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,

ANNUAL REPORT

SOLID STATE PHYSICS RESEARCH INSTITUTE

Virginia S t a t e Univers i ty Petersburg, VA 23803

Supported by NASA Grant NAG 1-416

Report Period: 1/1/85 - 12/31/85 L-

(HASB-CR-181255) [ AC!IIVITI€S CE THB SOLID li87-28U 30

S t a t e Univ , ) 7 0 A v a i l : & I I S t C &04/BP I SSATE PIIYSLCS SIESIARCR I N S 3 1 2 E I E ~ Annual - - T H R U - -

I A 0 1 CSCL 20L G3/76 0093200

EeFort, 1 Jan- - f l Dec. 1965 (9irqinia ~ a 7 - 2 e4 33 Unclas

https://ntrs.nasa.gov/search.jsp?R=19870018997 2018-08-19T20:57:54+00:00Z

I I I I I I 1 I I I I II I I I I I 1 I

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Annual Report Solid S ta te Physics Research I n s t i t u t e

Virginia State University Petersburg, VA 23803

Supported by NASA Grant NAG-1-416 Report Period: 1/1/85 - 12/31/85

‘Rm ~olid state Physics Research ~nstdtute at V i x g i h i a State UniversLTy

w a s formally organized i n January 1984 subsequent t o the funding received

tixmugia NBsiA %ant SLG-1-416, The institute is a mUectLarn of tfn?ec xaeua~&~

programs. Two of these, muon spin rotat ion s tudies and s tudies of annealing

problems i n gallium arsenide, w e r e funded previously by NASA through separate

grants. ‘ThR MPSR proqrau WQS begun in 1972, while the G a l b sbdies were iza5thte8

i n 1982. A t h i r d program, Hall e f fec t s tud ies i n semiconductors, w a s i n i t i a t e d

with the establishment of the ins t i t u t e . C. E. Stronach is d i r ec to r of the in-

s t i t u t e as wellapr P/I of the MuSR program. J. J. S t i t h and J. C. Davenport

pilmic8 - rhrcfrm) am cwpriadw i n t r a ~ t o o s of t& Geas

program, while G. W. Headerson is P/I of the EEall effect program-

The p\nposes of t h i s i n s t i t a t e are threefold: (1) to perform state-of-the-

art research in both basic and applied aspects of solid state physics which is

intrinsically intaresting and which can be applied to problems of interest

to NASA; (2) to develop a self-sustaining physics research program a t VSU which

wjll kuhg disLirrctiaa to the rtniversity and its physics --st; and (3) to

provide t r a in ing and experiences t o students which w i l l prepare them for careers

i n research.

The following sec t ions describe the a c t i v i t i e s of each of the research

programs during the period January 1 - December 31, 1985. Following this is a

sect ion describing a c t i v i t i e s which do not f a l l s t r i c t l y within any of the three

1

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2

I I I I I I I I I I I I I I I I I I

programs, p lus descr ipt ions of student a c t i v i t i e s , equipment acquis i t ions,

and fu ture plans.

Muon Spin Rotation,Studies

T& mxm spin ro- mject efforts maatered aroolnd o-raprinents doae

a t the Alternating Gradient Synchrotron of Brookhaven National Laboratory.

=Aments Md bmtm d e w e l o p t a t done in 1983 and 1984 w e r e followed by a

number of experiments done i n March/April and May/J'une 1985. These include

s tudies of TI€& and YH2, TMMC, aluminum a l loys , and heavy fermion supercon-

ductors. Appendix 1 is an abstract of a papar to be presented a t t h e March

1986 American Physical Society meeting on t h e T i s results, along with a p l o t

of the -*2 b k a a fur an a2Utlagoa5 paper ap the alnsiMaa

alloy data.

Analysis of i ron alloy data shows t h a t the magnetic f ie ld sensed by the

muon, %, is greater i n magnitude for Fe(Au) than for pure i ron , but it is

sma l l e r b marm.jtude for Fe[I)y) ant¶ Pe(Ta1. The effect is valence amd %ence

electron densi ty related and follows the "Doyama rule" which w a s first stated

af ter analogousa positron sttrdies of alloys. That is; u4 {and e+) are r r p e ~ d

by impuri t ies t o the r i g h t of i ron i n the periodic table, but are a t t r ac t ed by

impurity atoms t o the l e f t of i ron i n t h e per iodic table. The Fe(Ta) r e s u l t s

are s t rongly dependent on sample preparation and a complete repor t on these

materials a w a i t s a study of Fe(Ta) alloys to be done a t Brookhaven i n May 1986

i n which the s h i f t s of F+, upon annealing are analyzed i n detail . A n abs t r ac t of

a paper presented on t h i s top ic a t t h e March 1985 American Physical Society is

I I I I I I I I I I I 1 I I I I I I I

3

included as Appendix 3.

W e are most pleased t o report t h a t the paper, "Uniaxial stress induced

symmetry breaking f o r muon sites i n Fe" was published i n the Ju ly 1, 1985

i ssue of Physical Review B. This study was a major ongoing e f f o r t fo r about

five years (1980-85) a d was supported both by NAG-1-416 and t he preceding

g ran t NSG-1342. A r e p r i n t of t h i s paper is included i n this report as Appendix 4.

--*- 'VaQr and two -te studentsr Zarchm 6aocbY Jr.

and Nana Mu, v i s i t e d the Saclay laboratory i n France i n June/July 1985 t o

study muon spin ro ta t ion i n N i and N i ( P t ) i n conjunction with the French group

led by DE. I.

Chemistry, Vitry-sur-Seine, France. The travel funds were provided by the

USA/France Muon Spin Rotation Program, which is supported by t h e National

of trw! Center f w r tbe stody of Metall-ical

Science Poudatlton, No NASS funds were used. The purpose of t h e experiment w a s

tm dtcazratsbdrrtbrrrp+ ; j ~ si4pt) trap at sites near tfre ft atuns for u % i s substantially d i f f e r e a t fIpm that for pure Ni. An extensive study at 77K

showed no such trapping.

The pr inc ipa l i nvesaga to r served on the s c i e n t i f i c advisory committee of

the Enropean Worksbnp on Subatanic Species in Solids, which was held in Vitry,

t he NSF grant f o r the USAFrance Muon Spin Rotation Program and no NASA funds

w e r e used. A d iges t of t he t a l k is included here as Appendix 5.

Another round of VSR experiments is planned f o r May/Yune 1986. These are

expected to include additional Fe(Ta1 measurementsr addi t ional heavy fermion

superconductor s tudies , fa t igue studies i n metals ( i n collaboration with our

French colleagues), and s tudies of additional m e t a l hydrides.

I I 1 I I 1 I I I I I 1 I 1 I 1 I I I

4

An experiment recent ly done a t t h e KEK laboratory i n Japan (and

recent ly improved upon a t the TRIUMF laboratory i n B r i t i s h Columbia)

f o r fu tu re pSR research, par t icu lar ly w i t h regard t o its u t i l i z a t i o n

even more

bodes w e l l

i n the

study of surfaces. A low-energy v+ beam w a s projected onto tungsten f o i l s . Three

t o f i v e percent ( 2 0 t o 25% a t TRIUMF) of t he incident p+ were subsequently de-

sorbed with energies of a fe# electran - volts, - plan to design a beam baaed on

t h i s phenomenon t o provide extremely low energy p+ a t t he Alternating Gradient

Synchrotron 03rooWlewen) far studies of surfaces, Rei- shadies w i l l

commence during the May/June 1986 run.

Pregarctio8s for tbe l.986 LUII d J a d u d e & v . af the PDP U J 7 3

(programing, purchasing per ipherals and software) and a cryogenics system for

low-temperature s tudies . Electronic timing should be improved w i t h the acquisi-

tion of a higttcsr rsemlution thuwto-amplitude converter and a c o n w t - m i o n

discrdmin&mz*

The V i r g i n i a State University participants in these -intents were Carey

E. Stronacfi, director of the institate, Lucian R. (;oode, Jr-, and NE~M Adu,

physics graduate students, and Michael R. Davis, an undergraduate physics major.

The Brookhaven program is under the overall leadership of W i l l i a m J. Kossler,

prof- uf phpsilcs at the College! of W i l l i a m and ~ a r y . Other par t ic ipants

included William F. Lankford of George Mason University, Harlan Schone of

W i l l i a m and Mary, Gabriel Aeppli of Bell Labaratories, M a i n Yaouanc of CNRS.

Grenoble, France, O l a Hartxnann and Roger mppl ing of the University of Uppsala,

Sweden, Joseph Budnick of t he University of Connecticut, and two graduate

students *am & u i u i a l and Hary.

