Results obtained using a recently developed calculational method for determining the nucleon-meson cascade induced in thick materials by high-energy nucleons and charged pions are presented. The calculational method uses the intranuclear-cascade-evaporation model to treat nonelastic collisions by particles with energies approximately or smaller than GeV and an extrapolation model at higher energies. The following configurations are considered: (1) 19.2-GeV/c protons incident on iron; (2) 30.3-GeV/c protons incident on iron; (3) solar and galactic protons incident on the moon, and (4) galactic protons incident on tissue. For the first three configurations, experimental results are available and comparisons between the experimental and calculated results are given

Alsmiller, R. G., Jr.

Armstrong, T. W.

Chandler, K. C.

English

NASA Technical Reports Server

MONTE CARLO CALCULATIONS OF HIGH-ENERGY NUCLEON-MESON CASCADES
AND APPLICATIONS TO GALACTIC COSMIC-RAY TRANSPORT 1
T. W. Armstrong
R. G. Alsmiller, Jr.
K° C. Chandler
Oak Ridge National Laboratory
Oak Ridge, Tennessee, 37830
Results obtained using a recently developed calculational method for
determining the nucleon-meson cascade induced in thick materials by high-
energy nucleons and charged pions are presented. The calculational method
uses the intranuclear-cascade-evaporation model to treat nonelastic collisions
by particles with energies _ B GeV and an extrapolation model at higher
energies. The following configurations are considered: (a) 19.2-GeV/c
protons incident on iron, (b) 30.3-GeV/c protons incident on iron, (c) solar
and galactic protons incident on the moon, and (d) galactic protons incident
on tissue. For the first three configurations, experimental results are
available and comparisons between the experimental and calculated results
are given.
INTRODUCTION
Nucleon-meson transport calculations that uti-
lize Monte Carlo techniques in conjunction with the
intranuclear-cascade-evaporation model for treating
nonelastic collisions were previously carried out
for a variety of problems involving solar protons
and other sources (refs. 1 to 3, for example). The
calculational method employed for these problems is
restricted to particle energies _ 3 GeV because of
limitations imposed by the particular intranuclear-
cascade model used (ref. 4). To enable transport
calculations to be performed for galactic protons
and other high-energy sources, the calculational
method has been extended to higher energies by us-
ing an extrapolation model (ref. 5) to obtain the
description of products from nonelastic collisions
3 GeV. This extrapolation method uses the dif-
ferential cross sections for the production of nuc-
leons and pions from 3-GeV nucleon-nucleus and
2.5-GeV pion-nucleus collisions as predicted by the
intranuclear-cascade-evaporation model, together
with energy, angle, and multiplicity scaling rela-
tions that are consistent with the sparse experi-
mental data available for high-energy interactions,
to estimate the particle production at the higher
energies.
iThis work was partially funded by the National
Aeronautics and Space Administration, Order H-
38280A, under Union Carbide Corporation's contract
with the U. S. Atomic Energy Commission.
This recently developed high-energy transport
method has been applied to compute the nucleon-
meson cascade induced in thick targets for several
source-geometry configurations, and the purpose of
the present paper is to present some of the results
obtained. The following cases are considered:
(a) 19.2-GeV/c protons incident on a thick iron
target, (b) 30.3-GeV/c protons incident on a thick
iron target, (c) galactic and solar protons inci-
dent on the moon, and (d) galactic protons incident
on tissue. For the first three cases, experimental
data exist so that comparisons with the calculated
