This work was supported by National Science Foundation Grant PHY 75-00289 and Indiana Universit

Bacher, A.D.

Debevec, P.T.

Emery, G.T.

Gotow, K.

Jenkins, D.A.

Pickar, M.A.

Roberson, P.L.

English

IUScholarWorks

STUDIES OF PION PRODUCTION NEAR THRESHOLD 
A.D. Bacher, P.T. Debevec, G.T. Emery, M.A. Pickar ,  K. Gotm*, 
D.A. Jenkins*, and P.L. Roberson* , 
Studies  of t he  (p,.rro) reac t ion  with bom- 
barding energies  near  and above threshold have 
been i n i t i a t e d .  Eight  t a r g e t s  have been in-  
ves t iga ted ,  with thresholds ranging from 127.2 
t o  145.0 MeV, and n e u t r a l  pions have been 
observed f o r  each t a rge t .  
The experimental method i s  t o  observe 
coincidences between high energy photons 
from the  IT" decay. Measurements during the  
period of t h i s  repor t  were ca r r i ed  ou t  wi th  
two 6" x 6" x 10" lead-glass Ferenkov de- 
Figure 2. Var ia t ion  of t he  coincident  gamma y i e l d  
t e c t o r s  borrowed from Brookhaven National  a s  a function of  proton bombarding energy f o r  en- 
r iched ~ O B  and 1 1 ~  t a r g e t s  and f o r  a n a t u r a l  carbon 
~abora tory . ' )  The de t ec to r s  were t e s t ed  and t a rge t .  For t he  1 0 ~  and C t a r g e t s  t h e  threshold 
behavior is  indica ted  schematical ly by the  smooth 
ca l ib ra t ed  a t  t he  Space Radiation Ef fec t s  l i n e s .  Below threshold the  observed y i e l d  i s  con- 
s i s t e n t  with t h a t  expected from small  i s o t o p i c  
Laboratory using a momentum-analyzed e l ec t ron  impur i t ies  i n  t he  t a rge t s .  
beam i n  t he  energy range from 20 t o  100 MeV. While no cerenkov l i g h t  i s  generated i n  these  detec- 
/ 
I 
I 
I 
I 
I 
I 
I 
/ 
/ 
0 ' " ~ ( p . ~ o )  Tth 139.831 MeV - 
W 
L - 
no DETECTION SYSTEM 
w-- " B ( ~ , W ~ )  ,T,,, 130.586 MeV - 1; I ,C) 144978 MeV " C(p*ro) T ( C)= 137.953 MeV 
I _ 
'138 140 142 144 148 148 I50 152 
a 
lo 
Figure 1. Experimental geometry f o r  t he  detec- 
t i o n  of coincident  gamma rays from the  decay of 
n e u t r a l  pions. 
- 
- A - *  
t o r s  by IUCF protons ,  they d id  have alpha-source- 
impregnated sodium iodide  chips a t tached t o  t he  
f r o n t  su r f ace  f o r  monitoring the  pulse  he ight  respons. 
from each c r y s t a l .  Three inches of aluminum absorber 
was used i n  f r o n t  of each de t ec to r ,  t he re fo re ,  t o  
keep s c a t t e r e d  protons from depos i t ing  energy i n  
t h e  NaI chips. The experimental geometry is  shown 
i n  Figure 1. I n  c lo se  geometry wi th  the  two Eerenkov 
de t ec to r s  pos i t ioned a t  90° on oppos i te  s i d e s  of t he  
beam, each de t ec to r  subtends a s o l i d  angle of 1.0 
s te radians  . Lead sh i e ld ing  around the  cerenkov 
de t ec to r s  reduced background from coincident  muon 
events i n  cosmic ray  showers. 
made; these  range from a few nanobarns t o  a few 
microbarns. 
The observed y i e l d s  a r e  l a r g e r  than expected 
-. 9 5  A'"' 
Tp = 151.5 MeV 
I V Tp = 143.3 MeV I 
MASS NUMBER OF TARGET 
Figure 3. Rela t ive  cross  s ec t ions  a s  a func- 
t i o n  of the  t a r g e t  mass number f o r  t a r g e t s  f o r  
which the  indica ted  proton bombarding energy 
is we l l  above threshold.  
Such de t ec to r s  have r a t h e r  poor energy 
r e so lu t ion  f o r  gamma rays  i n  t h e  re levant  energy 
r a n g e ,  40-100 MeV, s o  i n i t i a l  w o r k  w a s  concen- 
t r a t e d  on t h e  coincidence y i e l d  and i t s  varia-  
t i o n  wi th  energy. The o v e r a l l  time r e so lu t ion  
was t y p i c a l l y  15 ns  ( fwhm) . With a t a r g e t  
thickness of about 100 mg/cm2 and beam cu r ren t s  
of about 2 nA, random coincidences were no 
