDHOVEN, OP GEZAG VAN DE RECTOR MAGNlFlCUS, PROF.OR.P.VAN DER LEEDEN, VOOR EEN COMMISSIE AANGEWEZEN DOOR HET COLLEGE VAN DEKANEN IN HET OPENBAAR TE VERDEDIGEN

OP DlNSDAG 16 MEl 1978 TE 16.00 UUR

DOOR

JOSEPH PETRUS MARIA GERARDUS MELSSEN

GEBOREN

TE

eRUNSSUM

DI'l' PROEFSCHRUT IS GOEDGEKEURD

DOOR DE l'ROMotOl\lm

PRQF.DR. D.J. POPPEMA

EN

CONTENTS

CHAPTER 1 IN'rRODUCTION AND SUMMARY

Referen~e:S

CHAPTER

n

Tll:» l>XPERlMENTAL ARRANGI':MENT FOR MEASUREMENTS

WITH A pOLARIZED PROTON BEAM 2.1 lntrodu~tio~

2.2 The polariz~d proton source

2.3 Th~ inje<:.tion and the acceleJ:"stion of the beam

2.4 B~am transport system

2.5 The 5~att~rins chamber and polari~aticn monitor

2.6 The eleou~onic equipment

Referen~e5

CHAPTER III PROCEDURE FOR MEASUREMENTS WITH THE POLARIZED

PROTON BEAM

3.1 IntroQuction

3.2 Experimental pJ:"oceduJ:"e

3.2.1 The mee-surement of the analys;i.ng power and the

5 6 6 6 9 10 II 13 17 18 18 18

differential cJ:"oss section 18

3.2.2 Be~ tuning and determination of the energie

of the beam 20

3.2.3 re-rgets 21

3.2.4 Scattering by a polyethylene and a ~lar

J.3 Sources of ~y"Cematic errors

3.3. 1 Non proper spin tIip

3.3.2 ,he (3.~tual s~atter~n8 "ogle

3.3.3 uncertainty in the polarization of the beam

3.4 The analysing power for 12

CCp

,p)

3.5 Analysis of the energy spectra

Refere.nt.es

CHAPTER IV SOKE ASPECtS OF TIlE THEORY OF ELASTIC AND

INELASTIC SCATTElUI'IG

4.1 Incroduction

4.2 Description of the ~"att"ring proceS5

4.1

The optical pocential

(,.3. I The phenome.nological optical potential

4.3.2 The refo~latcd optical potential

4.4 The Distorted Wave Born Approximation

4.4.1 General expressions

4.4.2 Macroscopic description

4.4.3 Microscopic description References

CHAPTER V THE SCATTERING OF POLARIZED PROTONS BY

lRON AND NICKEL NUCLEI

5.1 Introduutiol"l

5.2 ElaHic 5catteTing

5.2.1 Optical model analysis

5.2.2 Normalization of the differential cross

gec.t:io[~ 5.2.3 Di.aussioD 5.3 Inelastic scattering 5.3.1 DWRA analysis 5.3.2 Discussion References 22 22 23 23 25 25 28 29 Z9 30 34 34 36 37 37 39 42 46

48

48 48 48 52 57 60 60 76 17

CHAPTER VI ll'! 89y

THE SCATTERING OF 21.1 MeV POLARIZED PROTONS

6.1 l~trodu~tion

6.2 The experiment

6.3 Elastic scatt~ring

6.4

Inelastic scattering

6.4.1 Macroscopic DWBA analysis

6.4.2 Microscopic DWBA ana~ysis

6.5 Conclu",ions l\eferences SAMENVATTING NAWOORD LEVENS LOOP 79 7~ 80 82 83 83 89 97 98 101 103 104

CHAPTER I

INTRODUCT~ON AND SUMMARY

Toe study of nuclear scattering is an impdrtant ~ource of

information on nuclear structure. Especially the ~~attering of

protons ~[\d neutrons should be sensiti"e to details of the nuclear

wa"efunction~ because of the weak ab~orption of nucleons in the nucleus.

A more stringent test of the spin dependent parts of the interaction involved in the soattering process is provided by experiments with

pOlarized beams. In this thesis we present results of scatt~ring

experiments performed on yttri~ and some iron and nickel isotopes

with polarized proton beams at energies around 20 MeV.

In a scattering experiment a beam of particles is incident on a tat"get foil. An incident pat"ticle may be scattered by a target nucle·"S.

If the internal energy of the target nucl~us remains unchanged the

sca"tering is called elastic, whereas in an inelastic process a definite amount of the energy of the incident particle is used to excite the nucleus. A schematic diagram of a scattering prOcesS is given in figure

1.1, where the scattering angle

e

and the nOmlal to the scattering plane

Fig. 1. 1 Sah",matia diagram ()

f

a 8aattering pI'oae88.

+ ~ +

n are defined; k_i is the momentum of the inc~dent particle and k_f the

mo-mentum of the scattered particl~. As shown in figure 1.2 the energy spectrum

of the scattered particles at a fixed scattering angle reveals peaks wh~ch

correspond to the energies of the excited states of the nucleus. The

exci-tation strength of such a state is characterized by the differential

crOSS 'section do(9)/ dQ given by the n~ber of COl,lnlS in a peak, normalized

yith respect to the nuwber of incident particles, the Ul,lmber of targer

nuclei <atoms/cm2) and the solid angle in which the scattered protons are

'"

M'';[~.1'1

I" ,~I •. ~M,o\.I '~:ii')-rD'

'~I ~':'fl'((J,~,)

'"

F~I;g. 1.2 £'nel'gy "p&et:rum of 8oatteY'(ld pmtorlfJ. 'the loweY' and uppBr 5n oh(J,nncd" eorreepona to the diffBrent spin ori.mta'bions ( ) f the incoming beam.

~n experirn~I1ts with p,,] ad zed beams. 1n these experiments the differential cross section is given by:

dcr(e)/dn

-.

{J+P'~

A(S)}

do(8)/dtl

unpol (I. I)

whe:>:.;, p ,s the polari."atLon of the incident proton beam. Thus the analysing power i~ given by (1.2) as th~ difference ill cross sections for the opposjte spin directions, normalized to their sulll and to the d"gro!c of pola:dz-nioD of the beam;

A(S)

_p"

I _{(I. 2)}

The experi.mental arr.;inge.ment used in O\lr €:x-pe;r:i,.ments to roe~Sl.lre the. angular distrihutiol1s "f the dfffe>:enti<ll c>:oss sections and <Ina.lysi.ng powers ~8 described in chapter 2. In chapter 3 w~. rep'));-, IIP"n "ur

ex-perimental procedure and data analysis.

Information about an excited nuclear state like spin, parity and details of the wavefunc:tion i~ obtai.ned by comparing the angular distribution of the expe.rimentco1 oifterential cross sGOction and <lItalysing powo!r with I'r",di(O.tions from th"oreti<:al models. Usually the D.i.torted Wave Born App<oximation (DWIlA) is used to describe the. reaction at the bombarding

energies a~d for the target nuclei investigated in our expe~iment5. In this approximation it is assumed that the elastic scattering is far out

th~ most important process that occurs, so the inelastic processes can

be treated a6 perturbations. The n,htive motion of the protOn before and after the inelastic event is then described by elastic scattering wave-functions that are calculated in the optical model. In this model the

interaction of the projectile with the target nucleus i~ appro~imated

by a spherical potential which consists of a central comple~ part and a

spin-orbit part.