results can be made in order to check the validity
of the calculational method.
RESULTS
19.2-GeV/c Protons Incident on Iron
Citron et el. (ref. 6) have measured the longi-
tudinal and lateral development of the nucleon-meson
cascade induced in a thick iron target by a narrow
beam of 19.2-GeV/c protons. Figure 1 shows a com-
parison of the experimental results, the results
from the present calculations, and the results
available from calculations made by others for the
longitudinal development of the cascade. The cas-
cade development is given in terms of both the star
density and track intensity. For the present cal-
culations, the star density was calculated using
the cross sections for nuclear star production in
emulsion given by Hess et el. (ref. i0), and the
track intensity was taken to be the flux due to pro-
tons above 500 MeV and charged pions above 80 MeV.
117
https://ntrs.nasa.gov/search.jsp?R=19720009966 2020-03-17T03:48:25+00:00Z
In the experiment,the iron absorberconsistedof
slabsof iron of variousthicknesseswith air gaps
betweenthe slabs. Resultsfor the presentcalcu-
lations in figure1 aregivenwithandwithout
theseair gapstakeninto account.Asindicated
in figure l, theresultsof thepresentcalcula-
tions for the longitudinaldevelopmentof the cas-
cadeagreereasonablywell with the experimental
resultsandwiththe results fromothercalcula-
tions.
omc-m,G 7_-,_cl
,,j,,-- pRES_N T CALCULATK_NS. WITHOUT A_n GAP_
--_LCULAT[O. ST_TAHE_ (_ILL[R _0 _)
..... C_CUL*TEO. _,'ONTe C_RLO (R*NFT)
IOt __ _--C&LCULATED ' PAS$OWI$ &pPROX]_TIO_ IO'_,EN)
* UEASU_EO (C_TRON. et w/._
,oo
TI _,_-, e4--,
_ _,_-, .
" _ TRACK INTENSI _--"
,o-3 1,_ -,,."
I0-4 . ,
OI[pTH 11/_ 2)
30.3-GeV/c Protons Incident on Iron
The lateral development of the nucleon-meson
cascade induced in a thick iron target by a narrow
beam of 30.3-GeV/c protons has been determined ex-
perimentally by Awschalom et al. (ref. ll). The
quantity measured was the 18F production in alumin-
nm foils placed at various depths in the iron.
Calculations have been carried out to determine the
energy and spatial distributions of the nucleon and
charged-pion fluxes for this configuration. These
fluxes and available cross sections for producing
18F from aluminum (ref. l) were then used to com-
pute the 18F production as a function of distance
from the beam axis. The energy dependence of these
cross sections is such that, roughly speaking, the
18F production can be interpreted as a measure of
the nucleon and charged-pion fluxes above _ 50 MeV.
A comparison of the calculated and experi-
mental results is shown in figure 2 for several in-
termediate depths in the iron. The agreement is
quite good although the calculations give a con-
sistently higher production near the beam axis.
However, because of the small area and alignment of
the aluminum foils used in the experiment, the ex-
perimental 18F production is expected to yield an
underestimate of the actual production very near
FIGURE l.--Star density and track intensity versus
depth for 19.2-GeV/c protons incident on iron.
Results from the present calculations are com-
pared with the straightahead calculations of
Alsmiller and Barish (ref. 7), the Monte Carlo
calculations of Ranft (ref. 8), the calculations
of O'Brien using Passow's approximation (ref. 9),
and the measurements of Citron et al. (ref. 6).
The lateral distribution of the track inten-
sity at various depths has also been calculated
and compared with the measurements of Citron et al.
The calculated and experimental results for the
lateral distributions are not in good agreement.
The reason for this discrepancy is not known at
present. However, as discussed later, the calcu-
lated lateral development of the cascade is in good
agreement with other experimental data (ref. ll)
for 30.3-GeV/c protons incident on iron. In prin-