Computer S i m u i at'i on o i Ftaaiat i on Damage

ONGINAC PAGE LQ OF POOR QUALITY

During t h e pas t year t h r e e graduate s tudents and one

undergraduate p a r t i c i p a t e d i n t h e r a d i a t i o n damage research

p r o j e c t . A con t i nua t ion of t h i s l e v e l o f student p a r t i c i p a t i o n i s

a n t i c i p a t e d f o r t h e coming year. John S t i t h , one o f t h e p r i n c i p a l

i n v e s t i g a t o r s , attended two p ro fess iona l meetings du r ing t h e

year(The 1985 IEEE Annual Conference on Nuclear and Space

Rad ia t ion E f f e c t s i n Monterey, CA and The Eighteenth IEEE I . *

Pho tovo l ta ic S p e c i a l i s t s Conference i n Las Vegas, Neyada). A

graduate student, L a r r y Brown, accompanied John S t i t h t o t h e

Nuclear and Space Rad ia t ion E f f e c t Conference. A La te News Paper

which was co-authored by John S t i t h o f V i r g i n i a S ta te U n i v e r s i t y

and John Wilson of NASA Langley Research Center was presented a t

t h e Pho tovo l ta i c S p e c i a l i s t s Conference by John.St i th . John S t i t h

a l s o spent., rgproxiqately 5 i x weeks a t t h e NASA Langley Research

Center du r ing t h e summer.

Graduate s tude p a r t i c i p a t i o n i s an essen t ia l component o f !!I t h e research grant: Sresent ly , t h r e e graduate s tudents a re

i nvo l ved i n research p r o j e c t s d i r e c t l y r e l a t e d t o t h e r a d i a t i o n

damage stud ies. These students w i l l even tua l l y use t h e i r f i n d i n g s

or r e s u l t s t o w r i t e theses which they w i l l use as a p a r t o f t h e i r

requirements f o r t h e Master o f Science degree. One o f these

s tudents i s scheduled t o graduate i n May. H i s research p r o j e c t o r

t h e s i s t o p i c deals w i t h an impor tant aspect o f r a d i a t i o n damage

s t u d i e s u t i l i z i n g computer s imu la t i on s tud ies. He has made a

comparative study of t h e e f f e c t o f us ing two d i f f e r e n t p o t e n t i a l

f unc t i ons i n t h e model used f o r t h e s imulat ions. Th is s tudy i s an

extremely s i g n i f i c a n t aspect o f r a d i a t i o n damage s t u d i e s

5

+ * . * t

1 I It I I I 1 I 1 I R 1 1 I I

I 1 .

:I

u t i 1 i z i ng computer sirnu? a t i 0;; L--L- L E I - I I I I A ~ L W S s i n c e t h e i n t e r a t o m i c

p o t e n t i a l is o n e of t h e most i m p o r t a n t p a r a m e t e r s ; t o b e c h o s e n i n

d e v e l op i ng si mu1 a t i o n s model s,

T h i s a s p e c t of t h e p r o j e c t demanded a g r e a t deal of t i m e a n d

i n p u t from t h e p r i n c i p a l i n v e s t i g a t o r s who are a s s o c i a t e d w i t h

t h e r a d i a t i o n damage s t u d i e s . Formal c o u r s e s o n r a d i a t i o n damage

s t u d i e s are n o t o f f e r e d i n t h e d e p a r t m e n t , c o n s e q u e n t l y t h e

p r i n c i p a l i n v e s t i g a t o r s mus t p r o v i d e i n d i v i d u a l i z e d i n s t r n c t i o n s /

a n d s u p e r v i s i o n f o r t h e s e s t u d e n t s p a r t i c i p a t i n g on t h e p r o j e c t .

. .

C o n s e q u e n t l y , t h e p r o j e c t has; s e r v e d a n i m p o r t a n t a n d i n f o r m a l

m e c h a n i s m f o r e n h a n c i n g s t u d e n t s ' g r a d u a t e t r a i n i n g a n d I

e x p e r i e n c e s .

T h e r a d i a t i o n damage s i m u l a t i o n research h a s b e e n

c o n c e n t r a t i n g m o s t l y on s i m u l a t i o n s of r a d i a t i o n damage p r o d u c e d

i n a gallium a r s e n i d e c r y s t a l when i t is i r r a d i a t e d w i t h p r o t o n s

a n d e lec t rons . The s i m u l a t i o n s w e r e p e r f o r m e d w i t h a m o d i f i e d

v e r s i o n of t h e b i n a r y c o l l i s i o n s i m u l a t i o n code called MARLOWE.

T h e m o d i f i e d v e r s i o n -w c h h a s b e e n d e s c r i b e d i n a n earl ier c$1 r e p o r t is r e f e r r e d t o as MARS! A p p r o x i m a t e l y o n e h u n d r e d

d i f f e r e n t c o m p u t e r r u n s were made d u r i n g t h e y e a r i n o r d e r t o

b u i l d up a s u b s t a n t i a l d a t a base a n d t o test t h e s u b s t a n t i a l

number of m o d i f i c a t i o n s t h a t had t o b e made i n t h e code t o k e e p

i t c o m p a t i b l e w i t h t h e compute r o p e r a t i n g s y s t e m r j a t N A S A . T h e s e

m o d i f i c a t i o n s were made n e c e s s a r y b y t h e s e e m i n g l y c o n t i n u o u s

u p g r a d i n g of t h e c o m p u t e r system a t N A S A . I n order t o p e r f o r m

~iseful s i m u l a t i o n s w i t h t h i s c o d e a n a c c e p t a b l e a n d r e a l i s t i c

-6- ORIGINAL PAGE Ls OF POOR QU-

model w a s f i r s t d e v e l o p e d f o r t h e g a l l i u m a r s e n i d e c r y s t a l . One

of t h e most i m p o r t a n t aspec ts of t h e model is t h e s e l e c t i o n o f a n

i n t e r a t o m i c p o t e n t i a l f u n c t i o n t o b e u s e d f o r t h e i n t e r a t o m i c

i n t e r a c t i o n s t h a t are s i m u l a t e d . The Moliere a n d t h e born-Mayer

p o t e n t i a l f u n c t i o n s were c o n s i d e r e d b e c a u s e of t h e b e h a v i o r of

t h e s e two f u n c t i o n s f o r r e l a t i v e l y l a r g e n u c l e a r s e p a r a t i o n ( = > l

A'') w h e r e t h e o u t e r e l e c t r o n s h e l l s become i m p o r t a n t . T h e s e l a r g e

n u c l e a r s e p a r a t i o n s a r e e x p e c t e d d u r i n g c o l l i s i o n s b e t w e e n a .

r e l a t i v e l y l o w e n e r g y p r i m a r y recoi l atom a n d o t h e r atoms i n s i d e . ,-

I t h e c r y s t a l . The Moliere p o t e n t i a l f u n c t i o n is

3 V ( r ) = ( ( Z 1 * Z 2 * e ' ) / r ) * f ( r )

f ( r ) = (0 .35*exp (-(>.30*r/a) +(:].55*exp ( - 1 . 2 + r / a ) +(I. l(3wez:p (-6.(:)*r/a) )

w h e r e ' a ' is t h e s c r e e n i n g r a d i u s a n d ' r ' is t h e i n t e r a t o m i c

separa t ion . The Born-Mayer p o t e n t i a l f u n c t i o n is

V ( r ) = A e x p ( - r / a B ) where ' r ' is

t h e i n t e r a t o m i c s e p a r a t i o n , 'aB' is t h e s c r e e n i n g r a d i u s land t h e

a v e r a g e v a l u e o f '4' f o r g a l l i u m a r s e n i d e is 9,415 e V . P l o t s o f

t h e Moliere a n d Boy Mayer p o t e n t i a l f u n c t i o n s f o r a r a n g e of

i n t e r a t o m i c s e p a r a t i o n s are shown i n f i g u r e 1. The Born-Mayer

p o t e n t i a l f u n c t i o n w a s f i n a l l y s e l e c t e d a s t h e f u n c t i o n t o b e

u s e d i n t h e model b e c a u s e of t h e way i n wh ich i t a p p r o a c h e s z e r o

a t r e l a t i v e l y l a r g e i n t e r a t o m i c S e p a r a t i o n a n d t h e f a c t t h a t i t

w a s d e r i v e d f r o m e x p e r i m e n t a l r e s u l t s .

T h e s i m u l a t i o n c o d e ha5 b e e n u s e d t o g e n e r a t e r e s u l t s f o r

r a d i a t i o n p r o d u c e d damage i n g a l l i u m a r s e n i d e b y k e e p i n g t r a c k o f

t h e a c t i o n o f a s i m u l a t e d p r i m a r y recoil atom a s i t moves among

t h e l a t t i ce s i tes o f t h e c r y s t a l . T h e p r i m a r y recoi l atoms are

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I

g iven a range o f energies corresponding t o some o f t h e poss ib le

energy t r a n s f e r s from 1-MeV e lec t rons t o atoms of g a l l i u m o r

arsenic. The maximum t r a n s f e r from t h e 1-MeV e l e c t r o n i s

approximately 65 e V . The 1-MeV e l e c t r o n was chosen because o f i t s

importance i n equ iva len t e lec t ron f luence studiesZ.However,

f u r t h e r s tud ies performed dur ing t h e year on t h e concept of

equ iva len t e l e c t r o n f luence y ie lded r e s u l t s t h a t i n d i c a t e d t h a t

1-MeV e lec t rons should be replaced by 10-MeV e lec t rons i n order *

t o make the equ iva len t . e lec t ron f luence concept more v a l i d . The

s t u d i e s are descr ibed i n greater d e t a i l i n re ference‘4. A copy of

. I *

re fe rence 4 i s inc luded i n the appendix o f t h i s repo r t .