~o different models are currently used for the description of tIle

nuclear states. The collective model treats the nucleus as a whole and

the excited states are considered either as collective vib~ations of the

nuclear ~urface or as collective rotations of a permanently deformed

nucleus. Then the optical potential ~Dntains nonspherical parts which

give rise to the excitation of the nucleus, With this macroscopic DWBA

description only information about the colle~tive behaviour of the nucleus

is obtained. A more detailed picture of the nuclear states i~ provided

by the shell model, where the nuclear states are described in terms of

the motion of the individual nucleons. In the microscopic DWBA, based

on this model, the interaction which is re$ponsible for the exc~tation is

then ~omposed of effective two-body interactions between the projectile

nucleon and the target nucleons. The £0~li6m of the optical model and

the DWRA is summariZed in chapter 4.

'he macroscopic DWBA has been shown to reproduce the shape of the

angular distributions reasonably well for an e~tensive number of cases,

(5a70) x. Generally it is used as a reliable tool to determine the orbital

angular momentum transte~red to the target nu~leus. Mo~eDVer deformation

pa~amete~s obtained in this way agree well with the values determined from

other types of experiments. HoweVer, it is also known that the analysing

powers for the first excited 2+ states of some closed neutron shell

nuclei (N=28, N=50), m~a~ured with protons of abOut 20 MeV, are found

to be much larger as compared to neighbouring nu¢lei yith an open nelltron

shell or as compared to the ne~t excited state with the same target spin

(GI67, He69, G169J. Thi~ di$tinct behaviour can be de$¢ribed by the

macroscopic DWBA only if the spin-orbit term in the opti~al model

is deform~d two to three time~ a~ much as the central part, whereas

~ A li~t of references is given at the end of each chapter.

for n",i.ghbouring nuclei or higher "xci ted states no significant higher spin-orhit d",formation is n,;,.,d.,d. There sre indications that this e£fect might depend on the projectile energy. E~periments at 30 MeV and at 40

MEV show that th" analysing pow"r of the first excited 2+ state in

54Fe differs not significantly from analysing pow",rs of other 2+ states in this mass region (Ka70, Fr67); also in a recent experiment at 30 MeV on 90

z"(

and 92Zr no di.fferen"e~ are found between the first excited 2+

states of theses nlJclel. (3w]6).

To investigate a possihle energy dependence we performed .~ sed a8 of experiments On 54po;" 56 FIl , 58Ni , 60Ni and 62Ni with proton energies around 20 M"V, The results of these experiments are presented in chapter 5 togethe, with a macroscopic DWBA-8nalysis, In the data on th~ first "xcit"d state in 54Fe the anomalous

behavio~r

shows IJP indeed and also

it~ ene~gy

rlepen-dence is dearly ascertained" With t:atios of the deformation of the spin-orbit to the central part ranging from 1.5 at 24.6 MeV to 3.0 at 17.2 MeV good fits are "btained for th" measured analysing powel:"S, Ho"'ev",r, at an <In<lrgy of 15.3 M"V this parametriz{'Ition in terms of a larger spin-orbit deformation fails and we can not achieve a J:"easonl'ble h t to our data.

One can argu", whether full micro",cop~" ~alclJlations would be mor~ succcssflJl in des"ribing the soave menti.oneo effect~. Investigat£ons

of Raynal (Ra71) in this direction emphasi:<:ed the structural differences in the excited stat~s. wt,ich [0,," th.e closed neutron shell nuclei are expected te be dominat<ld by proton excitations. since the two-body ~pin-orbit intera~tion i~ strongeBt between like nu~l~ons indeed l.arger Rpin-orhit d-eformatioTIs,. in the ID.d.Cl"oscopi.(: DWllA1 s.r~ e:K-p"ct"d for proton~ exciting protons th9,n for protons exciting neutrons. S" far the D\icroscol'it:! analyses do not succeed very well in reproducing the data. 'rhi" might be partly due to the vse of i.nadequate expressions for th" nt.lcle.~r ",avefun~tions. Abo th" information abovt the non-central parts of the effe~.ti.ve nueleon-nuc.leon intGl:"actiol1 is scarce at preSent:.

To stlldy the micro"col?ic DWllA and to acquire information about the eff",ctiv" two-body spin-orbit force we performed an experiment on 89y . The gro1lnd and first exc:ited states of 89y are gener{'ll1y believed

L(' be well described by simp 1 e zero order 8hell model waVe flJnctions. Tne1 asdc sc.nteri.ng to these Rtate~ is thus regarded as a good test. for the eff"ctive interaction. Th" experimental result" al.d the

rnac~o5copic and ftIicro~copic DWBA analyses of this experiment are given in ch.pter 6.

Th" microscopic calculations reveal that only a reasonable fit to both

the diffe~ential cro~e ~"-etion and the an.lysing power is obtained if

along with the cOntribution of a sing.e-pa~ticl~ excitation also a

macroscopic corc-polari2ation component is taken i~to accQu~t. Iu

general th~ infL~~nce of the core-polarization contrib~tion i$ So

la~s:e that it obscl)1;es the information on the effective n~cl,eon-nucleon

interaction. Definite conclusions should ther~fore await a microscopic

description of the core-polarization contrib~tion.

REFERENCES

Fr67 M.P. F1;icke. E.E. Gross and A. Zucker,

Fhys. Rev. ~ (1967) 1153.

G167 C. Glashausser, R. d~ Swiniarski, J. Thidon and A.P. Hill,

Phys. Rev .

.0i

(l967) 1437.

Gl69 C. Glashausser, R. de Swinisrski, J. Coudergues, R.M. Lombard,

B. Mayer and J. thirion,

Phys. Rev.

l&i

(1969) 1217.

H~69 O.L. Hendrie, C. Glashausser, J.M.Moss and J. Thirion,

Phys. Rev. ~ (1969) 1188.

KaYO O. Karban, P.D. Greavee, V. Hnj,zdo. J. i,owe and G.W. Greenlees,

Nu<'-l. Phy~. ~ (1970} 461.

RaJl J. Raynal, Structure of Nuclei, Trieste Lectures 1971, p. 75.

SalO C.R. Satchler. Froe. third Int. Syrup. on Polarization Phenomena

1n Nuclear Reaction~, Madison. 1970 (eds. H.H. Barschall and

W. Haeberli, Univ. of Wi~conein Press, Madison, Wise. 1971)

p. 155.

Sw76 R. de Swini~rski, C. Bagieu, M. Massaad, Dinh-Lien Pham.

M.

Bedjidi~m.

J.Y.

Grossiord, M. Gusakow, J.R. pi,-z~ and

CHAPTER II

THE ExPERIMENTAL ARRANGEMENT POR MEASUKEMENTS WITH A pOLARIZED PROTON BEAM

2.1 Introduction

The experiments described i.n this thesis l1av", been performed with

the polarized proton beam of the Eindhoven Univer~i ty of Technology cyclotron (V,,62). 1ft the sections 2,2, 2.3 and 2.4 the polarized proton .~our(:e, the inj ecti on of the polari.ed beam into the c.yclotron and eh", beaUlguiding system are descdbed respectively. With this se.t. '"'1' we have S(lcce<:ded to obt"in a l'roton be"'m of, on the ",verage, 20 [\A on the taq~"t with an energy resolution 6E/r. of (!.bout 4 x 10-3

..."nd a polari&at.ion of 7,'5'7". For Ovr experiments we u~ed a sc..atterj ng

ehamb"r with a m,dti-detettor system, which is d",scribed in section Z.5. 1he ,'l.C~.eSBory electronics will be discussed in s",c60n 2.6.

