Development of model for description of nucleon-nucleon and pion-nucleon collisions at high energy and Monte Carlo description of Nucleor Cascad

Matlock, R. L.

English

NASA Technical Reports Server

Louisiana State University in Shreveport 
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Final Technical Report on Grant NGR-19-012-001 
Dr. Rex L.  Matlock, Principal Investigator 
The purpose of t h i s  work was t o  develop a model f o r  the description o f  
nucleon-nucleon and pion-nucleon co l l i s ions  a t  h i g h  energy and to  incorporate 
this model in to  a complete Monte-Carlo description o f  a Nucleor Cascade. 
In the i n i t i a l  phase of the work an attempt was made to  use the s t a t i c a l  
model or iginal ly  proposed by Fermi a T h i s  attempt was prompted by the suc- 
cess of the author ( i n  an e a r l i e r  work) to  describe proton-antiproton annihila- 
t ions a t  r e s t  w i t h  a thermodynamic version of Fermi's model. 
this simple model to  correct ly  describe the angular d i s t r ibu t ion  of the pa r t i -  
c l e s  produced i n  h i g h  energy nucleon-nucleon co l l i s ions  led t o  i t s  reject ion.  
The next phase of the work consisted of a study of a thermodynamic model 
1 2 
The f a i l u r e  o f  
3 developed by Hagedorn . 
experimental r e su l t s  a r e  available tha t  the Hagedorn model yields  ra ther  good 
agreement w i t h  experiment. 
model fo r  the description o f  h i g h  energy pa r t i c l e  co l l i s ions .  
I t  was found tha t  i n  the energy region where r e l i ab le  
The Hagedorn model was thus adopted as the basic 
The e f f o r t  i n  this research was then directed toward calculat ing,  based on 
the Hagedorn model 
a Monte-Carlo description of a Nucleor Cascade. 
t r ibu t ions ,  f o r  the case of proton-proton co l l i s ions ,  were readily avai lable  
from Hagedorn's3 calculations.  The momentum dis t r ibu t ions  f o r  the pion-proton 
case were worked o u t  by the author i n  collaboration w i t h  Dr. Hagedorn. 
worth n o t i n g  here tha t  the d is t r ibu t ions  f o r  the pion-proton case needs fur ther  
experimental ver i f icat ion i n  order to  insure t h e i r  va l id i ty .  
d i s t r ibu t ions ,  within the framework of  the Hagedorn model, a r e  qui te  a problem. 
the momentum and pa r t i c l e  number d is t r ibu t ions  necessary f o r  
The required momentum dis- 
I t  is  
The pa r t i c l e  number 
https://ntrs.nasa.gov/search.jsp?R=19710017335 2020-03-11T20:05:18+00:00Z
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This problem has not  been s a t i s f a c t o r i l y  resolved as o f  this wr i t i ng .  I t  
t u r n s  o u t  t h a t  w i t h i n  the energy region where re1 i ab l  e experimental results 
a r e  a v a i l a b l e ,  the par t ic le  number d i s t r i b u t i o n s  a r e  t o  a good approximation 
Poisson. 
toge ther  w i t h  the Hagedorn model momentum d i s t r i b u t i o n s  t o  form a complete 
nucleor model f o r  high energy p a r t i c l e  c o l l i s i o n s .  The au thor  i s  continuing 
work on the p a r t i c l e  number d i s t r i b u t i o n .  
made, i t  will be made a v a i l a b l e  t o  the Cosmic Ray Branch of NASA's Manned 
Spaced-Craft Center i n  Houston. 
One can then use ' 'as a s t o p  gap measure" the Poisson d i s t r i b u t i o n  
When a s a t i s f a c t o r y  c a l c u l a t i o n  i s  
The d e t a i l s  o f  how t o  incorpora te  the Hagedorn model momentum d i s t r i b u t i o n s  
i n t o  a Monte-Carlo desc r ip t ion  of a Nucleor Cascade program a r e  suppl ied  i n  the 
appendix t o  this r epor t .  
References: 
1 .  
2.  
3 .  
E .  Fermis Progress of  Theoretical  Physics 5,570 (1950) 
Ph .  D.  D i s se r t a t ion  by the Author (Unpublished) 
R .  Hagedorn and J, Ranft,  Supplement t o  Nuovo Cimento 6,169 (1968) 
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Appendix t o  Technical Report on Grant 
NGR-19-012-001 
I e Momentum and angular dis t r ibut ion tab1 es 
The following momentum and angular d i s t r i b u t i o n  tables  need t o  be calculated 
and saved. 
section 2 below. 
DMIJK(P,E) = Momentum dis t r ibut ion tabular value. 
A description of how these tables a re  t o  be used i s  given i n  
Where 
I = 1 f o r  nucleon (proton o r  neutron) table.  
+ 
= 2 fo r  T and v0 table.  
= 3 f o r  71 table .  
- 
J = 1 f o r  newly created par t ic les .  
= 2 f o r  "Through going" par t ic les .  
K = 1 f o r  "Thermodynamic contribution". 
= 2 f o r  'Isobar contribution". 
= 3 f o r  sum of "thermodynamic contribution" and "Isobar 
contribution" e 
E = Laboratory energy o f  the incident par t ic le .  
P = Magnitude of a secondary pa r t i c l e  of type llI". 