The r e s u l t s from t h e s imu la t ions i n c l u d e t h e fo l l ow ing : a.

number o f d isp laced atoms; b. number o f improper replacements; c.

number o f improper replacements; d. number o f proper

replacements; e. i n e l a s t i c energy loss; f . range o f t h e pr imary

r e c o i l atom; g . number o f i n t e r s t i t i a l s atoms; h. number ’

vacancies; and i. number of Frenkel p a i r s .

A t h e o r e c t i c a l 9nderstanding o f displacement e f f e c t s i n ’

semiconductors r e q u i r e s a d e t a i l e d a n a l y s i s o f t h e dependence o f

t h e q u a n t i t i e s l i s t e d above on t h e energ ies o f t h e pr imary r e c o i l

atoms. T h i s ana lys i s i s done by p l o t t i n g graphs and s tudy ing t h e

r e l a t i o n s h i p between t h e var ious r e s u l t s from t h e s imulated

r a d i a t i o n and t h e energy of t h e pr imary r e c o i l atoms. These

graphs represent some i n t e r e s t i n g and impor tant r e s u l t s . A graph

o f t h e t o t a l number o f displacements versus energy i n f i g u r e 2

i n d i c a t e s an approximately l i n e a r r e l a t i o n s h i p between t h e t o t a l

number o f displacements and t h e energy o f t h e pr imary r e c o i l atom i

I I I I I I I I I I I I I 1 I I I 1 .I

I

f o r t h e range o f energ ies used i n t h e s imu la t ions . Curve 2 i n

t h i s f i g u r e was p l o t t e d using r e 5 u l t s obtained from a

computat ional model developed e a r l i e r by Wilson, S t i t h , and

Stock'. Curve 3, i nc luded i n t h i s f i g u r e , represents a p l o t o f

t h e number o f Frenkel p a i r s versus energy. F i g u r e 3 i s a p l o t of

t h e i n e l a s t i c energy losses o f t h e pr imary r e c o i l atoms versus

t h e i n i t i a l energ ies o f t h e pr imary r e c o i l atoms. F i g u r e 4 i s a

p l o t o f t h e r a t i o s between the i n e l a s t i c energy losses and t h e .

i n i t i a l energ ies o f t h e pr imary r e c o i l atoms versus t h e i n i t i a l

I I .

energ ies of t h e pr imary r e c o i l atoms. From t h e graph' i n f i g u r e 4

i t appears t h a t t h e percentage of t h e pr imary r e c o i l atoms'

energ ies t h a t is l o s t dur ing i n e l a s t i c c o l l i s i o n s approaches a

maximum o f approximately 20 percent. F i g u r e 5 i s a p l o t o f t h e

t o t a l ,number of d e f e c t s versus energy. The t o t a l number o f

d e f e c t s i s t h e s u m o f t h e number o f improper replacements, t h e

number o f i n t e r s t i t i a l atoms, and t h e number of vacancies.

Fur ther s t u d i e s w i l l be made on t h e above r e s u l t s du r ing t h e

coming year. A s t u d 4 o f t h e e f f e c t of temperature on t h e

produc t ion o f d e f e c t s w i l l be included. r

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R e f e r e n c e s

1. FInnual Report of t h e So l i d S ta te Physics Research I n s t i t u t e ,

V i r g i n i a S t a t e Un i v e r s i t y j Pet ersburg , V i r g i n i a. Hepor t Per i od :

1/1/84-12/31/84

2. Wilson, John; S t i t h , John; and Walker, G i l b e r t : S ix teenth IEEE

Photovo l ta ic S p e c i a l i s t s Conference-1982, 82CH1821-8, 1982,

pp. 1439-1440.

3. Wilson, John; S t i t h , John; and Stock, Larry : NASA Technical

Paper 2242, December 1983. I 9 .

4. S t i t h , John and Wi lson, John; Microscopic Defect S t ruc tu res

and Equiva lent E l e c t r o n Fluence Concepts. Present'ed a t t h e

1985 IEEE S p e c i a l i s t s Conference, October 1985.

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I I E I

THE HALL EFFECT ANNUAL REPORT 932 o(

During the year the Hall effect research program rwved

through several milestones. The equipment was acquired which

will allow conventional Hall effect measurement to be made at

Urrpinid State University. The program involved two . .

undergraduate5 and one graduate students In t h e system * I -

development, P, working relationship was developed with the N a v a l

Research Laboratory tlas also commenced. T h i s contact will allow

I

the performance o f Quantum Hall effect.

We a l s o consulted O r . Robert Coleman at the University o f

Virginia. He is during Hall Effect experiments. The principal

Investigator also attended a 3bQrt course i n Radiation Damage

throuph the auspices o f the SfEE B Monterey, California.

The measurement s y s t e m at Virginia S t a t e University . %

consists o f B WalkeF Scientific Power supply Cfrom 0 to 50 amp) ,

an alpha MaOnet , a digital Gaussneter, a HIY 98r6 computer with

peripherals, a 3497A data acquisition will be used to acquire and

analyze the data . A cryostat has a1z.o been acquired.

Roscoe Ledbetter, an undergraduate stuaarrt has

developed a computer propram for data acquisition. A program t o

process and analyze the data is nearing cempletim. The decision

has been made to operate two systems o f sample geometries. One

THE HALL EFFECT ANNUAL REPORT

employs the standard Hall sample confipuration. The other will

utilize the Van der Pauw technique.

The ep,pcrimental procedure as we have perceived it

consists o f the measurement o f t h e Hdll coefficient, resistivity, 8 I .

and Hall mobility a s a function o f temperature o f a s?mple o f

Gallium Plraenide b e f o r e and after irradiation with low and hiph

enerpy protons. In order to compare the results with the known

damapes that are produced by proto irradlation , one need t o know

the relationship among the quantities that radiation damage and

the Hall effect measurements have in common.

It is known that the effect of radiation dameoe is

associated with the carrier concentration and the Hall

nobilities , The manifestation o f the radiation defects

are "intrinsic defects". In order t o establish and test the *

theory , B theoretical model is being developed using

Lindhard's theory of atomic coilisions.

The second nost impwtant step is to link

the quantum Hall effect and the changes

produced by proton collisions. Work has

bapun on t h e the development of a theory and

subsequently experiments will be designed and

perf orned.

I' APPENDIX I

RESISTIVITY fiND HALL COEFFICENT MEASUREHENTS VAN DER PAUW METHOD

The measurement theory developed by Van der Pauw involves the use o f

arbitrary Owmetric confiqurations . Incumbent adjustments w e made f o r the

chosen geometry. For our system consider a lamella

I ( In order to make resistivity measurements a current I is passed through t w o .

adjacent contacts e.g. ( 2 and 3 1 , the voltape U is then measured a c r o s s the

other contacts. The equation R = V / I is used. Next a current I' is passed

throuuh the next pair of contacts ( 3 . 4 ) and the voltage V ' 1s measured across

the other contacts. The equation R ' 5 U'/I' i s used, The resistivity ' '

of sample o f thickness 't' is related t o R and R' through the relation

E x p ( - tR/ 1 + Exp(- tR'/ 1 = 1 . The resistivity can thus b e obtdined.

In order t9 determine the value o f the Hall coefficient, a current I ia

passed throuoh two non adjacent contacts and t h e voltaqe V is measured across

the other two. The relation R = R/I is used. The maonetic field 15 now

energized and the meaprements of V ' and I' are then made on the same

contacts. The Hall coefficient RH can now be determined from u = RH/ . The nsasurement process consists passing a current throuph both

directions and averaoing the results. The magnetic field ia reversed and

measurements taking in both direction and averaped.