2.2 The polariz~d proton ~ource

for the production of polarized l'rotons (l.n jon-source of the

atomi" beam type is used. The method employed in such <I source

~tem [rOl!! a,l idea. by R. Fl"ischmann(C1.56). A general review .,l)Ol1t

polarJ.~ed ion Aources has been given, among oth",rs, by Haeberli (Ha67),

whereas l'rogre5$ reports on the construction of these sourceH w£re

gi ven by F lei$c\l1M.[I[l (FJ (5), Glavi sh «(.170), Dona lly (Do70) and Clegg (e175) at the fiv".-annual symposia. on polarization phenom"ns. So he.r~. we shall only bd efly r~vie.w the general princi pIes of the atomic heam metho(\ ",nd at the ~am", time report the ess~ntial p(!.rs-meters of the Rindhov<i!ll source. The. basic concepts of this particular source originated [rom the work of Van del' Heide (He7l).

A scllcmatic diagram of the ion sou);"ce is ~hDwn i,l figure 2. I.

On the b",si~ of thi. diagram we will olltline ,.he principle of this

type of source. Til the dissociatQr hydrogen atoms are produced by

dissociating molecular hydrogen in a high freqllency discharge. TDig

discharg~ is exc.i t.ed insid" a ws.ter cooled quartz tube. Thr.ough an

oriUc.e at the end of thi s tube hydrogen atomR can esc(!.pe from the

dis~harg~ formirtg, after collimatio~ by ~ sm~11 diaphragm (the

~kimmer). an atomic beam that ente~s into a sextupole magnet.

2000 I " Hg dlff. pump 'tIfiI'~'''''Ptlllj+..",t!I ... k fi.;.h:1 tr:mslUCln ul'lit 300() II. lJildiff. pump 400110 vzn:. ion pump + Ti.!!IlJbl. W.F, cop

The electron '>nd proton spin of a hydrogert atom decouple in a strong magnetic fteld in the way schematically shown irt figure 2.2. Irt the irthomogerteous field of the sextupole magnet the atom

experiences a force of which the direction depends on the orierttation of the electron spin. The atoms with electrort spirt up are focussed

toward~ the '>xis of the magnet, whereas the atoms w~th elect~on

spin down are deflected from this axis. Thus a Stern-Gerlach separation between the hyperfine structure states 1+2 and 3+4

is obtained. With an appropriate diaphragm behirtd the ~extupole

magnet the compOrtent~ 1+2 are selected,yielding an atomic heam

which is polarized £u the elect-r;on spirts. Next the atomic beam is polarizEd in the proton spins in a weak field transition unit where

hyperf~ne transitions from 5ubgtate I to substate 3 are effectuated

following a method suggest~d by Abragam and Winter (Ab62). These

transitions are induced by mearts of an alternatirtg magnetic f~eld

directed along the bEIIlll axis and a static field perpendicular to the axis. After the beam hag passed the transition unit it practically

only ~ontairtS particLes in substate 2 and 3. The atomic bea~ is then

ionized by electron bombardmertt irt the strong magnetic fiEld of a solenoid and thus a longitudinal polarized proton bEam is obtained. By a system of electrodeS this beam is extracted from the ionizer and accelerated to 5 keV sinCe the ionizer is operated at +5kV against

earth. Finally the spin direction is rotated by 900 in crossed

E1Ec """1 -,-- 'mj 1m)

t

mF _{~1/2 ~112_}

·112 -112

Fig 8.2

Energy-level d'l:agnxm oj" ~he hyd"ogen 3 atom bl (~ magn"t"ia fidd. :I'he (lmt:t'gY

F=O -6

4

·1/2 -1/2 iG giVen in units 5 :::: a 5.82xl0 eV -2

-1/2 +1/2 and the magneUa field 7:n units

-- I B (J

=

5.07)(10-;11'.

0 2 i, 6

,---B/B_e

tric and magnetic fields, a ~()-called Wien filter. By s",itching both

the electric and magnetic field~ the spin direction of the protons

can be reversed. Th~ esSential parametere of our source are listed

in t8ble 2.1. Th" sotl.-ce deliv.,~cd about:> \.IA OI1. " cup just behind

t.11e ionizer.

.... .. 'II'I'\·\wIIB.I \11.Ij}rt..~ I:~Jlf~ i 1\1\('1' Iii UI~I' !.I"f (I ffilC'l

I('nroll! :<7P f IIIICI

~mli':"l" d.i,Jmc~.;:I.· nOilj.lJ.~ 1.(0. - I.~ I~I'I

I. II i ~1'hilr".Q.!' f'l:'("IIII'CWY

1\m.lC'T" di~l;':illilll"ll hI' 11~1·.i IIN·.~!r

11 r (. ~,t:1J 1'"" i 1'1 I h \~ Ii i lie" 1 I ~C i

A.c-,~ <) 11 j c.:t I I; t \11 I"' I! Ii

II!) I~' CI i "!I'nI·t~'1" ."pl'!' I 111'1' i I'CllU d i :;r.:.IlI1';:~' I:() -:Ii r.~ll,"i III III" "n 11111.

"'"X ""I><~lC" 11'l1l~Lh'l

,t i '" .Hnl"I' "I'I''''~ L t,' F)l'li {- ti F"l~ I (J I1iITI

1.'\,ld I. t PI) I" 1 i]1~

1."Llj1.lI1 III .;':'lH\)I~'llr'

1.-1" ;111. (i~' 1 ,I t,.. :11, /. i ~, I <> T'L " " , . \ : I)" (~ T 'N~[) mill :+ lill. j '" r j Q I d \), ~f .~. () m"" "'V('''' S() mill !)'\'J ~II;,; ~~ 'I () 11

1111,,"~·,~jJli'lj1. m~~nt'~j.;: fi.eld "'TTlrl;t~I~I(' n.t In'!, frCI11Jo:'n.;:y ~7 ~Il:r

0, I~b T I'YO rom

2.3 The inj<oction and the accelel"ation of th" b"am

Through a system of focussing ami steering elements the polarized

proton beam is tr;-ansp0l:ted to th" "ntran"-e of « ':rochoidal injection

~ystern. oy which the beam is radia<ly injecte.d into the cyclDtron.

This sy~tem is an exact copy of a second ver;-siol1 of the. Sac lay

~~-

median -plane

bea~;~:;:S- ~

E§

_~~.

centre

~'ig. 2. 5 The system used fot' the :Mclia~ injection of thlil l?O~wiBed

proton oell1'1 into th$ cyclotron. The maqnetic f-il?-ld i$ pl?-xp03ntiicula:r to ,the plane of the d:rGllling.

injector, the principles of which have been described by Beurtey and Durand (lle67). The main part of the inj ector, which is shown

in figul:e 2.3, consists of two pail: of copper electrodes which

8.l:C opposite.ly charged. During operation of the injector the voltages on the two pairs of electrodes are adjusted in such a way that the Lorentz force acting on the pr;-o"ons is balanced electrostatically. By the construction of the injector an electric field results that together with the magnetic eield possesses strong

focusing pr;-opel:ties. With this system we were able to tranem~t about

70% of the incoming beam to the centr;-e of the cyclotron.

Notwithstanding this high tl:3nsmissiol1 it first seemed impossible

to extract any a~celerated beam from the cyclotron. One should realize

that the electrodes of the injector form a vertical aperture of 8 mm

through which the beam accelerated oy the cyclotron has to pass about

300 times. A <ypical d~agram of the «ccelerated beam current against

the estimated distance frOm the centl:8 is shown in figure 2.4. These

currents were measured with a target of 10 rom height and 3 rom length

having an inSUlating strip of about I mID in the middle which divided

the target in an upper and lower part. This target was attached On the "weathe1:-side" of the injector system and could be moved outwards.

oA

I " ...

