Current theories, in which the observed antiproton component is attributed strictly to secondary production in high energy inelastic collisions of protons with the interstellar medium or the atmosphere, apparently fail to explain the relatively high p vertical intensities measured at mountain and balloon altitudes. Therefore, a more careful calculation of the theoretical secondary intensity spectra is required before more exotic sources for these excess p's can be explored. A one dimensional diffusion equation is used to calculate the expected vertical intensity of p's due only to secondary production in the atmosphere; any assumed primary p spectrum is also included. Two adjustable parameters, the inelasticity and charge exchange in nucleon-nucleus collisions, were included in the algorithm. In order to obtain an independent estimate of their values the proton vertical intensities in the atmosphere were calculated, adjusting the parameters until the curves fit the experimental proton data, and then assumed that these values were identical in antinucleon-nucleus collisions

Bowen, T.

Moats, A.

English

NASA Technical Reports Server

PROPAGATION AND SECONDARY PRODUCTION OF LOW ENERGY 
ANTIPROTONS IN THE ATMOSPHERE* 
T. Bowen and A. Moats 
Department o f  Physics 
University o f  Arizona, Tucson, AZ 85721, USA 
1. Introduction. Current theories, i n  which the observed antiproton component is 
attr ibuted s t r ic t ly  to  secondary production i n  high energy inelastic collisions of  
protons wi th  the interstellar medium or the atmosphere, apparently f a i l  t o  explain 
the relatively high p vertical intensities measured at  mountain and balloon 
altitudes. Therefore, a more careful calculation of the theoretical secondary 
intensity spectra is required before more exotic sources for these excess p's can 
be explored. 
I n  this paper, we have used a one-dimensional diffusion equation (valid i f  
elab '5 20' down to  sea level) t o  calculate the expected vert ical intensity o f  F's 
due only t o  secondary production i n  the atmosphere; any assumed primary p 
spectrum can also be included. Two adjustable parameters, the inelasticity and 
charge exchange i n  nucleon-nucleus collisions, were included i n  our algorithm. I n  
order to  obtain an independent estimate of their  values, we f i r s t  calculated the 
proton vert ical intensities i n  the atmosphere, adjusting the parameters unt i l  our 
curves f i t  the experimental proton data, and then assumed that  these values were 
identical i n  antinucleon-nucleus collisions. 
2. Results. Our calculations followed a method suggested t o  us by T. K. Gaisser 
i n  which the atmosphere was divided in to  "slabs" o f  equal thickness Ax; slabs of  1 
g/cm2 were used. I n  calculating the di f ferent ia l  proton intensities, a primary 
proton spectrum of the form1 j - 2(E + 2.15)-2*75 -2  P - crn -s -sr"-G~V-', where E is the proton kinetic energy i n  GeV, was assumed. Protons and neutrons f r om 
higher Z nuclei were assumed t o  have the same spectral shape, and a l l  protons and 
nuclei whose momenta were less than the vert ical cutof f  r ig idi ty were excluded. 
Then, working from the top of  the atmosphere down to  sea level, the proton 
intensity o f  the i + 1 slab was calculated using the equations n(i + 1) = n(i) + 
(dn(E)/dx)Ax and a 
wi th  a similar equation [without the ionization loss2 term (dE/dx)(Anp/AE)l for  the 
neutron intensity, nn. A l l  o f  the values of  n on the right-hand side are the values 
f rom the slab i above. Xalr is the inelastic mean-free path of  proton-air nuclei 
collisions, scaled from p-1v1data.3,4 The last term i n  the equation above adds i n  
the protons gained from inelastic collisions o f  higher energy protons wi th  a i r  
nuclei, w i th  ~N(E,E,)/~E defined as the probability o f  a proton with in i t ia l  energy 