She followinp relations are typical for the experimental determination o f

the resistivity and Hall nobility. 1911 measurement are made as a function of

temperature.

t/ln?(U23/21,4 t

PI? I NT 120 PRINT

130 PRTNT 148 GOSllB 150 ! 5ClR 1G@ GOSUB 178 GOSUB 180 GOCJUB 198 ti0SUB 2Q0 GOSUB 210 GOT0

L IMINAT I or4 18

ORIGINAL PAGE IS OF POOR QUALITY

580 I GET THE m - r A THE D A T A 800 1 SQUHRE U? THE M H T H I i a?80 1 SET UP THE M A T R I X 5986 I GAUSS- JOliOAN Sr)LUT I ON 1 OB@ I PRINT 'THE R€SULTS -?@@a 1 O A T 6 80

520 ! GET THE DATA 5 18 1.NPUT "NUMBER 17F DATA POINTS" ,N 1 528 INPUT' "POLYNOMIHL ORDER" ,NZ

540 I F N 2 4 1 TtiEN 9599 530 i~ r i m THEN 5 3

550 u-w+ I

If N3=1 THEN 620 FOP 1=1 T O NI READ X { I ) , Y l [ I ) NEXT I RETIURN

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4140 NEXT t: 50Q@ 1 JORDAN MASHIX IN1JEF.'9iOPi AIK) SrJLClTION 5810 1 FEB '1, I966 501 1 I IDENTIFIERS 5012 ! A ri COEFFlClENr M A T R I X

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I

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PLOT X ( I ) ,Y( I )

PdEXT I MWE G1 ,O f O R K = \ TI! N I P L O T x ( h' ) , Y2 < K 1

NEXT i.: PRINT " I F YOU WANT ri HARD COPY OF GRAPH PRESS UtJMP GRiiF'HICS" PRINT " I f NOT PHESS C O N T I N U E " PHUSE GRflF'HICS OFF

INPUT Z $ Li?BEL TIME$(TIMEOATE 1 ,DATE$( TIMEDATE ) IF ? $ = " Y " THEN 188

RE TURN 6,RAPHICS OFF

EN 13

PRINT "00 YOIJ u h r u TO PLOT ANOTHER 5E.r OF D H T A Y i r d "

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WTPUT 2 USING "t ,K";Cb

ORIGINAL PAGE IS OF POOR QUALITY,

REFER E NC E

6 . U, Shemasv Chanoes i n t h e E l e c t r u p h y s i c a l characteristics G f n - t y p e S i l i c o n as a Resuit o f Irradiation b ~ i t h 6 . 3 Mev P r o t c m 5 0 9 , P h y s . Semicond. 1B(Z ) fzbruary 1984

ORIGINAL PAGE IS OE POOR QUALITY

I 8 I I I 8 I 8 8 I I 8 I 8 1 I I 8 I

Student Par t ic ipa t ion

During the Spring

i n the program, Lucian

1985 semester six graduate students were par t ic ipa t ing

R. Goode, Jr., Akpan E. Akpan, Nana Adu, W i l l i a m Bolden,

Larry Brown and Karamali Shojaei. Goode, Adu and Shojaei a r e working on MuSR

projects ; Akpan, Bolden and Brown are working on computer modeling of rad ia t ion

damage in solids. I n September 1985 another graduate student, LL-Tai Song,

joined the i n s t i t u t e and is working on H a l l effect s tudies .

Michael Davis, Roscoe Ledbetter, Cornelia Belsches and Raymond N o e l . Fa l l 1985

Other Ac t iv i t i e s

The d i r ec to r of t he i n s t i t u t e par t ic ipated i n an expe rben t on i n e l a s t i c

s ca t t e r ing of polarized protons from 12C a t the Los Alamos Meson Physics F a c i l i t y

in New Mexico dmring July/August and Ncmember/December 198s. Uramalz ' Shojaei,

a VSU graduate student, par t ic ipa ted in t h e July~pmgust run. Other collaboraturs

included Bernard J. Lieb of George Mason University, Eerbert 0. Funsten, Charles

F. Perdrisat and J. Michael Finn of t h e College of W i l l i a m and Mary, Hans S.

Plendl of Flarida State University, Joseph Comfort of Arizona State Vniversity,

and one graduate student each from William and Mary, Florida State and Arizana

S t a t e .

A n abs t r ac t of a paper t o be presented a t the April 1986 APS meeting is in-

cluded as Appendix 6. We are seeking other sources of funding f o r our p a r t i c i -

patian in these srrperimMI and hope far success in the neax future .

Two papers based on work done a t the Tri-University Meson F a c i l i t y (Vancouver,

BC) i n 1979-80 and supported i n p a r t by NASA grant NSG 1646 were completed in

1985 with extremely minor support

publication by Physical Review C.

from NAG-1-416. Both were accepted for

"Energy dependence of the 7Li (p ,d) 6Li

reaction" appeared in the September 1985 issue and a reprint is included

here as Appendix 7. "4He($,d)3He reaction at 200 and 400 MeV" is scheduled

to appear in the February 1986 issue and a preprint is included here as

Appenafx 8-

The director participated in the revision of a paper baaed on pb&-

nucleus reaction experiments carductal at USMPF in 1980 amd supported in

part by NASA grant NSG-1646. This revised version has been submitted to

p h y c i d &err* C and a * isiacuded bere as Agpenaix 9-

The director of the institute has served as the Virginia State Univer-

sity representative on the board of trustees of the Southeastern Universities

Research Association since October 1983. During 1985 he served on the SURA

industrial aff i l iais COmrmittee and in easly J" 1986 was 8pphted to

the science and technology camanittee of SURA. %is committee will provide

SURA oversight for the Continuous Electron Beam Accelerator Facility, which

is a 4-GeV continuous wave electron accelerator to be constructed in Newport

News, V i r g i n i a -

In May 1985 the director completed a one-year term a6 chahmsn of the

-.- * a n d p h y s i c s m * of the V i E g i n i a Academy of science-

He was also appointed to the local organizing committee for the International

Symposium on the Physics and Chemistry of Small Clusters, which will take

place in October 1986 in Richmond, Virginia.

Jaa~s C. Dave!np& semred as director of the 5mmer student program at

Fermilab (Batavia, Illinois) during the summer of 1985. He also served on the

Committee on Minorities in Physics of the American Physical Society this past

year.

George W. Henderson, John J. S t i th and Larry D. Brown (graduate student)

received course c r e d i t i n the summer of 1985 f o r an IEEE-NSRE t u t o r i a l shor t

course on radiat ion e f f e c t s through the New Jersey I n s t i t u t e of Technology.

Eqyipment and Supplies

The following items were pyrchased during the reporting period:

1 J d s supertran h e l i u m transfer tu35e 4 EHI 99078 photumuLeiplier tubes 3 O r t e c 265 tube bases 3 Ortec 218 phototube shields 1 EGCG/Or tec 567 Time-to-amplitude converter 1 PAP U 7 3 capater (l-magabytn memcary, 31- bard disk dxjve,

1 Inter face Standards IS=l l /CC CAMAC crate con t ro l l e r 2 Keithley 175 multimeters 1 Keithley 197 multimeter 3 Hewlett-Packard HP-15C calculators

1 1-megabyte memory board f o r HP 9816s computer 1 Hewlett-Packard terminal emulator 1 Hewlett-Packard 9816s camputs with accessories 1 Hewlett-~cSard W 3497A data acquis i t ion control d t 1 MICRO/RSX operating system for PDP-11/73 computer 3 PVC i n s e r t s and magnetic shields f o r phototubes

dua l floppy disk dr ives, terminal and printer

100 r e p r i n t s of our paper on MuSR i n s t ra ined s ingle crystals of iron

In addi t ion, the i n t e rna l account a t Brookhaven National Labarstory

continued i n force. This enables the i n s t i t u t e t o purchase equipment, suppl ies

and materials from BafL directly w h i l e e x p e r m t s are in progress-

Three peripherals for the PDP 11/73 computer were ordered ( p l o t t e r , modem,

and Advanced Programmers Kit) are still on order. A quadruple constant f r ac t ion

discriininator and a s c i e n t i f i c word processing program are a l so on order.

. .

Summary

The second year of support from NASA for the Solid State Physics Research

Institute was a year of growth and consolidation. The MuSR program saw a major

publication, substantial progress on several other projects and near completion

of the new data acquisition and analysis system (which should be complete in

t h fbls @xperhmmto in the Spring of 1906. The radiation damage studies have

gone into production mode, and the Hall effect apparatus is essentially com-

plete. The number of student participants increased substantially over the

1984 level.

Tbe aigbr level of s- Me has enahled tbe pxincipl investiga-

tors to set higher standards for student eligibility for research stipends,

and the quality of student involvement showed marked improvement as we began

the spring 1986 semester.

We look f-d to another active and mccessfaal pear in 1986, and we

appreciate the support €zmn NASA which makes these activities possible.

Respectfully submitted,

Pa* r L r d i.2

CareyE. StroMch Director Fehruary 14, 1986

. . . L

I I I I I I I I I I I I I I I I I I I

200 MeV n+ Induced Single-Nucleon Removal from 24Mg

Donald Joyce and Herbert 0. Funsten College of William and Mary

Williamsburg, VA 23185

B. Joseph Lieb George Mason University, Fairfax, VA 22030

Hans S. Plendl and Joseph Norton Florida State University, Tallahassee, FL 32306

Carey E. Stronach Virginia State University, Petersburg, VA 23803

V. Gordon Lind, Robert E. McAdams and 0. Harry Otteson Utah State University, Logan, UT 84322

David J. Vieira Los Alamos National Laboratory, Los Alamos, NM 8 7 5 4 5 "

Anthony J. Buffa California Polytechnic State University

San Louis Obispo, CA 93401 \ A

I I I 1 I I I 1 1 I I ' I 1 I I I I I

' 1 I

ABSTRACT

Nuclear 7-rays in coincidence with outgoing pions or protons

following single nucleon removal from 24Mg by 200 MeV T+ have

been detected with Ge(Li) detectors. Differential cross sections

are reported for 7-rays from the first excited mirror states of

23Na and 23Mg in coincidence with positive pions or protons

detected in particle telescopes at 30', 6 0 ° , 90', 120' .and 150';

angle-integrated absolute cross sections and cross section ratios

u ( 23Mg/~ ( 23Na) are calculated.

the predictions of a Pauli-blocked plane-wave impulse approxima-

tion (PWIA) and the intranuclear cascade (INC) and nucleon

These results are compared with

charge exchange (NCX) reaction models. The PWIA and the INC

calculations generally agree with the angular dependence of the

experimental results but not the absolute magnitude. -

The NCX

calculation does not reproduce the obsented cross section charge

ratios. ,

PACS number: 25.80 HP

. I I I 1 I 1 I 1 I I I I 1 I I 1 I 1 I

I. INTRODUCTION

The ( ~ r , n N ) nuclear reaction offers the potential of a new

means of understanding nuclear structure and, at the same time,

of studying the propagation of a strong baryon resonance, the A,

in the nuclear medium. Before this potential can be realized,

however, a better understanding of the reaction mechanism must be

developed.