~--'::--'-~..."c-....-'--'-...J

',vi) I~"

dl~l.cn~1I 'rllm ~ .. ""~ [m/m)

Pig. Y. >I The meat:;UX'e.d acce.L<$y.ated beam cU.N'e.nt aqair,f;'t ·the.

8ctimate.d d{stanclFJ to the. aentY'e. of i;/18 cyalotY'or!.

in the fjrst revolutions the beam intensity stror>gly diminishes and

up to about SO !Inn a vertical oscillatory pattern of the beam shows up.

I t 15 also seer> that the middle of the beam does nO!;. coincide with

the median plane of the injector and that the current measured on the

·Iower part seems to cut off at about 60 \llIl1. From that distance the

total intensity diminishes Slowly and at 140 mm a current of approximately

4 ()A is 1 eft. At radii. 1 arger tluln 200 rnm 1 t was impossible to find any

mea~urable curr"nt. Sil"(1ilar results Were obtained with. a diapl1rai'\m

attached to th .. conventional. (unpolarized) ion source. 1'hi~ diaphragm

had ~ vertical aperture similar to that of the inje~tor. It was only

possible to J.cce.lerate th", beam further outward if one o~ both of the

inner two pair of correction COli" wert' exci ted asymme t:d. cally , as

suggested by PoussaTd (Po74). In thi.s way, finally, mean vah)es during

our exp<:Timent~

or

so

nA of internal beam and 35 nA of extracted beam were obtJ.J."",d.

Z.l1 Ileam t ... "sport SyS teID

The beam extracted frOm ehe cyclotron WaS transported by means of

bending magllets, steering magnets and quadrlJpole lenses (Ha70), as shown in figlJre 2.5, to the scattering chamber located at experi.ment

~tation IV. At various positions beamstops were used to meaSure the

8 I'.~.,.m l(oC:"rlrl~(

corm:il",!! ~~...,

~ ~:~~~O';IL~~~

~ 'Ihl

I, r:g-r~>lIfIlIIl:I'1 .. 1,}11iJ(I

Pig. 2.5 Beam guiding system of the ayalo·tron lahoratory. Out' experiments are .;;a1'1'ied out at e;q;oeMment etation IV.

beam c~rrenC. rn~ cwo 45° bending ~gn~ts MB4 and Me] and the

quadru-~ole lenses between these were operated in a doubly achromatic ~de

(Sc73). Th~ slits between the quadrupoLe Lenses QE2 and QE3 wer~

ad-j~st~d to form an aperture of 3 by 3 mm. Wi th approp"date setti,);1gs

of the beam transport elements this ap~rture was ~maged On a target

foil in the scattering chamber, giving a beamspot of about 1.5 rnm £);1 diameter.

2.5 The scattering cha~ber and polarization monitor

In fig~re 2.6 an outli);1e of the scatter~);1g chamber and ~olari~ation

monitor is sh~. The scattering cha~ber has an inside diameter of

560 mrn and a);1 ~);1side height of 90 mm. In the centre a target of ]0 mm

in diameter is mounted 0);1 a );1i~kel trame of 14 mm by 26 mID. To su~pres?

slit-scattered protons we placed at the entrance of this chamber two

diaphra~$ ot succe$siv~ly 6 and 8 mID in diamet~r.

the protons scattered by th~ targ~t foil are detected by

two arrays of fOur 3 mm 5i (Li) detectors, ea~h ~ount~d in

the median plane of the scatteri);1g ~hamber and adjustable at

different angle settings. The detectors are placed obliquely,

under an angl~ of 45° with respect to the incoming scattered

Pig. 2.6 r;chemaUo dra/.J·ing

of

I;he eaattet'htf)' dl(JJTlber and po[ar'/:zation mordtor.

protoos. The array ueed for th~ detection of protons s~attered in ehe fOn.7ard region (200-900) -th" forward hlock- is pl aced at the ri ght sid" of the beam. The detectOr~ in this array arc 5° apart at a distance of

250 mm from tIle targ",t. By a diaphragm ~n fxont of each deCce.tor a hori:oontal. ang:ular acceptance of about 1° results. The second arxay, which is used for the more backward angles (60o-1650) -the backward block- is p l.aced at the. left ~ide of the Qeam at a distanc<'o of 125 rum from the larget; her~ the d~tectors are 10° ~part and an id"ntieal di~­ phragm a~ used tn the forward block define,:; a hori.zontal angular accept-ance of about 20. Channels i.n the detector block .• , in front of the angle d':'fining ~lits, restri.~t the view of the detecto'(S to the direct envi rO);lment of the target. Permanent magnet" ar", ph.ced at the top and

bottom of th".e charmcJ.s to ~weep away th~ secondary elec::trons arriving from the t<lrget..

Tn the vertiCal plalle. through the beam two 500 )lIn si detectors wi til a'1 uminium degraders in front are placed ~t a forward sc.att{)ring

angl~_ of {,So. ,(h", total numher of ela~tically scat:tered protons

detect«cl itl these "out of plan~" detectors is used for nOJ:l1H,U",ation purposes.

Th", degree of polarization of the beam is cont:~nuou"ly monitored in the polarization monitor: a separate small sClOltted.ng chamber loc~ted

dDwnstream the main chamber. Here th" proton energy is degraded by means of 811 alumi.nium ~he.et to an enexgy of 1.5.5 MeV. After colli.m,<tCion tllese protons are s~attered froIl\ a thick carbon target (ab0ut 0.3 rom). The

elastically scatcered protons are detected in the ho~izonta1 plane On both sides of the beam at a scattering angle of 52.5°. From the

well-known analysing power of 12C in this ~nergy region (Me76) the polsrization

of the beam can be deduced.

2.6 The electronic equipment

The detection system, which i~ the same for each of the eight detectors,

is shown schematically in ~igure 2.7. In a semi-conductor detector an

Fif!. 2.7 Blook diagram of th~ ~teotion syst$m.

Detector>: 3 rom Si (Li) PhiZips EPX 12 h'eaJrtpUfier-: Canbel'I'a model 970D

Main anopZifier; Ortec model 48.S Lineair flate and

<"weokeI': ORTEC model- 412

FiZt",r amplifier': aWE model, Disoriminator: LRS moikt (J21.AL Levd adapter: LRS modeZ 6S81lL

incident proton creates by ionization electron hole pairs. Due to the

electric field across the detector these charge carriers are collected,

which results in a charge pulse proportional to th~ ~nergy loss of the

proton. After pre~ljfic~tion and COnv~rsion into a voltage pulse the

signal is fed into a pulse-shaping cir~uit and a fast logic circuit.

In this f~st circuit a disoriminator generates a logical pulse whenever

the filter-amplifier output ~xceedB a minimum puls~ heigh~. corresponding

co an energy of about I MeV. This log~~al pUlse is fed into a routing

unit, which may enabl~ a linear gat.e. Next t'.,e amplified and strechted

analog signal is sent. throuBh a mixer to an analog to digital converter

(ADC) where the pulse is converted into a channel-address pr<;>portional

to tl~e i.nput pulse amplitude. In all our experiments a cOnve1:sion Bain

of 1024 "hanneh is used of which by subtraction of 512 channels only the upper half of a spectrum is stored in the memory of a FDF-9 computer.

Instead of the fast logic circuit. des~r£bed ahove, we uSed in our

first experiments at 17.2 MeV, 20.4 MeV and 24.6 MeV a discriminator with a relatively large dead time. Sin"e in the following experiments larger boam "urrents were obtained a pile up inspecti<;>n was included, fDr which the present rouch faster discriminator was \1.eeded.