ciple, there is no reason that the calculational
method should be less accurate for 19.2-GeV/c in-
cident protons than for 30.3-GeV/c incident protons.
g/cm 2
D_STANCE FROM BEAM AXIS (g/cm 2)
FIGURE 2.-- Calculated and measured (ref. ll)
lateral distribution of 18F production in alu-
minum foils at various depths in iron for 30.3-
GeV/c incident protons.
118
thebeamaxis (ref. 12). Theagreementat the in-
termediatedepthsshowni figure 2 is fairly typi-
cal of the agreementobtainedfor othercomparisons
that havebeenmadeat depthsrangingfrom0 to
1045g/cm2. The laterally integrated 18F production
is not available from the experiment, so the calcu-
lated longitudinal development of the cascade cannot
be compared with experiment for this case.
Galactic and Solar Protons Incident on the Moon
The depth-dependent radionuclide activity in-
duced in the moon by galactic and solar proton bom-
bardment has been calculated and compared with
measurements made on Apollo ll and 12 samples. As
an example of the calculated results obtained, fig-
ure 3 shows the depth dependence of the 26A1 activ-
ity. The total 26A1 activity (i.e., the sum of the
solar and galactic contributions) is shown in fig-
ure 4, together with the measured activity in two
moon rocks. Additional comparisons between calcu-
lated and measured activities are given elsewhere
(ref. 15).
_oz
_o4
ioo
_o-,
_ F_ GCR pROOUCT ON SOLAR MINIMUM _ _:_
_o 1oo i_o 2oo 2_o 3o0 3_o 4co 4so sod sso soo sso 700 7so SOD
FIGURE 3.-- 26A1 activity versus depth in moon due
to solar cosmic rays (SCR) and galactic cosmic
rays (GCR) at solar minimum and solar maximum.
ORNL- DWG 70-tSE99R
i
! f
2 I I !
T i i
'°a "!ll .I . ! ' )
_-> 2 -- - I
i
lO t -- I I
2
_0 o
CALCULATED
__ A ...... MEASURED, APOLLO _2 ___
MEASURED, APOLLO 11 --
...... r .... _
119
0 5 t0 DEPTH {_cm2) 15 20 25
FIGURE 4.-- Comparison of calculated and measured
(refs. 13, 14) 26A1 activity induced in the moon
by cosmic-ray bombardment.
The depth dependence of the neutron spectra in
the moon has also been calculated. The thermal-
neutron flux in the moon has been inferred from the
Apollo measurements (ref. 16) and is in good agree-
ment with the calculated flux.
The same calculational method as used here to
determine the induced activity in the moon has been
applied recently by Gabriel and Santoro to determine
the induced activity in the soil surrounding a 500-
GeV proton accelerator (ref. 17).
Galactic Protons Incident on Tissue
The absorbed dose and dose equivalent induced
by galactic protons in an infinite slab of tissue
30 cm thick have been calculated using the high-
energy transport code. An isotropic flux of galac-
tic protons having a solar minimum energy spectrum
(ref. 15) was taken to be incident on one side of
the tissue slab. The nucleon-meson cascade in the
tissue produced by incident protons in the energy
range from 30 MeV to 200 GeV was calculated, and
the depth dependence of the absorbed dose and dose
equivalent was determined as described in reference
18. The electron-photon cascade resulting from the
decay of neutral pions and the electrons and posi-
trons from muon decay were taken into account in an
approximate manner (ref. 18). The following com-
position (in at. %) was used for the tissue: H,
63.3; O, 25.8; C, 9.5; N, 1.4. A tissue density of
1.0g/cmSwasused.
Theabsorbeddoseandaveragequality factor
asa functionof depthin thetissueareshoe in
figure 5. Theaveragequality factor wascomputed
bydividingthe doseequivalentin a givendepth
interval bythe absorbeddosein that interval. In
determiningthe doseequivalent,the quality fac-
tors for eachtypeof particle asa functionof
linear energytransferwereobtainedin thesame
mannerasdescribedin reference17. Fromfigure 5,
the absorbedosefor anomnidirectional(over27
solid angle) flux incident on one side of the tis-