The (n,~rN) reaction has been extensively studied using two

general types of experiment. In one type of experiment, the

residual nucleus or specific states of the residual nucleus are

identified through radiochemical techniques [e.g. Ref. 1,2], or

via detection of prompt de-excitation y-rays [e.g. Ref. 31.

Since no kinematical or angular information is obtained, these

experiments integrate over both quasifree and non-quasifree

components. -

Interest in these experiments has centered on the charge

dependence of the cross section ratios which were found to differ

from the free nN ratios. For example, the cross section ratio

o ( A + ) / o ( T - ) for A induced neutron removal from 12C was found to

have a value of 1/1.7 instead of 1/3 [l] . In the other type of experiment [e.g. Ref. 4 , 5 ] , the

outgoing pion or proton is detected. With the proper geometry,

the experimenter can select quasifree events: but only recently

has the charged-particle energy resolution become sufficient to

identify the final nuclear state. In the work of Kyle &

a. [5], the n + / ~ - ratio for proton removal from l60 was found

I R 8 I I I I t I I I I 1 I 1

to be as

increase

large as -40 at forward R angles.

over the free nN value of 9 to a reduction in the n-p

They attributed this

quasifree amplitude through destructive interference with another

process. They identified the interfering process as AN knockout.

The present study includes features of both types of

experiment by detecting prompt de-excitation y-rays in coinci-

dence with the outgoing pions or protons.

kinematic information with the ability to measure excitation of

specific nuclear states.

It thus combines

We studied 200 MeV X+ incident on a 24Mg target. Outgoing

charged particles (scattered X+ and knocked out protons) were

detected by scintillator telescopes at 30°, 6 0 ' , 90', 120' and

150' and identified by their dE/dX. Coincident nuclear r-rays

were detected in one of two Ge(Li) detectors and identified by

their energy. One can thus study several different (x,RN)

reaction channels. For example, 23Na 7-rays in coincidence with

a X+ or a p can result only from a direct proton knockout with no

charge exchange. 23Mg 7-rays in coincidence with a X+ can result

only from a direct neutron knockout.

7-rays in coincidence with a proton can only result from a charge

exchange reaction.

-

On the other hand 23Mg

24Mg was chosen as a target because single nucleon removal

from 24Mg results in mirror nuclei 23Mg and 23Na.

a test of both single proton and single neutron removal

mechanisms with pions.

spectroscopic strengths (2d 5/2 and lp 1/2 ) for 23Na and 23Mg from

This provides

Furthermore, the single nucleon removal

3

I

24Mg are concentrated in two low-lying excited states which

7-decay directly to the ground state [ 6 ] . For both 23Na and

23Mg, the first excited states (~0.15 MeV, 5 / 2 + ) have spectro-

scopic factors of -4 to 6, and the 1/2' excited states (at 2.64

MeV in 23Na and at 2.77 MeV in 23Mg) have spectroscopic factors

of -4 as determined from the analysis of single-nucleon removal

reactions on 24Mg [ 6 ] .

occupation number C2S = 2,Sone-half the Id

24Mg. (C is the isospin coupling coefficient, (Tfrfl1/2~~1Tiri)

= J1/2.)

spectroscopic factors. They predominantly feed the first excited

state, but the combined effect of this 7-ray feeding should be

less than ~ 2 5 % of the overall strength of the first.excited state

(if all states were populated - in proportion to their spectre-

scopic factors).

This yields for the 5/2+ levels an

shell limit of 4 in 5/2

Other bound excited states have considerably smaller

The suitability of a 24Mg target for (~r,nN) reaction work

was established previously by the results of an inclusive study

of 7-rays from T+ reactions on 24Mg [ 3 ] .

states in 23Na and 23Mg with large spectroscopic factors were

strongly excited; there was no evidence for background 7-rays

that might overlap these states.

tion of a 24Mg target was its suitability for a parallel study

[7] of the angular correlation of 7-rays from ( T , x ) ) scattering.

The two above-mentioned

Another reason for the selec-

A feasibility study of the techniques employed in this work

was undertaken at LAMPF using a single gamma-ray detector in

coincidence with a single charged particle telescope [ 8 ] . The

I t R 1 I I I I

4

results of that study suggested the need to develop a large-scale

coincidence measurement system sensitive to de-excitation gamma

rays, knockout nucleons and scattered pions. Such an improved

system was developed and used in the present work.

5

11. EXPERIMENTAL APPARATUS AND PROCEDURES

The experiment was performed with a 200 MeV ?r+ beam from the

high-energy pion channel (P3) of LAMPF. This beam had a contami-

nation of 6.6% I.(+ and 2.0% e+ as well as a muon halo of roughly

three times the beam diameter. The beam spot size was typically

2.5 cm in diameter, and the momentum resolution was ~ 0 . 5 % . The

target consisted of natural magnesium metal (79% 24Mg) with an

average density of 0.57 2 0.02 g/cm2.

The experimental geometry was defined by six scintillation

telescopes f o r charged particle detection and two Ge(Li) spectro-

meters to detect y-rays (see Fig. 1). Each of the six particle

telescopes consisted of the six NE 102 scintillators (Q,A,E,

rear, left-side veto, and right-side veto) . Each sacintillator

was coupled to a 5 cm photomultiplier tube, except for the E

scintillator, which was coupled to two 12.5 cm photomultiplier -

tubes, one at each end. The detector thicknesses were 0.160 cm

(n), 0.320 cm (A), 0.635 cm (vetos and rear scintillators) and

15.75 cm (E). The dimensions of each telescope component were

the same for each telescope with the exception of the n scintil-

lators.

30' and 150' had to be moved further from the target to avoid the

The n scintillators for telescopes 1, 5 and 6 at k

beam halo: they were made correspondingly larger so that all the

telescopes subtended the same solid angle.

The 0 and A counters together defined the solid angle (-0.18

sr) of each telescope, and the E scintillator determined the

I .

6

All three scintillators were used for particles particle energy.

identification.

had not stopped in the previous scintillators. The two side veto

scintillators tagged particles scattering out of or into sides of

the E scintillators. During off-line data analysis, however,

this feature was not used. Calculation of the telescope solid

angles was performed following the method of Gotch and Yogi [9],

considering the size and location of the sa, A and E scintillators

for each telescope. All telescopes except number 6 were mounted

together on a pivoting table with their axis directly under the

target centerline. Telescope 6 was mounted on a similar but

smaller table pivoting on the same axis.

The rear scintillator tagged particles which

Two Ge(Li) y-ray spectrometers were used in the present

experiment, an Ortec 9% efficient and a Princeton Gamma-Tech 11%

efficient lithium drifted germanium detector. -

Both detectors

were fitted with NE 102 anti-coincidence scintillators cups to

tag charged particles entering them. They were mounted on one

rolling table to facilitate positioning and shielding. One ,

detector was located at -75' and the other at -122' relative to

the pion beam line axis (see Fig. 1). Additional experimental

details are given in Ref. [ 7 ] .

The beam intensity was monitored with a 7.6 cm thick ion

chamber filled with argon, and the beam profile was monitored

with a LAMPF wire chamber system [lo]. The absolute cross

sections were normalized to the differential inelastic A scatter-

ing cross sections from the 2' state of 24Mg [ll].

7

The six telescopes were calibrated in energy by tuning

the channel for low-intensity protons at 50 MeV, 133 MeV and

191 MeV and placing each ofthe telescopes in the beam. The

telescopes were also calibrated with the pion and proton quasi-

elastic scattering peaks from the experimental runs as well as

with the maximum energy deposited in the E scintillators for

pions and protons.

to determine the efficiencies of the six telescopes. They were

found to average 96 k 2%.

The telescope calibration runs were also used

The energy responses of the two Ge(Li) detectors were

periodically calibrated by placing 228Th, 54Mn and 137~s sources

at the target location. Well-known strong 7-ray peaks in the

experimental data provided additional energy calibration,

including the 24Mg first excited state to ground transition and

the 23Na first excited state 'to ground transition. The maximum

deviation of the calibration data from a linear fit was 0.7 keV.