On the basis of figure 2,8 we will poi\1.t out soroe further f€atureB

of our eJ.ectronic "et up, the main fun~tion5 of which are processed

hy the routing un; t and the control unit.

The routing un; t. handles the following J:ive task.:

a) After the routing unit has been triggered by a discriminator pulse a gate signal is sent to the corresponding linear gate and strechter whieh enables the input,

I)) Within 20 IlS after a OiscrIminator p(llse is receiv€d by the

routing ulli t any othe'r discriminator pulse will b<!l disabled

by mea~s of internal input gates. Mor~over a check is performed

On IIcd.dental coincidences between t.wo detector channeh. 1£

such a coincidence is detected the gate signllls to the lineair

gate~ nrc soppressed.

c) A (10.~d time signal is gi"-'en as SOO\1. aR a discriminator pulse

i~ registered. This signal lasts until a ready signel, indicating

that the event. is stored in the memory of the computer, is

re-ceived. the routing unit is reset by thi~ ready signal or by an

internally generated sig\1.al, if in JO!. pre!'let tim.., the AbC has

not started a conversion.

d) The pile up protection wOl:ks ai'l follows,

~leIl~ver a puIs.., is accepted for analysis a stal:C signal is fed

into the start input 01' a time to pulse height converter (TPHC),

During t\1e enalysis of a pulse the dis<;.riminator pulses, which

co-.;"(espond wit.h an eve:n.t in the :=i,ame channel, arc tyan.F,lmitt~d

through the routing unit to the stop input of the TPHC. When a time interval smaller than 2))s is measured a prohibitive signal

is fed into th~ ADC. We established that for a longer interval

no distortion of the spe~trum occurred by pile up effect~.

e) The detector whi<::h has triggered the routing unit :i. s i,d",ntified

by three routins bits.

The control unit handles the following four tasks:

a) After a pr~set number of ~ounts i~ detected by th'" two

"out of plane" dete<;tor~ a signal is sent to the poh.rized

ion sotlrce where th~ direction of the potarizatiem is changed

by re~"rsing the magnetic and electric ~ields in the Wien-filt",r.

b) This );eversal is checked togethe); wi, th a number of essential

operating conditions of the ion source and the injection ~ystem.

An experimental run is stopped whenever one of th,,-~,,- conditions

is not fulfilled.

c) A routing bit is generated which indicates th~ direction of the

pol~ri.zat~on,

d) After a preset number of spin direction reversals an interrtlpt is sent to the routing unit and the FDP-9

an eXFerimental run is stopped.

c0lIl!'ut"r by which

The four routing 1:>£t$, three for the detector identification and

one for the spin di);e~tion, tog~ther with nine bits from the APe output

give a di\lisioIl. of the PDP memory illto 16 x 512 channels. The numbe);

of ~lastically scatter<!ld protons detected by ~ach of the two "out of Flane" detectors and each of the two detectors in the polarization

monitor ar~ r~gist~r~d for the two spin orientations in scalers. After

an experim~ntal run the total number of ~OUIl.ts in each scale. togeth~r

with the aCcumulat~d spectrtlffi of 16 ~ 512 channels are sto);ed on

DEC-tape. For further analysis the spectra may be transmitted to a

s7700

computer.

In addition to the above mention~d actions severat others are possible

which can give us some insight in the status of the experim~nt by means

of a plot or a di~play of the spectrum and a first estimate of the peak

contents in a rough p",ak scan. All these action~ are governed by the

~xperiment monitor system KORAM (Ra77).

16

analog input A.D.C.

det.1-B

T.P'H.C.

-+

S.C.A.

gate signals

J

1

routing A.D.C. busy

discr. signals ~ unit routing bits det. identif.

; -dead

\sto P time

f-

control routing bit uP/down

det. 9~10 _unit

l

-t

uP/down

det. 11~12

~

scalers cont rol p.O.P. 9

~

ion

f

-source

Fig. 2.8 BIod: gclwma indieating the funeUon oj" the vou6ng urdt and "tho; eonl;l'o7~ um:t, q$ ",:tiptain-,~d t:n the teftt.

REfERENCES

Ab62 A. Abrag~m ~~d J.W. Wi~t~r,

Compo R~nd. Ac~d. Sc. 255 (1962) 1099.

Ee67 R. Eeurtey and J.M. Durand,

Nucl. Instr. ~ (1967) 313,

C156 C. Cl~usnit~er, R. Flei6chmann and H. Schopper,

Z. Phys.

l±!

(1956) 336.

e175 T.B. Clegg, Proe. 4th Int. Symp. on Polarization Phenomen~ in

Nuclear reactions, Zurich 1975 (eds. W. Gruebler and

v.

Konig,

Birkh~user Verlag, Basel, 1976) p. Ill.

0070 B.L. Donally, Proe. 3rd Int. Symp. on PoLariz~tion Phenomena

~n NutLe~r Reactions, Madison 1970 (eds. H.H. Barschall and

W. H~eberli, Univ. of wieconsin Press, Madison, Wisc., 1971) p.295.

F165 R. Fleischmann, PrOt. 2nd Int. Symp. On Pol~rization Phenomena of

Nucleons, Karlsruhe 1965, (eds. P. Huber and H. Schopper,

Birkhauser Verl~g, Basel, 1966) p. 21.

Gl7 H.F. Glavish, Froc. 3rd Int. Symp. on Polarization Phenomena

in Nuclear Reactions, Madison 1970 (eds. H.H. B~rschall and

W. ij~ebe~li, Univ. of Wisconsin Press, Madison, Wise., 1971) p. 267.

Ha67 W. H~eberli, Ann. ~ev. Nucl. Sci. ~ (1967) 373.

Ha70 H.L. Ha~edoorn, J.W. Broer and F. Schutte,

Nucl. lnstr. 86 (1970) 253.

He72 J.A. van der,Heide, thesi$. Eindhoven University of Technology, 1972.

Me76 H.O. Meyer, W:C. Weitk~, J.S. Dunh~m, T.A. Trainor, M.P. Baker,

Nucl. Phys. ~ (1976) 269.

Po74 RaJ7 Sc73 Ve52

Poussard, C.E.N. Saclay, priv~te communication.

A.J. de Raaf. into repor~, Eindhoven, J977 (in Dutch) .

F. Schutte. thesis. Eindhoven University of Technology, 1973.

N.r.

Verster,

a.L.

Hagedoorn, J. Zwanenburg, A.J.J. Franken

and J. Geel, Nucl. Instr. ~,-li (1962) 88 •

CHAPTER III

P1tOCEDURl:: ~'OR tillASUREtillNTS WITH THE ?OI..ARiZ!D )'ROTON BEAM

3.1 Introduction

irt this chapter we will describe artd discuss the procedure we

followed irt me""uring th" artal~,,,ing powers and differential cross

section~. Our general proc~dure is outlined in section 3.2. In

section 3.3 the influence of possibl~ sourc~s of RY5tematic errors

caused by a non-proper spin flip, unc"rtairtti". irt the actual scatteri.ng

angles and unCertainties in the beam pol<1rization are cstimated, At.

lcast with r~spoct to the inelastic scattering data, these errors are

£<>und to> be negligible as compared to the statistical errors. in

section 3.4 we give our results on the analysing powers in the elastic

scatte~ing

from 12C, which we collected alternately with the data on the

i,rant nicke:l a~1d yt.trfum o.~lclei.. Generally these data are found to be

<;DnRistent with those from the literature, Fin-l'Hy in section 3.5 -I'

de~"ription of the an8.1ys~s of the energy spe.ctra is given.