Eo possessing energy E af ter  collision. A uniform probability distribution ranging 
f rom 0 to  EO for dN(E,Eo)/dE, wi th  average elasticity €12, was assumed. s and 
- 
the probability a of charge exchange were our adjustable parameters. With the 
values a = 0.333 and s = 0.9, our computed proton intensities matched the 
experimental data quite well (see Fig. 1). We then used these values for s and a 
i n  our antiproton intensity calculations. - 
334 OG 6.1-3 
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Fig. 1. The curves show the 
calculated results for  vert ical  proton 
intensities at 710, 747, and 1030 
g/cm2 depth. The data is a 
compilation by Barber e t  al., Ref. 14. 
Using the same method, the antiproton intensity due only t o  secondary 
production was calculated w i th  equations analogous to  Eq. (I), but w i th  the term, 
added on the r ight side fo r  the production spectrum of  p's i n  proton-air collisions, 
which is taken from a parameterization of  Tan and ~ 9 , ~  attenuated w i th  an 
attenuation length of 122 g/cm2 as depth increases. The form of dE/dx and 
dN(E,EO)/dE were the same as used i n  the proton calculations. @Ir, the fi mean- 
free path i n  a i r  for  annihilation and inelastic scattering, was estimated by scalin 
a power-law fit to  i5-12c reaction cross sections f rom data compiled by G. Bruge 9 
and provided t o  us by J. C. Peng, LAMPF; ' the result is shown i n  Fig. 2 curve d, 
along with another estimate,' curve e. Three different forms of  kykl, the 
antiproton mean-free path i n  a i r  fo r  ine!astic, non-annihilation collisions, were 
tried, as shown i n  Fig. 2. I n  version c, X81r was assumed t o  be equal to  for 
protons. A curve from Szabelski and woff%dale7 was used i n  version b. Finally, 
i n  version a, we attempted a realist ic estimate for  by assuming that  'bl / 
= ua nih(jTp)/qnel(~p). Since there is l i t t l e  data available on qnel(Fp)~on- 
annihilation?, we assumed that  it is the same as the'pp inelastic cross section." 
Below 0.5 GeV, depends entirely on quasi-elastic p-nucleon scattering; for 
our realist ic estimate shown i n  curve a, the quasi-elastic scattering was taken t o  
be 1/10 as probable as for the nucleon case, based upon special Monte Carlo 
runs using ISABEL INC for j5-"C inelastic scattering at  1BO and 400 M ~ V '  
arranged for  us by P. L. McGanghey a t  Los Alamos. 
':;; 
lu 
:ll 
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li ti  ti      i tt ri   
 l    ~- cl    ci l  rl  
 i  L   15- 2C ti tt ri  t 80  eV 9 
      t  a os. 
Fig. 2. Antiproton-air interact ion 
lengths (mean-free paths) em- 
ployed i n  the calculations: (a) 
-air Xlnel derived f rom our most real- 
ist ic estimate of  ainel$-air); (b) 
Xair a l r  Inel from Ref. 7; (c) Xinel derived 
a i r  if ainel(p-air) = u (p-air); (d) R 
derived f rom our f it t o  u R ( ~ - l 2 c )  
data; (e) xgr from Ref. 7. 
The results o f  our antiproton calculations, along wi th  experimental data fo r  
the p vert ical  intensities a t  mountain altitudes, are shown i n  Fig. 3. A t  mountain 
alt i tude both curves a and c are consistent wi th  observations by the Arizona 
group,1d although we feel  that the comparison wi th  curve a, our most real ist ic 
estimate, is the more significant one. A t  balloon altitudes, our secondary p 
intensity estimates are an order o f  magnitude below the intensities reported by 
Buff ington e t  al." and Golden e t  a1.12 
Fig. 3. The curves show calculated antiproton intensities produced 
by atmospheric interactions at  747 g/cm2 11 g/cm2, and 5 g/cm2 
depth. The data points are taken from Refs. 10, 11, and 12. The 
desi nations (a), (b), and (c) correspond t o  ut i l iz ing curves (a,d), (b,e), 
and 9 c,d), respectively, f r om Fig. 2. 
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T~ (GeV) 