D A I J K ( e , E )  = P Angular d i s t r i b u t i o n  tabular value. Where I,J,K, and E a r e  
defined as  above and e= angle tha t  the momentum of  the 
secondary makes w i t h  the co l l i s ion  axis .  
For def ini t ions of the W(p) and Q(E) functions used below see section I11 of 
t h i  s appendix 
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1 Through Going Protons ( I= l  J=2) 
= ~ O B O M  * M = 938 MeV; See Section I11 fo r  ~ o , $ o  values. 
'ma, P '  P 
4- 2 .  Newly created n and (I=2, J=1) 
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= ~ O B O M I T ;  MIT = 140 MeV: See Section I11 f o r  ~ O , B O  values.  'max 
P, Q x f" 
3. Newly Created IT- ( I = 3 ,  J=1)  
= ~ O B O M I T ;  HIT = 140 MeV; See Sect ion I11 f o r  ~ O , B O  values.  'max 
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+ 4. Through Going and ( I=2,  J=2) 
J 
0 
= Y O ~ O M I T ;  MA = 140 MeV; See Section I11 f o r  yo,Bo values. pmax 
5. Through Going IT- ( I = 3 ,  J=2) 
c 
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J 
0 
= yo6oM1~; MIT = 140 MeV; See Section I11 f o r  yo,Bo values. plnax 
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11. Precr ip t ion  f o r  picking momenta and angles from Dis t r ibu t ion  Tables 
1 .  Pick an energy valueg E ,  such t h a t  
(1 )  Dis t r ibu t ion  t ab le s  have been ca lcu la ted  f o r  E 
(2)  Ei  E [10w'/2E, 10'/2E) where E i  is the inc ident  p a r t i c l e s  energy. 
2. Through Going Nucleon case 
( 1 )  Pick a number X from the uniform d i s t r i b u t i o n  
f o r  o<x<k 
k 
0 otherwise 
f, 
DM123(p,E). 6"" / Where K = --A 
I-". d 
(2)  Pick a momentum value,  P ,  such t h a t  
3 
r- I '- 
X < ) DM123(p,E) < ) DM123(p,E) 
(3)  Pick a va lueg  0 ?I such t h a t  
3. Newly created IT' and IT' case 
(1 )  Pick a number X from the uniform d i s t r i b u t i o n  
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( 2 )  P i ck  a momentum value P, such t h a t  
(1) P ick  a number X f rom the  un i fo rm d i s t r i b u t i o n  
(2 )  P i ck  a value, P, such t h a t  
.P 
r----F 
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(3) P i ck  a value, o such t h a t  
0 0 +A&' 
)- D A 3 W P 2 )  p- -? X < Qr(Ei) / DA3ll(p,E) < Qr(Ei)  
i---I 
8': a B t  0 
+ 
5. Through Going IT and TO case 
(1) P i ck  a number X from t he  uni form d i s t r i b u t i o n  
f ( x )  = i' 1 f o r  o<x< k 
k 
i o  otherwise 
Where K = ?'[DM221 (p,E) + DM222(p,E)]. 
k-----nd 
P= 8 
Pick  a value, P, such t h a t  (2) 
IT+- A F' 
,-' P .y---7 
x <  ' i [DM221(p,E) + DM222(p,E)] < ,) [DM221(p,E) + DM222(p,E)] 
G I  
P r  0 
(3) P i ck  a value, o , such t h a t  
L-. 
P = 0  
0 0 .pa L?' 
X < )-: [DA221 (@,E) + DA222(o,E)] < )-' [DA221 (@,E) + DA222(o,E)] 
&Io 
6. Through Going IT- case 
(1) P i ck  a number X from the  uni form d i s t r i b u t i o n  
f l  
f o r  o<x< k 
otherwise 
- \  k ,i t: 
r- '--? 
p. 3 
Where K = ) DM321 (p,E) 
L--- 4 
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( 2 )  Pick a momentum value, P ,  such t h a t  
P ?+dP 
X < )-: DM321 (p,E) < DM321 (p,E) 
I 
L 1 
P =  (3 P=O 
(3) Pick an angular value, o , such tha t  
X < DA321(d,E) < DA321 (O', E )  
1 
Q'Z o 8h9 
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I I I a Hagedorn Model Momentum D i s t r i b u t i o n s  
1. Newly created T- 
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0 
T ( f ' )  will be supplied as a tabulated function. 
reference 3)  
(See pg. 300 of 
I .  
3 Hagedorn Model I1 )., 
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+ 2. Newly created IT’ and IT 
t 
The second term i s  the isobar decay term. 
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Newly Created 7~ Table 
M j ( M ~ v )  
M = 938.3 
M, = 939.6 
M, = 939,6 
P 
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3. "Through Goi ngl' Nucleons (proton and Neutron) 
I 
+ See IT case.  
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-I- 1 
t 1 
c 
sot- 
fat- Z‘? ( 
See T- case for a relation between y and A. 
See T” case for a relation between yo and yL = - . EL 
MP 
Proton tab le  
1) except + - + p a  
K A ) i s  the same as 
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4. "Through Going" IT- 
s 
0 
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r, i -__ 
1% ;:-' See through going proton case. 
I\irr ( ' A  !J See page (16) o f  this appendix. 
+ o  5. "Through Going" IT IT 
. .  
, -  
~ 
1 .5  x lo3 
1 .5  X lo2  
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1069 1 140 
1263 5 140 
Through going IT Table 
1 8 .3  X lo3  1 765 1 6 1 140 


High energy nucleon-nucleon and pion-nucleon collision model for nuclear cascade Final technical report

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