3.2 Experimental procedure

3.2.1 rhe m,;,asurement of the floa1ysing power and differential C1:0SS

s€'('tion

From the definition of the aLlfllysing power, given In chapter 1. it

is <:a.ily shown that One cao determine the analy~ing power from the

numb",r of particles recorded by nJO detectors placed on opposite sides

of the b"am at th" same scatte);ing angle, Dr from the numb",. of pa1:ti('les

recorded by OLle detEc~or at a fixed scattering angle in two separate );uns

with opposite spin directions. As we intended to measure angular

distributiuns over a ",ide angular region we ded.ded upon the eight single

detec.tor 5et up described in :section 2 . .5.

With t.his set U\? measurements with forward artd backwa.rd positioned detectors were done simultaneously. Generally the following measuring

scheme wa~ carried out;

forward block, detector~ at b"ckward block, detectors at a. 20° , 2So, 300, 35°; 900, lOOo, ]]0 0 , 1200; 1;>. 400 65°; ]JOo 160°; c. 600 75°; 95° 125°; d. 800 9So; 135° 1650; e. 800 95°: 60° 900; f. 800 950; 650 95°;

In the first four runs the target was positioned at an angle of 450

with the beam direction, by whi~h the forward ~cattered protons were

de~ec~ed ~n ~ransmission mode and the back~ard scattered protons in

reflection. In the last two rUnS thie ~i~ua~ion was re~ers~d by having

the target rotated over 900

•

fhi! diffences in cOUll'ting ra~e be~ween the forw"rd and backward

positioned detectors, due to the decrease of the cross s~ctions with

increasing scattering angle, wa. partly compensated by the ~our times

larger solid angles for the detectors in the backward block as compared to those in the forward block.

Usually we made several runs at the same angular setting. This precaution was taken, to avoid that a temporary decrease in the quality of an energy

spectrum re"ml~ed in a bad or evert a worthless measurement. In each run

the energy spectra were takert alt~rna~y for the opposite spin directions

w~th period~ determined by a preset rtumber of elastically scattered

pro~onB de~ected by the two "out of plane" detectors. So a measure of

the number of incident protons t~wes the number of target nucle~ was found.

To obtain the angular di~~ributions of the differential crO$~ sec~ion the

totat amO\Int of detected protons in one run in both "O\It of ph,ne" dete"tor~

together was taken to normalize the measurements at differ~n~ angular

se~tings. Thi5 normalization procedure was preferred over a normaliza~ion

based on the integrated beam curr~nt because in that way the accuracy might

have been affected seriOUSly by inhomogeneities of the target. Sinee ~he

elastic scattering cross section decreases rapidly with increasing scattering angle the counts registered by one out of plane detector should sensitively depend On the precise scattering angle. For this reason we used two detector.

situated at the same scattering angles above and below ~he beam. Thus to

first order changes in the beam position or beam dire~tion did not affect

the total number of counts detected. In several e~erime.nts the ratio of the

norma1iz~tion facto~s {or the diffe~euti~l crose se~tiou r~~ulting from the

integrated beam ~urrent and that from the out of plane detectors have been

compared. Deviations smaller than a few per cent have been observed for measurements with a fixed target position, whereas Jarger deviations,

up to 10%, occurred between measurem"nts with a diUerent position of

t.he target.

An additional check on the nO:rnl"lization was provided by th" mea~uring ~c""me, by ",hi~h at various stages of the experiment the

backward detectors comprised an angula~ ~egion which had heen measured

before. From inspec.tion of these IIle:a.!iiurements no systemaf;1.c diacrepancie.;8;

emerged.

3.2.2. Beam tuning and determination of the energy of the b"am.

By the beam transport system, as descrihed in seetio" 2.4, the proton

beam '"'as guided to tne ~catterin!): chamber. Art aperture of .3 mm in diameter,

ilt the target posi.t~on, ,",a~ used to st:eer the b;,am through the scattering

chamber and pOlarization monitor. To that end quadrupole and steering magnets wer", adju?1;".",d in such a way that the current lll.E!asured on this ap;,rture was liIinilillzed whih the current on the beam stop behind the

polarizat:iDn monitor waS kept at a Ulaximum. In all our experi..ments the

condi.tion was ililposed that this aperture intercepts one per cent: of the

beam int~nsity at most.

Il"c.ws€ of the unce~t~inty (3.bout the pre<;:ise radius at which the beam

is extracted from t.he cyclotron, the real b"am energy can be different [rom the en"rgy at which the cyclotron is set. We therefore d"t:"rmined, at the beginning of each series of experim"nts, the enenn of the beam

by ch~ "cross-over" mHhod {fJa64), (Sm64), In tbis method the "cr".~s­

over" <lIlgle .i.s determIned at whicb th~ protons scattered from the hydrog"n

in " polyethylene target have the same energy as thos;, scattered

in-elastically from 12C, thereby producing the fir~t excited state of t',is

ntl<:.l".\18 M. !'n excit!'tion energy oi 4,433 MeV. Since this angle dependS

strongly oIl the incident protem energy it J.;, an accurate measure fo~

thi.~ energ;y. The measurements were performed with one of tho:, detectors

of the forward block. To "liminatc errors due to II slight misalignment

o[ the scattering chamber with r"spect to the beam axis. tl~e c.oss over

angle was dete.mined from measurements on both sides of the beam. Both

angles generally wer~ found to bl;! equal withi. n 0,]°. The l)eam energy

was deduced f~om the ~ve~age of these val~es, wormally an a~~uracy of

~bout 0.1 MeV was at,a~ned.

3.2.3 Targets

As ,argetB self-suppo~ting foiis were used, which were obtained

frcrm A.E.R.~. Harwell. The thjcknes~es of these targets and their

purities are given in table 3.1,

54 Fe 56_Fe 58_Ni 60Ni 62Ni 89_y thickness in mg/c~ 1 3 p~rity in % 97.48 99.97 99.91 99.85 99.39 99.0

3.2.4 Scattering by a polyethylene and a mylar target

At each angular setting the measurements on a specifi~ target were

"sandwiched" between simUar measurements wjth a polyethylene and mylar

target of 2

~/emi

and I mg/cm2 thickness respectiVely.

Carbon and oxygen contaminants, which showed up in all our SDectr~

more or teas, were easily corrected for with the data from the polyethylene and mylar target •. From the position of the peaks corresponding to the

el~stic ~nd

inelastic

scatte~ing

by 12C we

calib~ated

the enetgy scale.

Moreover for scattering angles smaller than 45°,

al~o

an accurate

determination of the scattering angle could be made from the kinematical

shift of the Ig-peak. A further check on our experimental pro~edure was

performed. by

compa~ing

our results on the elastic

scatte~ing

from 12C

w~th results £ro~ the literature.

3.3 Sources of systematic errors

3.3.1 Non proper spin flip

The direction of the spin is reversed by reversing the electric and

magnetic field in the Wien filter. However, if the Lorentz~forcc acting

on the protons is not exactly cancelled by the elecnic J;orce, eMs

Wien filter also acts as a 8teerin~ element in the beam transport

syst"m h~tween the ionizer and the injector. In reversing the spin

dir.e~.ti on i t ; s thllS possible that the position and direction of the

protor1 beam at the entrance of the injector i" affected slightly. If

such chang~s in position and direction are conveyed to the scattering

chamber on the target one introduces a so-called nOn-prOper spin flip. These non-proper spin f1ip component? may give rise to cOI'lsidel".:1.ble

~Y5t~matic deviations (Oh75).

for Lhis reasOn our first e"perimcnts, on the iron ana nickel tluclej, have b""n don" by switching the hyper fine transition uni.t On and off. thus we measured alternately with a polarized and unpolarized beam, However, measl);dng the .. aymmetries between the number. of counts aetect"d in two runs with opposite spin airBction is a more efficient method. In

a two time.s short"r Illeasuring period ahout the s<lllIe accuracy is obtain~d

as compared La an e"periment in which the polarization is switched on

and 0[[. There[ore it was checked thoroughly that by a spin reversal by

me.anS of the Wi.e:n-filter no noticeable variations ~n beam position or

dj.reo::tion OCC\)r~a at the target, not even when the Wien filter was

deli.berately used as a steering element in such a way thar. the total beam current was di.minished by about a factor of two. So all our other experiments "hich we will report on we1:e done by switching the polarization direction of the beam wi th the Wien filter.