sue slab is approximately _ rad/y at all depths.
For a h_ incident flux (i.e., 27 incident flux on
both sides of the slab), the dose would be 8 rad/y,
which is in agreement with the value of I0 rad/y
quoted by others (refs. 19 and 20) for a h_ flux at
solar minimum.
6
o
_4__j
O
E3
(3
_J 2
m
O:
o
CO
0
3
{E
O
LJ
2
D
O
w I
rr
o
0 5
ORNL-DWG 7t-t608
---L___
I0 t5 2o 25 3c
DEPTH IN TISSUE (cm)
FIGURE 5.-- Absorbed dose and average quality factor
in tissue from galactic proton bombardment.
The contributions to the absorbed dose and
dose equivalent, respectively, from various kinds
of particles are shown in figures 6 and 7. The
total dose is obtained by adding all of the contri-
butions shown in the figures. The histogram lab-
eled "primary ionization" in figure 6 gives the ab-
sorbed dose from the excitation and ionization of
atomic electrons by those incident protons which
have not undergone nuclear collision. The histogram
labeled "secondary protons" gives the absorbed dose
from the excitation and ionization of atomic elec-
trons by protons produced from nonelastic nucleon-
nucleus and pion-nucleus collisions and from the
elastic collisions of nucleons and pions with hy-
drogen nuclei. The histogram labeled "heavy nuclei"
gives the absorbed dose from particles with mass
number greater than one produced from nonelastic
nucleon-nucleus and pion-nucleus collisions and the
absorbed dose from the recoiling nuclei produced
from elastic neutron-nucleus collisions and from
nonelastic nucleon-nucleus and pion-nucleus colli-
sions. The histogram labeled "charged pions" gives
the absorbed dose from the excitation and ioniza-
tion of atomic electrons by both positively and
negatively charged pions produced from nucleon-
nucleus and pion-nucleus nonelastic collisions.
The histogram labeled "photons from neutral pions"
gives the absorbed dose from the electron-photon
cascade produced by the photons which arise from
the decay of neutral pions. The histogram labeled
"electrons, positrons, and photons" gives the
10'
ORNL-DWG 71-t605
o
o
==
o
5
2
100
5
2
t0-t
5
2
10-2
5
2
10-3
+ HEAVY NUCLEI
x CHARGED PIONS
PHOTONS FROM NEUTRAL PIONS
"_ ELECTRONS, POSITRONS, PHOTONS
I X MUONSI I I I
5 |0 t5 20 25
DEPTH IN TISSUE (¢m)
3O
FIGURE 6.--Contribution by particle type to the ab-
sorbed dose in tissue from galactic proton bom-
bardment.
120
absorbedosefromthe electronsandpositronspro-
ducedbymuondecayandthe absorbedosefromthe
photonsproducedbynucleon-nucleusandpion-nucleus
nonelasticcollisions. Thehistogramlabeled"muons"
givestheabsorbedosefromthe excitationandion-
ization of atomicelectronsbybothpositivelyand
negativelychargedmuons.In figure 7 the histo-
gramshavesimilarmeaningsbut givethe doseequiv-
alent fromthesevariouskindsof secondarypa_--
tic les.
SECONDARy PROTONS
+ HEAVY NUCLEI
× CHARGED PIONS
PHOTONS FROM NEUTRAL PIONS
"_" ELECTRONS, POSITRONS, PHOTONS
] _ MUONS
.... 1 1 L I
5 _0 t5 20 25 30
DEPTH IN TISSUE (cm)
FIGURE 7.--Contribution by particle type to the
dose equivalent in tissue from galactic proton
bombardment.
It should be realized that only the protons in
the cosmic radiation have been considered in calcu-
lating the dose. Cosmic-ray nuclei heavier than
protons can contribute significantly to the dose,
especially at small depths. At present, the trans-
port code used for these calculations is not capable
of transporting particles heavier than nucleons.
ACKNOWLEDGMENT
We are very grateful to M. Awschalom, T. Borak,
a_d A. VanGinnekin of the National Accelerator Lab-
oratory for making their preliminary data available
to us prior to publication.
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122


Monte Carlo calculations of high energy nucleon meson cascades and applications to galactic cosmic ray transport

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