Relative and absolute Ge(Li) detector efficiencies were also

determined in the source calibration runs.

-

A valid data event consisted of a coincidence between a

particle telescope signal and a Ge(Li) 7-ray. For each event,

pulse heights were digitized for 0, A ? E (two photomultipliers),

and rear scintillators as well as the Ge(Li) detectors. All data

were read into a PDP-11 computer and written on magnetic tape for

later replay.

Particles were identified from their A and E pulse heights

using the method of Goulding et al. [12]. A particle which

I .

a

passed completely through the E scintillator (75 MeV pions) and

160 MeV protons) as indicated by the rear scintillator w a s

treated using the method of England [13]

typical dE/dx vs. E dot plot (for Telescope 1, 30*), with the

pions and protons identified.

Figure 2 shows a

During off-line data analysis, spectra were accumulated for

7-rays in one of the two Ge(Li) detectors that were in coinci-

dence with pions or protons in any one of the six particle

telescopes.

cuts on pion or proton energy. Figure 3 shows the spectrum in

the Ge(Li) detector at 75' in coincidence with a pion or a proton

in any one of the six telescopes. Figure 4 shows the random (off

Statistics were not sufficient to allow meaningful

timing peak) spectrum f o r this detector.

The r-rays in these spectra were identified by their energy, - and areas were determined by summing channels and subtracting

background. Cross sections were calculated from the relative

areas and from the Ge(Li) and the particle telescope efficien-

cies. As noted above, the cross sections were normalized to the

24Mg 2' differential inelastic scattering cross sections of

Bolger [ll]. Major sources of error were the following:

statistical errors, errors in the absolute normalization to the

inelastic data ( ~ 1 5 % ) ~ Ge(Li) efficiency calibration ( ~ 9 % ) ~ and

telescope solid angle determination ( ~ 6 % ) .

In addition to the strong first excited t/2+ states at 0.439

MeV in 23Na and 0.450 MeV in 23Mg (see Fig. 3), there was

evidence for the fourth excited 1/2' state in 23Na at 2.64 MeV;

9

but its Doppler-broadened width prevented a differential cross

section measurement. There was no sign of its mirror state in

111. COMPARISON OF ANGULAR DISTRIBUTIONS WITH REACTION MODELS

The experimental differential cross sections for production

of the 0.439 and 0.450 MeV 7-rays 'in coincidence with outgoing

pions or protons are listed in Table I for the two Ge(Li)

detectors. The averages (last column of Table I) were calculated

using the inverse of the fractional errors as weights.

cross sections differed greatly, the errors were increased in

Where two

order to be more conservative. Data from Telescopes 1 and 6 were

averaged to give one data point at 30'.

The cross sections were extracted from the data by assuming

isotropic 7-ray correlation with the outgoing pion or proton. -- -

This assumption would be rigorously true for direct plan wave

nucleon knockout and can be seen to be approximately true within

experimental uncertainties by comparing the relative cross

sections of Ge(Li) 1 and 2 listed in Columns 4 and 5 of Table I. -

(Ge(Li) 1 and 2 had an angular separation of SO'.)

of angular correlation is in contrast to the expected strong

sin22drq correlation that was observed in this experiment for

inelastic A+ scattering to the 1.37 MeV first excited state of

2 4 ~ g [73.

momentum transfer direction. )

This absence

(dyq is the angle between the 7-ray and the inelastic

Proton and pion differential cross sections were compared

with predictions of an intranuclear cascade (INC) code developed

by Frankel et. [14] and with the predictions of a simple plane-wave impulse approximation (PWIA) which assumes only a

10

11

In Section single collision of the incident pion with a nucleon.

IV, cross section charge ratios are compared with these models

and also with a model that assumes final-state nucleon charge

exchange (NCX) [15]

The INC predictions were based on 5 0 1 0 ~ cascades of 200 MeV

The program output was sorted to yield differential T+ on 24Hg.

T+ and proton cross sections at the angles measured in the

present experiment for events in which the final nucleus was 23Na

or 23Mg in a bound state. In performing these calculations, that

part of the code that evaluates evaporation subsequent to the

cascade was not used.

assumed to retain its identity if its excitation energy calcu-

lated by INC following the cascade was less than its known

particle stability energy.

details of nuclear structure or predict specific nuclear states.

It has, hwoever, no free parameters.) Since the INC-calculated

Instead, a 23Na or 23Mg nucleus was

(The INC code does not include -

contributions to the 23Na/23Mg bound states arose from the entire

nuclear volume and not just from the nuclear surface (i.e. ld5,2

shell nucleons), one should multiply the.INC results by the ratio

r = CpS' ( Jp) F ( Jp, 5/2+) /CpS' ( Jp) , where S' ( Jp) is the spectro-

scopic factor for neutron or proton removal to a 23Na or 23Mg

bound state of spin parity Jp and F(JP, 5/2+) is the relative

fraction of 7 feeding from an initial Jp state down to the 5/2+

first excited state.

ratios from ref. [ 6 ] , r h 0.6 for both 23Na and 23Ng. The INC

Using spectroscopic factors and 7 branching

. .

12

results quoted in the present paper have been reduced by this

factor.

Analysis of the output from the INC calculation showed that

a large fraction (~90%) of production of a bound a state of the

A-1 residual nuclei results from a single collision of the

incident pion pion on a nucleon with no further interaction. The

probability of the residual nucleus being left with a given

excitation decreases monotonically with increasing excitation

energy . The PWIA predictions for the cross sections were calculated

using the semiempirical free AN phase shift of Rowe et al. [16].

The resulting cross sections were reduced, at small pion scatter-

ing angles, by Pauli blocking using a degenerate Fermi sphere

uniformly filled up to a momentum of kF = 270 MeV/c. The Pauli

blocking was calculated from the quantity (V-N)/V, where N is the -

phase space volume common to the Fermi sphere and a similar Fermi

sphere whose center is displaced by an amount q = 2k, sin 8,/2,

and V is the sphere's volume. This caused the resulting cross

section at e, = 0' to be 0 and at e, 80' to approach the free

,-N cross section.

Id

state, C2S" = 2.2 defined above.

This cross section was then multiplied by the

proton or neutron occupation number for the first excited 5/2 It was necessary to addition-

ally scale the resulting PWIA prediction to the data by.multi-

plying by factors of -1/3 to 1/5. This indicates the

predominance of other processes such as pion absorption and

secondary scatterings.

13

The PWIA calculation was performed only to estimate the

trends of the experimental data. It, however, demonstrates the

role of Pauli blocking in reducing the forward angle pion

scattering from the free nN.

A. Pion angular distributions

Figure 5 shows experimental and calculated angular distribu-

tions for outgoing pions that are in coincidence with 7 rays from

the first excited states of 23Mg and 23Na.

represents the Pauli-blocked PWIA results described above: the

open circles are the results from the INC calculation. Without

Pauli blocking, the pion differential cross section would rise

steadily as 8 decreases below - 6 0 ' .

The solid curve

At 8 , = 30°, the PWIA cross

section is reduced by a factor of - 2 relative to the free case.

Both INC and PWIA calculations (and the data) display Pauli

blocking with decreasing 8 ; the INC cross section falls off more -

rapidly than the PWIA cross section. An effect that could

account for this discrepancy is nuclear shadowing of forward-

scattered pions for the INC calculation. In the PWIA calcula- ~

tion, this effect has not been included.

B. Proton angular distributions

Figure 6 displays the experimental angular distributions for

outgoing protons in coincidence with -/-rays from the first

excited states of 23Mg and 23Na, together with PWIA and INC

results (solid cumes and open circles, respectively). The

14

angular distributions have the general shape of free X-N scatter-

ing, in which case no protons would be emitted at angles greater

than 90'.

The E scintillator thickness (15 gm/czn2) was insufficient to

pennit derivation of pion energy spectra but was adequate for

determination of proton energy spectra by use of a fold-back

procedure [7]. The 30' and 60' 7-coincident proton spectra are

shown in Fig. 7 . The arrows indicate the energies for free XN

scattering; the dashed lines indicate the INC results. Coinci-

dent proton spectra for dp L 90' had few total counts: as

expected, no peak was observed. The apparent differences between

the 60' spectra and the INC predictions may be instrumental: the

steep left-hand shoulder is due to electronic low-energy cutoff,

and the high-energy tail is partially due to scintillator energy

resolution. The cross sections at 60' were corrected for the

low-energy cutoff. -

1 I

8 ' ' I e I I .I I I I I 1 'I I I i :I

I

I I

IV . ABSOLUTE CROSS SECTIONS

Table I1 compares experimental and calculated angle-

integrated absolute cross sections.

cross sections are -1/3 to -1/5 of those predicted by the PWIA

It shows that the observed

but are 3 times those predicted by INC. Particularly at the A

resonance energy, the assumption of a single rN interaction which

is implicit in the PWIA is questionable. The 200 mb free TN

cross section at the resonance yields a spatial width of -5f

resulting in a l1swel1ingI1 of the nucleon to a size encompassing

up to two adjacent nucleons. This llswellinglf yields total A-

nucleus cross sections that are typically twice the nuclear

geometrical cross section. For example, in 27Al, the geometrical

cross section is -450 mb whereas the total pion cross section is

-960 mb [16] and is divided approximately equally among pion

capture, nuclear elastic and non-elastic processes. The cross -

sections that remain for production of states obsenred in the

present experiment are thus a small fraction of the total cross

sections and would be sensitive to variations in any of the above

components.

The ratios ~ , ( ~ ~ N a ) / ~ ~ ( ~ ~ l ¶ g ) for the T+ coincident differen-

tial cross sections have values of -4, approximately independent

Of 6, (see Table 1).

Kyle et al. [ 5 ] at T, = 240 MeV in which the corresponding

This is in disagreement with the results Of

reaches a charge ratio R = u(T+)/u(R-) for 160(&,$p)15N g.s. very large value, R 1 30, f o r forward angles, 6 , I 35'. Kyle

15

I " ' 16

- al. suggests that this enhancement over the quasifree value of 9

comes from a reduction in the ~'p cross section, as n+p enhance-

ment is unlikely. In our experiment, however, the angle-

integrated r+ coincident 23Mg 5/2+ cross section, which corre-

sponds to the no cross section of Kyle et al., is relative to

PWIA, the largest of all four measured cross sections (see Table

11, column 7).

Kyle et al. occurs at scattering angles where Pauli blocking is

predominant.

It may be noted that the enhancement found by

Our n+ and p coincident 23Na cross sections are in agreement

with equivalent cross sections obtained from 12C(~+,~+p) data of

Piasetzky et al. [4] who used a double arm spectrometer system.

Their cross section values approximately equal those for free n+p

scattering; and assuming that four p shell protons are available,

their effective participation ratio is approximately 0.25, which

agrees with our results for 23Na (Table 11, column 7). However,

their 12C(~',r-p) cross section is -60% greater than our equiva-

lent A+ coincident 23Mg cross section.

-

The INC predictions as mentioned above fall below the

experimental results by a factor of =1/3.

particle histories generated by the INC code yields the following

further information on the 24Mg(n,rp) reaction:

An examination of the

A. INC predicts total, elastic, and absorption cross

sections of 980, 400, and 230 mb, respectively, in

17

general agreement with 960, 380 and 218 mb, respec-

tively, as measured by Ashery et al. [17] for 245 MeV

n+ + 27~1.

B . INC indicates that 75% of the A'S decay before striking

a nucleon. This is due to the short free decay length

of the A (-0.4 f), Our PWIA calculation indicates that

Pauli blocking of the decay is not predominant - only -1/3 of the A decays are Pauli-blocked.

C. According to the INC results, pions from A decay

predominately do not escape the nucleus: 75% of the

pions from A decay strike a nucleon to re-form another

A . Using the A decay probability given above in B,

this yields an average of two sequential A'S formed for

each T = 200 MeV pion incident on the nucleus. In a

single scattering, the pion loses an average of 60 MeV

lab kinetic energy; after two or more pion scatterings

through A formation, T, will have dropped considerably

below resonance energy. INC yields a pion scattering

mean free path A, of 1.2 f; cf. A, - 1/pX total

-

- 2.3 f. (Pion absorption occurs only through AN-.").

D. INC indicates that approximately 70% of the protons

resulting from A decay escape the nucleus without

further scattering.

agreement with xp = l/poP > 5 f obtained from free, but

Pauli blocked [18] NN total cross sections [19] and a

24Mg uniform nuclear matter density p of radius 1.315 f

INC yields xp = 4.5 f; this in

1 I I 1 I I I 1 I 1 1 I I I I I I I

E.

18

[20 J . estiamtes by Schiffer [Zl]. Of the scattered A decay

protons, approximately half undergo charge exchange

before escaping in the INC calcualtions.

The INC result is also in agreement with

Since only

30% of the protons do not escape, this yields a proba-

bility for NCX of -15%.

Approximately 40% of the total cross section for

incident pions results in pion capture

according to the INC calculation. Measurements by

Ashery et al. [17] indicate a ratio of capture-to-total

cross section of =30%.

In a recent paper, Frankel et al. [22] explored the effects

of using a different nucleon momentum distribution in the INC

code.

assumes a local, degenerate Fermi gas distribution. This was

changed to a shell model with harmonic oscillator wave functions.

The usual version (the one used in the present paper) -

The latter momentum distribution improved the INC code agreement

with the angular correlation data of Piasetzky et al. 141.

Since the A- induced nucleon removal is likely to be a surface

reaction, the use of a more realistic momentum distribution could

improve agreement with the present results.

The INC results discussed above suggest that pion mu1 t ipl e

scattering, occurring mainly by sequential A production and

decay, is a predominant process, being more important

1.2 f) than nucleon mu1 t ip 1 e scattering 5 f) which

19

was proposed some time ago [15] as a major process in pion-

induced nucleon knockout at A resonance energies. In the latter

process the nucleon from A decay undergoes subsequent incoherent

nuclear scattering with a probability of nucleon charge exchange

(NCX) , P 0.1 + 0.2 (151 as determined from cross section ratios

obtained in g(l2C(~+,X) 11C]/~[12C(~-,X) l k ] activation

experiments (13.

coincident cross sections for de-excitation 7-rays are

determined.

sensitive test of the NCX model than the previous activation

experiments, which sum over these two final states.

In the present experiment, both .rr+ and p

Hence the present experiment provides a more

The NCX calculation predicts cross sections for the final

states 231Jlg + x+ , 231Jlg + p, 23Na + n+, and 23Na + p to be in the ratio of (1+9P) :2: (9+P) : (9+P) . must be accompanied by both n+ and p, the final states 23Na + n+

and 23Na +p must have the same cross sections regardless of the

reaction model.

(see Table 11) were averaged, yielding ~ ( ~ ~ N a ( A v ) l = 48 k 8’mb.

There are then only two independent cross section ratios. Let

them be the ratios of o [ ~ ~ M ~ + A + ] and t~[~~Mg+p] to ~ [ ~ ~ N a ( A v ) j .

The first ratio,

Since the 23Na residual nucleus -

Hence, the two experimental 23Na cross sections

R1 = + .rr+]/~[~~Na(Av)] = .23 k - 0 4 ,

yields P = .12 f - 0 4 , consistent with values of P obtained from

activation work. (Quasifree R1 = 1/9). However, the second

. '

20

ratio, obtained from the proton component of 'the 23Ng final

state, has a value

R2 = o[23Mg + p]/~[~~Na(Av)] = -33 f . 0 5 ,

yielding a negative value of P, P = -2.9 k .9, which is inconsis-

tent with NCX, even though the uncertainty is quite large.

(Quasifree R2 = 2/9). Because of electronic cutoff and the lack

of. scintillators in. the forward direction where the proton cross

section peaks, we may be undercounting proton events and hence

R2. However, increase in R2 would worsen agreement with NCX.

A comparison of our experimental results with the results of

activation measurements can be made by summing the measured A+

and p components of the 23Mg cross section (see Table 11) . yields a ratio of

This

- o [ ( ~ ~ M ~ + ~ + ) + ( ~ ~ # g + p)]/~[~~Na(Av)] = . 5 6 2 - 0 6 ,

which in turn yields a value of P = . 2 4 k 0.07, consistent with

the value of P obtained from activation measurements.

The above results indicate that whereas the NCX model can

explain inclusive cross section results like those obtained by

activation measurements, it is inconsistent with the more

exclusive cross sections obtained in the present experiment. In

a recent paper, Ohkubo and Liu [23] include the effects of

quantum mechanical interference between quasifree and non-

quasifree (NCX and A charge exchange) reaction processes using

distorted waves. Their calculations result in significantly

21

better agreement with the experimental results for 22C (n+,xN) llC

cross section ratios [l] than the previously incoherent NCX

calculations [15]. In a'subsequent paper Ohkubo, Liu et al. [2]

conclude that both NCX and the interference effects decrease

considerably in magnitude as the target mass is increased from

A = 12. Their results suggest that these effects are small for

an A = 24 target.

A process in which an initial A subsequently interacts with

a nucleon in a (AN) T32 state can, by itself, reproduce measured

values of R1 and R2. Such a process, in which one of the (AN)

decay nucleons subsequently remains in the nucleus, yields

T=2

R1 = 0.22, R2 = 0.37, i.e. values close to those observed.

Although there has been evidence f o r a possible ( A N ) T=2 attrac-

tive potential [24], an examination of the magnitude of pion

double charge exchange cross sections casts doubt on this -

process. Even after allowing for the isospin recoupling, which

yields for pion double charge exchange a ( A N ) T=2 component -1/3,

any AN contribution that is sufficiently large to yield a

reasonable (n,nN) reaction would result in a pion double charge

exchange cross section too high by at least a factor of 10.