In effect these checl(s on beam variations were repeated in e .. ell experim€n

Small in plane variations should strongly affect the positions of the

protons scattered by the hydrogen i.n the pol.yethylene and mylar ene);gy

apectra. Variations perpend"o::ular to the sc,.tte~ing plane were checked

by the ratios of the counts collected by each of the two "out of plane"

detectors in the spin up and spin down states. From both checks w~

estimated upper values for a variation of the beam di~ectioll of 0.10

or. for a beam displacement of O.t rnm, at the target position, presupposing

3.3.2 The a~~uaL scatter~ng angle

The detectors and the diaphragms in front of the~ always were placed

at fixed positions in the detector blocks. The angular settings of these blocks were read, with an estimated error of 0.1°, from a graduation on the wheels, on which these blocks were attacned. me angular distance between the detectors in each block was verified by the observed kinematical

shift of the hydrogen peak in the polyethylene spectra meas~red for

scattering angle~ between ZOo and 60°. Thus the actual scattering angles

were found to be correct within 0.10 if the direction of the beam ax,s

coincided wir;h the zero line of the scattgring chamber.

:from the determination of ~he ener$Y of the beam ( Cf. section 3.2.2.)

slight misalignments appeared of at most 0.10• Bowever, in~table e~emente

in the ion-sou.ce, the injector, the cycLotron or the beam guiding sy~tem

could re~ult in random variations or a slow drift in the position or

d~rection of the beam. Since th~ spin direction was changed about ~v~ry

r;~enty ~econds such variations should unlikely affect the resulting

differential cross ~ections or the analysing powers, though the actual scattering

angle to which these measurements corresponded might devia~e from the nominal

settings. Until about 400 the scattering angles were calculated in each

experiment from the

position~

of the 12c-elasr;ic, the 12c-inelastic and the

IH peak in the energy

spectr~

obtained fo.

th~

scattering from the rnytar and

polyethylene targets. These calculations .evealgd deviations f~om the nominal

settings of 0.20 ?t mo~t.

Deviations of this order will only affect the elastic scatter~ng

cross se~r;ion and analysing power in r;hose region were rapid changes in

the angular distributions are observed, such as for the cross section at forward angles.

3.3.3 Uncertainty in the polarization of the beam

The beam polarization was continuously monitored in the pOlarimeter (Cf. aecCion 2.5.). Fluctuations in the beam polarization were automatically

correcr;ed for since we dete~ined the mean b~am polarization in an eXperimental

run from the total number o~ elastically scattered p.otons registered

by each of r;he polari~ation monitor detectors for each ~pin direction.

It is a disadvantage, however, of a single d~tector ~ystem that the

measured analysing power and differential cross s@ction depend in first

order on the difference in the beam polarizations for the up and down direction.

I f we deHne the polar.i ",at ion p+ in the Bpin up and p-j. in the spj.n

down st~te by:

pt p + 6p

F+ ~ P -

or

0.1.)

it is eaaily shown that to first order in OP the analysing pO>l'er A(8).

a.nn tlw. di.ff"renti,,] CrOBS section 0(6) are given .hy:

A(e) ( I ! AmBP)Am

00(8) ~ (1

+

AmOP)Om 0·2.)

where the analysing power Am and the di.fferential CTOSS ~el;tioll Ci_m

are m"a~ured, assuming op to be zero; the upper sign and lo~er sign

respectively refer to scatteriIlg to the left and to the righ:with re"pEct to the b~am direction.

Th" polar-hat. i on of the beam has to be de termined from the foIl oying

relatiOns: nN!'2_L!<:1.D 0 (I +P+A) \1N>"JREROO (I-PtA) n'N'O E D (l-PtA) L 1. 0 n'N'QRERoO(l+P+A) (3.3. )

whore T. and Rare tht: numbeT of elastically sC(l.ttered protons detected by the left. and right detector, n is th" I1umbcJ:" of incident prot.ons, N the target thi"kIlOSS (atmns/cm2), and P

L, 1\ and "R' llR arc the solid

(l.ngles and efficieIlc1es for the left and right det.ector, r<!spcctively. Assuming that the effective taJ:"get thil;kneBs nN "as the same for the two comlting periods we found val\les for op rallging hom -3% ti1l5%. However, variations in the eff"etive target thickness cO\lld readily accounL for the. s\lpposed differellces in th .. b .. am polarization or [or

til", Ul'ctl'"ttons ob"erVed in it. We remark thilt differ;ences in the

effective tars"t thickness fOT opposite. "pin directions mj,ght be caused by a Small nan-proper spin flip component a5 the lIle(l.sllri n g periodS for both spin dj re~.tions \ere deteTmi.ned by the effective target thickness of the targ".t placed in the scattering chamber.

S~nce ~e could not deduce the exact value of SF fr~ cUr

m~asu.ements, we omitted the co.rection (3.2.) and took the mean

pola.ization derived from the geometrical means of (3.3), which

is to first order correct in

oP.

Thi~ correction might only become

significant for the elastic scattering data, where it could give rise to systematical erro.s of about the Same order of magnitude as the statistical ones.

3.4 The analysing power for 12C(;,p)

In figure 3.]. we give the results for the analysing powers for

the elastic scattering from 12G,

~h~ch

we have measured alternately

with the data On the iron, nickel and yttrium nu~lei. TheBe data

may be compared to the numerou~ data from the literature. The dat~

of Mayer (Me76), Martin (Ma76) and Cra~g (Cr66) cover the energy

region of 11.5 MeV up till 28 MeV. Vrom these we learn that a consistency

check over the whole angalar region is on11 incidently possible because of the strong energy-dependence in this reaction. For this reason knowledge of the exact incident proton energy and the energy resolution

of the beam becomes

De

major importance if comparisons are to be made.

The analysing powers, given in figure 3.1., all agree qualitatively with the abOVe mentioned data. At thO$e scattering angles where the

energy dependence is not too strong the absolute ~elues are also

quantitatively ·consistent. From these values che absolute calibration of the beam polarization is found to be correct within 5%.

3.5 Analysia of the energy spectra

On th~ average a total of twenty spectra of 8191 channels were

~tored in one experiment on one target at one energy. These spectra

were enalyoed off-line with the aid of a PDp-g computer. This

analysis i$ brieflY described below.

Virst of all the spectra ~easured with a specific detector at a

specific scattering angle were ~ompared to each other, either by a

visual inspection on a display or by a ~hi~square criterion. In the

latter case the chi-square value of each spectrum with respect to that of each other spectrum has been evaluated. From these values we decided which spectra could be added. Eight new data blocks were

A 26 )0 so gO 12D ,~O ]0 60 90 'Z1I '$0 Ep"~M'V ~p,'7.H~.V

.

,

O.~ O.~ t '

,

.-... "

.

.