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i  r ction 
l t  ( - t s) 
l  in t  l ( ) 
iAinel ri  f  r st l-
ti  sti t  f 0 nel(fl-air); ) 
'l' ir ( ) 'l' ir . 
"inel    " nel erIV  
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,air ) AR  f  
 ult  f r nti r t  l l  i  x eri ntal t  r 
 rti al iti  t t i  l r  ho  in  t t in 
lti ci th   nd  r  i t t i  r ti y   
 lt   el t  ri on  r   r t alistic 
t , i   r  i if t  t ll n l r econdar  " 
i sit  sti  r   r f i  l   i i  rted y 
f t  t l 11  l n t l. 12 
--K Buffinglon,.1 01. 
747 g/cm2 depth 11 g/cmZ depth 5 g/cm2 depth 
Golden elaL 
~ /sembroski elol. 
),0' -~~-
'~ 
.   l l t  ti t  i  d 
 t ri  ti  t  2  2,   2 
  t  i  r        
ig ti  ,  d  tili i g  ,d), ,e), 
 ( d), cti l   
These results assume that there is no primary j5 spectrum. We then 
added to  version "a" a primary P spectrum normalized by passing through 
the point of Golden et al. 12 at 8.5 GeV of the form 
j-=(2.4~10-~)[(~+0.94)/9.441-Y. I f  y=2.75 as for the proton spectrum then 1 t i e  resultant low energy spectrum at mountain altitude (747 g lcm ) was 
2.0% greater than the purely secondary i5 spectrum; wi th  y=2.1 as 
suggested by Stecker and wolfendale,13 the primary j5 contribution at  
mountain altitude increases to 4.E0h. Then y was adjusted unt i l  the 
calculated low energy j5 intensity at 747 g/cm2, due t o  the primaries, 
equaled the difference between the data from Bowen et  al.' and the 
calculated result for purely secondary p spectrum [Fig. 3(747 g/cm2), curve 
a]. A rather f la t  spectrum, p0.95, is required. We also determined the 
most probable energy of  the primary antiprotons contributing t o  the low 
energy ji's a t  747 g/cm2: for y=2.1, it was 30 GeV; for yd.5, 240 GeV; fo r  
y=0.9, 3800 GeV. Obviously, more data on the antiproton intensities a t  high 
altitudes, as well as additional data on P cross sections, are needed before 
making an analysis wi th  fewer approximations. 
* This work was supported by NSF Grant PHY-82-07697. 
1. Compilation presented by D. Miiller, Proceedings of Workshop on Very 
High Energy Cosmic Ray Interactions, Philadelphia, Apr i l  22-24, 1982, 
p. 448. 
2. "Review of  Particle Properties,'' Revs. Mod. Phys. 56, No. 2, Par t  11, p. 
549 (Apr i l  1984). 
3. Compilation by N. J. DiGiacomo et al., Phys. Rev. Let t .  45, 527 (1980). 
4. G. Bel let t in i  et al., Nucl. Phys. 79, 609 (1966). 
5. L. C. Tan and L. K. Ng, J. Phys. G: Nucl. Phys. 9, 227 (1983). We used 
the parameterization fo r  the "Stephens spectrum" mult ipl ied by 1.43 t o  
account for nuclei w i th  Z > 1 and by 0.71 for shadowing o f  air  nucleons 
when comparing equal g/cm2 of air  and hydrogen targets. 
6. Compilation presented by G. Bruge, Symp. on Nuclear Spectroscopy and 
Nuclear Interactions, Osaka, March 21-24, 1984 (Report D Ph-N-Saclay 
No. 2136) o f  PS184 collaboration results along wi th  earlier results 
compiled i n  K. Nakamura et  al., Phys. Rev. Lett .  - 52, 731 (1984). 
7. J. Szabelski and A. W. Wolfendale (private communication). 
8. V. Flaminio e t  al., "Compilation of Cross Sections 111: p and p Induced 
Reactions, CERN-HERA 84-01 (17 Apr. 1984). 
9. M. R. Clover et al., Phys. Rev. C 26, 2138 (1982); M. R. Clover, P. L. 
McGaughey, and Y. Yar iv (private communication). 
10. T. Bowen, E. W. Jenkins, J. J. Jones, A. E. Pifer, and G. H. Sembroski, 
Papers of 18th Int. Cosmic Ray Conf., Bangalore, Aug. 22-Sept. 3, 
1983, vol. 2, p. 96. 
11. A. Buffington et  al., Astrophys. J. -9 248 1179 (1981). 
12. R. L. Golden et al., Phys. Rev. Lett .  -9 43 1196 (1979). 
13. F. W. Stecker and A. W. Wolfendale, Nature -9 309 37 (1984). 
14. H. B. Barber et al., Phys. Rev. D -Y 22 2667 (1980). 
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Propagation and secondary production of low energy antiprotons in the atmosphere

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