I ' V. CONCLUSION

The experimentally determined pion and proton differential

cross sections for de-excitation 7-rays from the 5/2+ first

excited states of 23Na and 23Mg in coincidence with outgoing\n+

or p from 24Mg(~+,~N) have been measured and compared with the

results of calculations based on several (n,nN) reaction models,

in particular on a Pauli blocked plane-wave impulse approximation

(PWIA), on intranuclear cascade (INC) models, and on charge

exchange of the outgoing nucleon (NCX).

Both the PWIA and the INC calculations reproduce the

approximate shape of the observed A+ and p angular distributions,

but not the magnitude. The PWIA calculation, which was done

primarily to illustrate the trends in the data , resulted in cross sections that were a factor of -3 to 5 too large. On the other

hand, the INC calculations, which can be considered absolute, -

were a factor of - 3 too small. These calculations indicate that

rescattering of the outgoing pions is a more important process

than interaction of the outgoing nucleons.

to a more sensitive test by the present experiment than by

previous activation experiments, since A+ and p coincident cross

section ratios for de-excitation y-rays are determined separately

rather than together.

experimental results.

The NCX model is put

The NCX results are inconsistent with

These comparisons with several reaction models suggest that

a more detailed description of the AN interaction in a nucleus,

22

a - *

23

such as the A-hole model of Hirata, Lenz and Thies [ 2 5 ] , may be

needed for a better understanding of the processes involved in

the ( A , AN) reaction

i '. ' 1 1 1

2 4

ACKNOWLEDGEMENTS

We wish to thank Jean Julien, Herbert 0. Funsten, I11 and

David C. Plendl for their participation in the data collection,

Peter Gram for valuable discussion on experimental details, a~nd

Robert Damjanovich and other members of the LAMPF staff for

technical assistance.

NSF; the participation of one of us (C.E.S.) was also supported

in part by NASA.

This work was supported in part by the

. .

i I '

1 8 1 I I

I

I i

:I

25

REFERENCES

1. B. J. Dropesky, G. W. Butler, C. J. Orth, R. A. Williams,

M. A. Yates-Williams, G. Friedlander and S. B. Xaufman,

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V. G. Lind, Phys. Rev. CJ9, 2405 ( 1 9 7 9 ) .

4 . E. Piasetzky, D. Ashery, A. Altman, A. J. Yavfn, F. W.

Schleputz, R. J. Powers, W. Bertl, L. FElawka, H. K. Walter,

R. G. Winter and J. Van Der Pluym, Phys. Rev. m, 2687

(1982) . 5. G. S. Kyle, P. A. Amandruz, Th. S. Bauer, J. J. Domingo,

C. H. Q. Ingram, J. Jansen, D. Renker, J. Zichy, R. Stamin-

ger and F. Vogler, Phys. Rev. Lett. 52, 974 ( 1 9 8 4 ) .

6. P. M. Endt and C. Van der Leun, Nucl. Phys. J4310, ( 1 9 7 8 ) .

7. D. Joyce, Positive Pion Scatterins on 24m. Ph.D. Thesis,

College of William and Mary (1982) . 8 . V. G. Lind, R. E. McAdams, 0. H. Otteson, W. F. Denig,

C. A. Goulding, M. Greenfield, H. S. Plendl, B. J. Lieb,

C. E. Stronach, P. A. M. Gram and T. Sharma, Phys. Rev.

Lett. 11, 1023 ( 1 9 7 8 ) .

9 .

10.

11

12.

1 3 .

1 4 .

15 .

1 6 .

17.

1 8 .

1 9 . 20.

21.

22 .

23.

26

H. Gotch and H. Yogi, Nucl. Inst. Methods 96, 185 ( 1 9 7 1 ) .

G. J. Krause and P. A. M. Gram, Beam Profile Monitor, LASL

Report LA-7142 (1978) . J. Bolger, private comunication ( 1 9 7 9 ) .

F. S. Goulding, D. A. Landis, J. Cerny and R. H. Pehl,

Nucl. Inst. Methods 21, 1 ( 1 9 6 4 ) .

J. B. A. England, Technicrues in Nuclear Structure Physics

Part 2, p. 419, John Wiley and Sons ( 1 9 7 4 ) .

2. Frankel, Phys. Rev. 130, 2407 ( 1 9 6 3 ) .

G. D. Harp, K . Chen, G. Friedlander, 2. Frankel and J. M.

.Miller, Phys. REV. a, 5 8 1 ( 1 9 7 3 ) .

M. M.,Sternheim and R. R. Silbar, Phys. Rev. Lett. 34, 824

(1975) . G. Rowe, M. Salolnon and R. H. Landau, Phys. Rev. u, 584

(1978) . -

D. Ashery, I. Navon, G. Azuelos, H. J. Pfeiffer, H. X.

Walter and F. W. Schleputz, Phys. Rev. Q3, 2173 ( 1 9 8 1 ) .

K . Nishijima, Fundamental Particles, p. 98 , W. J. Benjamin

(1963) . /

W. N. Hess, Rev. Mod. Phys. 30, 368 ( 1 9 6 8 ) .

Landolt and Bornstein, Nuclear Radii (Springer-Verlag,

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8 1 8 I 8 I I I

24. H. Toki, private communication.

25. M. Hirata, F. Len2 andM. Thies, Phys. Rev. Q8, 785

(1983) .

27

i * ' '

I 1 I I 8

2 8

FIGURE CAPTIONS

1. Experimental Geometry. The rear and side veto counters

surrounding each E counter are shown but not labeled.

2. A dE/dx vs. E dot plot for telescope 1 at 30'. The E signal

was from one of the two photomultipliers of that

scintillator.

Ge(Li) #1 7-ray spectrum in coincidence with a X+ or p from 3.

24Mg(r+,~N) in any one of the six particle telescopes (low-

energy portion).

4. Ge(Li) #1 7-ray s p e c t m in random coincidence (low-energy

portion).

Differential cross sections of outgoing X+ from 24Mg(~+,~+N) 5 .

in coincidence with 7-rays from the first excited states of

23Na and 23Mg compared with Pauli-blocked plane-wave impulse

approximation (PWIA) and intranuclear cascade (INC) calcula-

tions.

and by 0.38 for 23Mg.

-

PWIA values have been multiplied by 0.20 for 23Na

6. Differential cross sections of protons from 24Mg(~+,pp) in

coincidence with 7-rays from the first excited states of

23Na and 23Mg compared with Pauli-blocked plane-wave impulse

(PWIA) and intranuclear cascade (INC) calculations. PWIA

values have been multiplied by 0.17 for 23Na and by 0.28 for

23Mg.

mb/sr and hence do not show up on the semi-log plot.

PWIA and INC values at backward angles are <0.1

I& I I I I I 8 8 I 8 8 I I 8 I 8 I 8 I

29

7. Energy spectra of protons from 24Mg(~+,p) detected at 30'

and 60' in coincidence with 7-rays from the first excited

states of 23Na and 23Ng compared with INC calculations

(dashed line). The arrows indicate the energies for free

XN scattering.

I 8 8 I I

* I I 4 I j

8 1 1 I t

Table I

Experimental differential cross sections for 24Mg ( R I nN) .

u , ( ~ ~ N ~ ) is the differential cross section for production of .the

23Na first excited state (5/2+/ 0.439 MeV) in coincidence with a

R+.

Results are shown for each Ge(Li) and as an average which was

weighted by the fractional errors.

Telescope 6 for the 30' results.

Similar definitions apply for the other cross sections.

Telescope 1 was averaged with

Reaction Telescope Angle Ge (Li) 1 E Ge(Li) 2 Average

0% ( 23Na) 1 6 2 3 4 5

op ( 23Na)

u ~ ( ~ ~ N ~ )

1 6 2 3 4 5

30' 30' 60' 90' 120' 150'

7.321.9 4.821.3 4.421.2 4 . 021 . 1 6.321.7 6.221.6

30' 1.520.5 30' 1.420.5 60' 1 . 120.4 90' 0.8220.34 120' 1.220.5 150' 0 . 7220 . 28 30' 15.024.0 30' 18.024.0 60' 4.821.3 90' 0.5950.28 120' 1.520.5 150' 1.320.5

30' 7.622.0 30' 5.Ik1.4 60' 2.1k0.7 90' 0.4820.24 120' 0.4520.25 150' 0.9320.38

4.621.2 1.921.3 3.320.9. 1.620.5 4.121.1 4 . 221.1 1.920.5

0 . 7420 . 25 0 . 9720.30 0 . 8920.29 1 . 320.4

0 3120 15

16 . 024.0 11 . 023.0 4.021.1 0 . 8520.30 0.8720.3 1 0.4520 . 20 7.721.9 2.820.80

0.3 120.15

0.2820.15

1.320 4.

0 5920 25

5.221.1

3.920.9 3.021.0 5.221.0 5.2k1.0

1 . 420. 5 0.9020.22 0.9220.23 1.020.25 1.120.30

15.024.0

4 . 420.9 0.7620 . 20 1.220.3 0 . 9320.27 5.821.4

1.7+,0.4 0.3920.14 0.5450.18 0.6920.22

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