problem and t r u e  coincidence r a t e s  ranged from 
about 0.002/sec t o  about 3/sec. S tudies  of  edge 
e f f e c t s  on de t ec to r  e f f i c i ency  and pulse  he ight  
spectrum a r e  s t i l l  i n  progress,  s o  only pre- 
l iminary es t imates  of c ross  s ec t ions  can be 
from a comparison wi th  (p ,n+) cross  s ec t ions  a t  
154 MeV 2, and a r e  thus i n  b e t t e r  agreement wi th  
recent  I U C F  measurements3) of (p ,  lr') which a r e  
a l s o  somewhat l a r g e r  than the  previous work a t  
Orsay. Typical  r e s u l t s  f o r  t he  v a r i a t i o n  of coin- 
cidence y i e l d  wi th  bombarding energy a r e  shown i n  
Figure 2. The r e l a t i v e  cross  s ec t ion  (pe r  t a r g e t  
n u c l e ~ )  vs t a r g e t  mass number, a t  two f ixed  bom- 
barding ene rg i e s ,  is  shown i n  Figure 3, f o r  t a r g e t s  
f o r  which one is we l l  above threshold.  
To f a c i l i t a t e  f u r t h e r  ana lys i s  of these  and 
fu tu re  da t a ,  we have been developing programs t h a t  
w i l l  c a l c u l a t e  coincidence gamma-ray s p e c t r a ,  f o r  
comparision wi th  observation,  given an i n i t i a l  
COINCIDENCE EFFICIENCY 
o,O(lL- 6' x 9" n1.r 
MINIMUM OPENING ANGLE 
~ e o k  
Figure 4. Coincidence e f f i c i e n c y  ( a t  t h e  t o  f o r  
t h e  de t ec t ion  of n e u t r a l  pions from 1 0 ~  and q68Pb 
t a r g e t s  a s  a funct ion  of  t he  proton energy above 
threshold.  Also shown ( a t  t he  bottom) is t h e  mini- 
mum opening angle between the  two gamma rays.  
Figure  5. Energy dependence o f  t h e  n e u t r a l  
p ion  y i e l d  f o r  t h e  I ~ B  (p,  IT') 12c r e a c t i o n  
compared w i t h  t h e  expected dependence f o r  
phase space  (ak,) and f o r  t h e  s t a t i c  model 
(a.k;) f o r  two extremes of t h e  e f f e c t i v e  
d e t e c t o r  s i z e .  
1.2 
Figure  6. V a r i a t i o n  of  t h e  co inc idence  y i e l d  r a t i o ,  
R,  a s  t h e  d e t e c t o r  opening angle  i s  changed about  
t h e  minimum o en ing  angle.  R e s u l t s  a r e  shown f o r  P t h e  I ~ B ( ~  , T O )  2~ r e a c t i o n  a t  two v a l u e s  of t h e  pro- 
ton  bombarding energy n e a r  t h e  t h r e s h o l d  energy of 
130.59 MeV. 
- 
COINCIDENCE YIELD [@, =30°, 8, VARIED] Rz COINCIDENCE YIELD [a, = 8, =go0] 
pion angula r  and energy d i s t r i b u t i o n .  The pro- pion angula r  d i s t r i b u t i o n  i n  t h e  r e a c t i o n  CM frame 
grams a r e  be ing  designed s o  t h a t  t h e  calcu-  a r e  shown i n  F i g u r e  4. The a c t u a l  d e t e c t o r s  a r e  
l a t i o n s  may b e  done by bo th  a n a l y t i c a l  and 6" x 6" i n  c r o s s  s e c t i o n ,  b u t  one should expec t  
Monte Car lo  techniques.  Pre l iminary  r e s u l t s ,  edge e f f e c t s  t o  reduce t h e i r  e f f e c t i v e  s i z e  t o  a  
from c a l c u l a t i o n s  i n  which edge e f f e c t s  on somewhat s m a l l e r  a r e a ,  o f  t h e  o r d e r  of 5" x 5". 
e f f i c i e n c y  and v a r i a t i o n s  of e f f i c i e n c y  w i t h  Use of t h e s e  r e s u l t s  l e a d s  a l r e a d y  t o  some 
energy have been neg lec ted ,  have given a  f a i r  in format ion  about  t h e  mechanism of pion produc t ion  
i d e a  of t h e  v a r i a t i o n  of co inc idence  e f f i c i e n -  n e a r  th reshold .  Phase space  f o r  a  two-body f i n a l  
cy w i t h  bombarding energy. For t h e  d e t e c t o r  s t a t e  i n  a  ( p , ~ )  r e a c t i o n  v a r i e s  a s  k,, t h e  CM 
geometry o f  F igure  1, and f o r  e x c i t a t i o n  of a  p ion  momentum. I n  t h e  n a i v e  s t a t i c  model of pion 
produc t ion ,  4 ,  t h e  m a t r i x  element is  a l s o  p r o p o r t i o n a l  s i n g l e  f i n a l  s t a t e ,  reasonable  v a r i a t i o n s  i n  
t o  k,, l e a d i n g  t o  expected k; dependence of t h e  t h e  p ion  angula r  d i s t r i b u t i o n  have on ly  a  
v e r y  s m a l l  e f f e c t  on t h e  co inc idence  e f f i c i e n c y .  c r o s s  s e c t i o n .  These e x p e c t a t i o n s ,  fo lded  i n  w i t h  
R e s u l t s  of c a l c u l a t i o n s  assuming an i s o t r o p i c  t h e  c a l c u l a t e d  v a r i a t i o n  of  co inc idence  e f f i c i e n c y  
with energy, a r e  compared wi th  t h e  experimental 
d a t a  on ' l ~ ( ~ , r ' )  12c i n  Figure 5. Bombarding 
energies  f o r  t he  t h ree  experimental po in t s  a r e  
such t h a t  only t he  ground s t a t e  of 12c can be 
formed. The r i s e  of t he  cross  s ec t ion  from 
threshold is  cons i s t en t  wi th  phase space,  
and incons i s t en t  wi th  t he  expecta t ions  of 
t he  na ive  s t a t i c  model. 
Calcula t ions  have a l s o  been made t o  
explore t he  p o s s i b i l i t y  t h a t  de t ec to r  geo- 
metr ies  can be cons t ruc ted  t h a t  w i l l  al low 
information t o  be  obtained on the  pion angular  
d i s t r i b u t i o n s .  This is  e spec i a l l y  important 
a t  energies  c lo se  t o  threshold  where d i r e c t  
de tec t ion  of  charged pions is no t  poss ib le .  
For example, l e t  t he  de t ec to r s  be  pulled back 
s o  t h a t  each subtends a s o l i d  angle of 0.015 
s t e r ad i ans .  F ix  one de t ec to r  a t  a labora tory  
angle of 30°, and vary the  pos i t i on  of t h e  
o the r  de t ec to r  about t he  minimum opening angle  
f o r  gamma-ray p a i r s  f o r  pions going forward 
i n  t h e  labora tory ,  Bmin = 2 a r c s i n  ( l /y,) ,  
where y, is the  r e l a t i v i s t i c  d i l a t a t i o n  f a c t o r  
corresponding t o  t he  pion energy. The r e s u l t s ,  
shown i n  Figure 6,  i n d i c a t e  t h a t  t he  "search- 
l i g h t  e f f ec t " ,  which enhances t h e  coincident  
pion y i e l d  a t  t he  minimum opening angle,  is  
s t rong  enough even near  threshold  t o  d i s t i ngu i sh  
between i s o t r o p i c  and ( 1  + cos 8)  angular  
d i s t r i b u t i o n s .  
Future ca l cu l a t i ons  w i l l  inc lude  energy- 
dependent e f f i c i e n c i e s  and edge e f f e c t s .  The 
present  r e s u l t s  a l ready i n d i c a t e  t h a t  not  only 
t o t a l  c ross  s ec t ions ,  but  a l s o  IT' angular  d i s -  
t r i b u t i o n s  can be s tud ied ,  thus f a c i l i t a t i n g  
comparison of (p , aO)  with ( p , l f )  r eac t ions .  
Components f o r  a new de t ec to r  system have been 
ordered. The new system inc ludes  fou r  d e t e c t o r s ,  
designed t o  have l e s s  background and a s l i g h t l y  
b e t t e r  energy r e so lu t ion ,  and w i l l  inc lude  f a c i l i -  
t i e s  f o r  convenient movement of t he  de t ec to r s .  
Measurements w i l l  focus on those t a r g e t s  f o r  
which the  threshold  energy dependence can be s tudied  
f o r  a s i n g l e  f i n a l  s t a t e .  
* Virg in i a  Polytechnic I n s t i t u t e  and S t a t e  
Univers i ty ;  Blacksburg, V i rg in i a  24061 
1 )  We thank T.F. Kycia, Jr. ,  and Brookhaven 
National  Laboratory f o r  t he  loan of these  de t ec to r s .  
2) Y.  LeBornec e t  a l . ,  Phys. Le t t .  e, 434 
(1974); 61B 47 (1976). 
3) R.D. Bent e t  a l . ,  Bull.  Am. Phys, Soc. 22, 
81 (1977), and t h i s  r epo r t .  
4) J .V.  Noble, Phys. Rev. Le t t .  37, 123 (1976). 


Studies of Pion Production Near Threshold

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Studies of Pion Production Near Threshold

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