,

,

-Q.~

"

-0.5 Ep: 20.4 MeV II [p~2UM.V

,

,t _.'

.-0.5 ~ I' + I., I" " " ~.'

.

.,

....

'.

~ r I .

t"

...

- 0.5 -O.~ £P' ~I,,"M.V JO ~O $0 17~

,,0

O.S

_'"

.

D.S "

..

'I t

,

12Cq

l.

p1 - 0., -O,S lD 60 90 IlO 'SO -.3-(11l.(d@gJ

F·ia. J.l Analysi11{J pawer for the eZaeti" firJat-tering of

1" pl'o~ons by "c.

formed, o~t of the ~~~ed ijp~~tra and the correspond£~$ polyethyle~e

and mylar spectr~, that contained all the info~t~on collected with

a specific detector ~t a sp2cific scattering angle. These data

blocks were uijed in our further an~lysis which wa5 ~ompleted in

two stages.

In the first st~ge the polyethylene and mylar spectra were

considered by mea~s of a display. The peaks owing to the reactions

12C(p,p), 12C(p,p') (E = 4.433 MeV), IH(p,p) and 160 (p,p) were

x

localized succesively. ~rom th~ ~etimated width of a peak two

regions around the peak were defined to whi~h a rectilinear

back-gro~nd wae fitted. These regions were taken the same in the spectra measured for the two spin states. The peak region and the hackground

region could be adjusted Ln an interact~ve way. After the ba~kground

h~d been substracted, peak properties like the position and ~ontent

were c~lc~l~ted together with the total content and the ~symmetry for

the different spin states. From the position of the two carbon peaks

We determined the energy calihration, wh~reas from the position of

the hydrogen pe~k the s~attering angle ~ould be verified. Both c~~culat~on8

were Verformed with a relativisti~ description of the reaction

kine-matics. Next in the energy spectrum obtained from the targ~t studied

the elastic peak and the peaks due to the

scat~ering

from 12C and

160 impurities were analysed.

1n a second stage the energy calibration obtained from the analysis

of the polyethylene spect~um was ~~ed to calculate the position of the

peaks corresponding to the inel~stic scattering process. These peaks

were analysed in a similar f~shion as descrihed for the first stage.

No peak fitting was provided in o~r programmes for the analysis of

the spectra. Generally this was found to be redundant beca1,lse Ol.lr st~dy

concerned only a few strong excited levels, at low excitation energ~e6,

which were well

s~parated.

However, for the experiment on 54Fe at lS.3 MeV,

in which also reasonable statistics for higher excited states had been

obtained,

~nd

tor the

exper~went

on 89y , which revealed also other than

carbon and oxygen contaminants, a peak fitting programme had to be

used for a r~liable analysis. In these cases we made use of the automatic

peak search and fitting programme Poespas. This programme, which is a

8,,(,4 110M. Tlar~in, M.E. Ricky, Rew.Sci. lnstr. 3.5 0964) 901.

III 75 H.P. IHok, J,e. de Lange ano J,W. SchotI\\aIl, Nucl. In~tr. and Meth. ~ {197S) 545.

Cr66 R.M. er~ig, J.C. Dare, G.W. Greenle.s, J. Lowe and

D.L. WHs,m, Nucl. Phys,

!.2.

(J966) 177.

Ma76 P. Martin~ p~ivat~ communication.

Mu76 H.O. Meya,

w.r:.

Weitkamp, J.S. Dunham, T.A. Trainor,

M.P. lla1<er, Nucl. Phys. A269 (1976) 269 and priv"'t~_ communication

Oh75 e.G. Ohlsen, Proceeoings Df the 4th Intert1ational Symp. on

POlarization Phcnomem' in Nuclear Reactions, Zurich 1975,

28

(eos. W. Gruebler and V. Konig, Bil:khauser Verlag, llasel, 1976)

p. 287.

CHArTE~ IV

SOME ASPECTS OF THE THEORY OF ELASTlC AND INELASTIC SCATTE~!NG

4.1 Introduction

In the description of nucl~ar reactions one usually distinguishes

beCween tran~itions involving only a few degrees of freedom of the

~arget nucleus and those with excitations of many degree~ of fre~dom.

In the first class of tran~itions the initial and final stat~s differ

only slightly ft~ e~~h oth~r and it is therefore expected that the

~~citation proceeds via a direct r~action, wh~reas the ~acond class

may proceed via a complicated compound nucl~us mode.

of

course thi~

distinction i$ not so strict and in every reaction both modes will

be present. However, if th~ energy of the incident particl~ is

sufficiently high. there er~ so many states to which the compound

nucleus can decay that the probability of decay to anyone of th~m

will he small. It is therefore likely that for the bombardins energies used in our expetimente, which are well above the (p,n) threshold,

~he compound nucleus contributions are sufficiently small to be

neglected in our analy~is.

In this chapter we describe the di~ect reaction models employed

in the theoretical analyaee of our experiments. We mainly intended

to t~st th~ir applicability with regard to the analysing powe.s. So

no r~finements a.e suggested and th~refore w~ confine ourselves co

a discussion of some of the chsrBcterietic featureS. A detailed description of the use of these -modele and a justification of the

basic approximations are given for in~tance by Mc. earthy (Ca68),

Ja~kson (Ja70), Auste.n (Au70) snd Hodgson (Ho71).

In s~ction 4.2. we give a short outline of the genersl description

of a ~cattering process. It is indicated how the angular dist.ibutions

of the differential cross section and the analysing power can be

ca~culated fr~ crsneition amplitudes. Simplifying assumptions have

to be made which lead to manageabl~ ~xpressions for these amplituoes.

The elastic scattering can be described by the optical mod~l. In

our analyses we used the phenomenological optical model, in which the

interaction b~tween the incident particle and the nucleus is represented

by /l- comple" pote:ontial th~ parameters of which are d~termined empi:-icll-lly. This potcnti/l-l. )5 de!jcribed in section 4.3. In this ,section /l-lso

a short Outline of a soroewhat more fundamental model is given, wh;.ch is known as

one

reformulated optical mode.l. Though we did not u,>e this mood, its b~si.c concepts may be helpful in the interpretation of the p<l);'alllete.rs of the phenomenological potential.

The Dj.Horted Wave Born ApprO'dmation (OWBA) has been used to analys~ the inelastic:: scattering. The transition amplitude in this approximation

~. ~valliated in 8€.ccion 4.4. This ampl1tlide can be redUCed to .a form

in which the basic information about the excitation of the nucleus

~5 contained in a radial formfactor or transition density. E~pr~ssions

for the formfactor, both for a macroscopic and a microscopic DWBA description, are discussed.

4.2 Description of the scattering pro~ess

Here \lie will giv,:, a short description of a scatteJ':ing proc"-"s ~n

which an lncldel\t proton is scatte.red by a nucleus, wb).ch thereby may be exdted. The sy.tem of the projectile and the target nuc.leus is

dcsc"(iben by a Hami.l tonian H:

1/ ~ \l + T + V

o (4.1.)

wbich cOlnprises the Hamiltonian for the internal motion of th" target nucleus Ho' the kine.tic: ent!rgy operator for the relative motion of the projectile and the target uuc.leuS T w (-1\2/ 2\.1)1\ and the interaction V

between t\le projectile and the nucl.,tts. The C1:058 section for a scattering process can be obtained by solving the time-independertt Schrodingcr Equation

o

(4.2.)

Evidently such a solution 1)1(+) of this equation ill sought that, i];1. the );'"gion where the interaction has fallen to zero, it consists of an in-comirtg plane wave in th~ initial chann~l i and outgoing scattere.d waves in all the possible fiIlal channels f: