This work was supported by National Science Foundation Grant PHY 76-84033 and Indiana Universit

Bacher, A.D.

Emery, G.T.

Pickar, M.A.

English

IUScholarWorks

RESPONSE CAT.,CULATIONS FOR LEAD-GLASS CERENKOV DETECTORS 
M.A. P ickar ,  A.D. Bacher, G.T. Emery 
To f u r t h e r  our understanding of t h e  response 
c h a r a c t e r i s t i c s  of t he  lead  g l a s s  de t ec to r s  used i n  
our prel iminary (p, no) studies1), and t o  f a c i l i t a t e  
a n a l y s i s  of  t h a t  and f u t u r e  da t a ,  we have found i t  
necessary t o  cons t ruc t  a program incorpora t ing  a s  
much of t he  physics involved i n  t h e  de t ec t ion  
mechanism a s  poss ib le .  Because of  t h e  l a r g e  number 
and t h e  complexity of  phys ica l  e f f e c t s  involved, 
such  a program of neces s i t y  must u t i l i z e  Monte 
Carlo techniques2).  A number of such s t u d i e s  have 
been performed i n  t h e  pas t  3, 9 4, 9 5, 9 6, 7) , however, 
these  s t u d i e s  have genera l ly  been on ma te r i a l s  
o the r  than lead  glass5) and have genera l ly  
confined themselves t o  showers generated by 
photons and e l ec t rons  w i t h  ene rg i e s  g r e a t e r  than 
o r  equal  t o  100 MeV. 
Our research  n e c e s s i t a t e s  having a program 
capable of s imula t ing  showers i n  a v a r i e t y  of 
types of  l ead  g l a s s  i n  any geometry, and of 
considering inc iden t  photons and e l e c t r o n s  w i th  
energies  a s  low a s  20 MeV. Another problem wi th  
these  previous ca l cu l a t i ons  has t o  do wi th  t he  
way they t r e a t  t he  p a r t i c l e  t r anspor t  processes 
i n  t h e  energy region below 50 MeV. I f  one cons iders  
t he  Cerenkov l i g h t  output  of an e l ec t ron  i n  a 
t y p i c a l  lead  g l a s s ,  (Schott LF5),  ( ~ i g .  I ) ,  one 
s e e s  t h a t  i t  i s  probably necessary t o  t r ack  t h e  
p a r t i c l e s  i n  a cascade down t o  an energy of a t  
l e a s t  2 MeV. Hence one would suspect  t h a t  a 
Number of Photons b/w A, and A, 
Emitted by an Electron in Pb Glass 
Te (MeV) 
Figure 1. 
good desc r ip t ion  of  t he  phys ica l  processes 
a f f e c t i n g  the  t r anspor t  of p a r t i c l e s  i n  t h a t  low 
energy region might be important. Research i n  
t h e  l a s t  few yea r s  has  enabled one t o  have a much 
b e t t e r  q u a n t i t a t i v e  desc r ip t ion  of such processes.  
The r e s u l t s  of  such research  a r e  being incorpor- 
a t ed  i n t o  our code. Further,  t he  inf luence  of 
var ious  approximations used i n  t he  low energy 
region a r e  a l s o  being inves t iga t ed .  
The phys ica l  processes inf luencing  cascades 
incorporated i n t o  our code a r e :  
1 )  p a i r  production 
2) Compton s c a t t e r i n g  
3) photoeffec t  
4) bremsstrahlung 
5) Mhller and Bhabha s c a t t e r i n g  
6) posi tron-electron a n n i h i l a t i o n  i n  
f l i g h t  
7) i on iza t ion  l o s s  and mul t ip le  
s c a t t e r i n g  
The manner i n  which these  processes a r e  incorporated 
i n t o  the  code i s  s imi l a r  t o  t h a t  of o the r  authors3) ,  
4, 95) y6) s7).  To obta in  the  response spectrum of 
a de tec tor  we included the  generation of Cerenkov 
l i g h t  and the  de t ec to r  o p t i c s  i n  the  main code. 
We compute the d is tance  t r ave l l ed  between 
e l ec t ron ,  o r  pos i t ron ,  s c a t t e r i n g  po in t s  and the  
average momentum and d i r ec t ion  between those 
points.  This information g ives  us  the  number of 
photons emitted between the  wavelengths chosen 
a s  cu to f f s  and the  d i r e c t i o n  of t r a v e l  of t he  
photons. Since the  number of such photons 
emitted v a r i e s  a s  ' /A2 ,  the  wavelength of each 
such photon must be chosen according t o  t h a t  
d i s t r ibu t ion .  These photons a r e  then tracked 
through the  de t ec to r  u n t i l  they a r e  absorbed, 
escape, o r  meet t he  phototube face.  The t racking 
rou t ine  takes  i n t o  account the  v a r i a t i o n  of 
transmission wi th  wavelength and the  v a r i a t i o n  
of t he  p robab i l i t y  of r e f l e c t i o n  wi th  angle of 
incidence on the  de t ec to r  walls .  F ina l ly ,  i f  
one such photon does make i t  t o  the  phototube 
face ,  t h e  p robab i l i t y  of de t ec t ion  of such a 
photon must vary  a s  t h e  quantum e f f i c i ency  of 
t he  phototube. 
Preliminary ca l cu la t ions  have been performed 
using t h i s  code. I n  the  ca l cu la t ions  the  model 
de t ec to r  was a 6" X 6" X 10" block of Schott  
LF5 l ead  g l a s s  w i th  a RCA 4525 (b i a lka l i )  
phototube mounted on the  back 6" X 6" face.  
Elec t rons  wi th  momenta 50, 75, 100, 125, 150 and 
200 MeV/c normally inc iden t  on the  center  of t he  
f r o n t  6" X 6" face  generated the  showers. I n  each 
case 1000 showers were generated,  and the  
p a r t i c l e s  i n  each shower were tracked u n t i l  they 
had a momentum of 2 M ~ V / C .  At t he  end of each 
shower the  number of photoelectrons generated 
was s tored .  At the  end of t h e  1000 showers, t he  
number d i s t r i b u t i o n  of photoelectrons was 
evaluated.  To reduce f luc tua t ion ,  events  were 
grouped i n  b ins  of 10 photoelectrons.  The 
r e s u l t  is  expected t o  correspond t o  the  response 
spectrum of t h e  de t ec to r .  Calcula t ions  f o r  50, 
100,. and 150 MeV/c e l ec t rons  a r e  shown i n  (Fig. 2) . 
Experimental measurements corresponding t o  t h i s  
simulation show t h a t  t he  v a r i a t i o n  of peak 
pos i t i on  with e l ec t ron  bombarding energy is  very  
l inear8) .  This behavior i s  e a s i l y  reproduced by 
t h e  code (Fig. 3). 
3 
Response Spectro for o Pb Glass Detector 
1000 Showers Simulated 
P, =50 MeV/c Momentum Cutoff = 2 0 MeV/c - 
I 
100 200 300 400 500 600 
Nwnbw of Photoelectrons 
Figure 2. 
Variation of Peak Position 
with Electron Momentum 
I I 1 I 1 
1000 Showers 
Momentum Cutoff = 2 . 0  MeV/c 
5 5 0 0  
. - 
Figure 3 
A more s t r i n g e n t  t e s t  of t he  v a l i d i t y  of t h e  
model, however, i s  t h e  a b i l i t y  t o  reproduce 
the  energy r e so lu t ion  t h a t  i s  measured. Experi- 
mental ly one f i n d s  t h a t  a very good expression 
g iv ing  t h e  v a r i a t i o n  of r e so lu t ion  a s  a 
funct ion  of energy t o  be 
FWHM = AE(FWIIM) = c / K  
Peak Pos i t i on  E 
Variation of Resolution 
with Electron Momentum 
Resolution FWHM/Peak Position  
1000 Showers 
Momentum Cutoff = 2 . 0  MeV/c 
Figure 4 
1 )  IUCF Technical and S c i e n t i f i c  Report, Nov. 1, 
1975 - Jan. 31, 1977, p. 31. 
2) We thank J . D .  Bowman and M.D.  Cooper (Los 
Alamos S c i e n t i f i c  Laboratory) f o r  t h e i r  he lp  
and suggest ions i n  i n i t i a t i n g  these  s tud i e s .  
3) M. Ya. Borkorskii ,  S.P. Kruglov, Soviet  Journal  
of Nuclear Physics,  16, 194 (1973). 
4) M. Tamura, Progress of Theore t ica l  Physics,  
34, 912 (1965) . 
-
5) E. Longo, I. S e s t i l l i ,  Nuclear Instruments and 
Methods, 128, 283 (1975). 
(E i n  MeV). 
6) H.-H. Nagel, Z.  Physik, 2, 319 (1965). 
where C i s  a constant  depending on t h e  type of 
g l a s s  and phototube used. Typically i t  
v a r i e s  between about 3.0 and 6 .  08). Our 
7) H.  Messel, F. Crawford, Electron-Photon Shower 
D i s t r i b .  Function Tables f o r  Lead, Copper, and 
A i r  Absorbers, Pergamon Press (1970). 
8) M.D. Cooper, p r iva t e  communication. 
program i s  again successfu l  i n  meeting t h i s  
t e s t  (Fig. 4) . 
I n  the f u t u r e  t h i s  program w i l l  be used 
t o  enable us t o  e x t r a c t  absolu te  c r o s s  s ec t ions  
f o r  t h e  (p,nO) r eac t ion  near threshold  from 
our  observed y-y coincidence y i e ld s .  


Response Calculations for Lead-Glass Cerenkov Detectors

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Response Calculations for Lead-Glass Cerenkov Detectors

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