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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
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; NOV 18 ROSS
CALCULATION OF THE NUCLEON-MESON CASCADE IN IRON INITIATED BY
1- AND 3-GeV PROTONS AND COMPARISON WITH EXPERIMENT*
R. G. Alsmiller, Jr.
Oak Ridge National Laboratory
Oak Ridge, Tennessee
and :
J. Barish
V Oak Ridge Central Data Processing Facility
Oak Ridge, Tennessee
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LEGAL NOTICE
This report was prope red as an account of Government sprzsored work. Neither the United
States, nor the Commission, aor any person acting on behalf of the Commission:
A. Makes any warranty ol' ropresentation, expressed or impliod, with :ospoct to tho accu-
racy, completongis, or uso indo: of tho infcrmation contained in this roport, or that tto uso
of any information, apparatus, method, or procoso disclosed in this raport may dot infringe
B. Assumos any liabilities with rospoct to the uso of, or for damages rosulting from the
uso of any information, apparatus, method, or process disclosod in this report.
As used in the above, "person acting on behalf of the Commission" includes any em-
ployoo or contructor of the Commission, or employee of such contractor, to the extent that
such omployee or contractor of the Commission, or enploy6o of such contractor preparos,
disseminates, or provides access to, any information pursuant to his emaployment or contract
with the Commission, or his employment with such contractor.
privately ownod rights; or
ABSTRACT
L
One-dimensional nucleon-meson cascade calculations have
been carried out for the cases of l- and 3-GeV; protons inci-
dent on steel. The thick target cross sections are calculated
and compared with experimental values. The calculated values
are generally larger than the experimental values for large
depths.
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I.
INTRODUCTION
in massive incidentia sumon t
In a series of previous reports? (hereinafter referred to as 1), one-
dimensional nucleon-meson cascade calculations were presented for a variety
of cases of interest in the design of the transverse shield for the 45-GeV
linear electron accelerator at Stanford University. In order to carry out.
the computations many assumptions were required, and thus it is very desir-
;
.
able to have experimental verification of the methods used.
5
... In a previous paper (hereinafter referred to as 2), cascade calcula-
tions were presented and compared with experiment for the case of 10- and
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*Research sponsored by the U.So Atomic: Energy: Comuniission:under. Contract
with the Union Carbide Corporation.
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19.2-GeV/c protons incident on a steel shield. In this paper similar į
calculations are presented and compared with a recent experiment on the
cascade induced by l- and 3-GeV protons in irons (hereinafter referred to
as 3).
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The notation, the cascade equations, the data used to represent the
nuclear properties of iron, and the method of numerical calculation are
the same as in 2. In particular, the cascade intensities are obtained
only for energies greater than 32 MeV as in 1 and 2.
In Section II the calculations are discussed and the comparisons with
experiment made. In computing the thick target cross section, defined in
3, for 18F activation only the calculated intensities are required because
::
the activation cross sections are such that there is no contribution from
particles with energy less than 32 MeV. In calculating the thick target
cross section for 24 Na activation, however, this is not the case. There
is a large contribution from neutrons with energy less than 32 MeV and
thus the low-energy neutron spectrum must be estimated before the computa-
tion can be carried out. This low-energy spectrum is estimated here, as
in 1, by making the ad hoc assumption that the low-energy equilibrium
neutron spectrum in a thick shield has the same shape as the equilibrium
cosmic-ray neutron spectrum in the atmosphere.
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II. RESULTS AND COMPARISON WITH EXPERIMENT
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The experiment consisted in putting a high-energy beam of protons in
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Iron and measuring the longitudinal and lateral development of the cascade
by means of the 28F and 24 Na activity induced in 27A1 foils. It is this
induced activity integrated over a plane transverse to the beam axis with
which the calculations may be compared. The integration over the trans-
verse plane is necessary because it is only this integrated quantity which
the one-dimensional calculation can hope to approximate.
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Using the equations and data discussed in l, the proton, neutron,
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--
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charged pion, and muon intensities are obtained as a function of energy
(for energies greater than 32 MeV) and distance by numerical integration.
From these intensiiiee the measured thick target cross section, i, mey
be calculated from the definition
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@j(r) = J OLP(E,F) OKP(E) DE
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:
J=P,N,
04(E,F) Oz4(E) DE, k = F,Na, (2.1)
... ...-
...
Ek
...
.
where
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...
P, N, 1 = proton, neutron, and charged pions, respectively,
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04p(E,1') = primary proton intensity per unit energy range at depth i',
1.e., the number of primary particles per unit energy range
at depth r per incident particle,
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(E,r) = intensity of secondary particles of type j per unit energy
range at depth rs
O, (E) = cross section for the production of a nucleus of type k bý
a particle of type j with energy E,
E = kinetic energy of incident proton,
E = the energy below which 01, for all j can be taken to be
zero (see discussion below). .
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The cutoff energy E is introduced only because the intensities in
this paper are not calculated below 32 MeV. If the intensities were known
at all energies, then E, would be tüken to be zero. In the case of 181
activation, the cross sections Opa are essentially zero below 32 MeV 50
Ex = 32 MeV and the function may be obtained from the calculated .
intensities. In the case of 24Na activation, the cross section Open has
a large peak in the vicinity of 15 MeV and thus the function cannot
be obtained direct]: from the intensities calculated here.
Let us consider first @ The cross section Opp has been measured. *.
The cross section of is not known and is therefore assumed to be equal to
O pp. The cross section of has been measured at energies greater than
450 MeV and is essentially constant above this energy.5 In order to carry
out the computation it is assumed that one remains constant at the lower
energies and that offert is equal to offer with these assumptions and the
calculated intensities, opnay be calculated from Eq. 2.1.
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The calculated and measured @g's are shown as a function of r for
the case of l- and 3-GeV Incident protons in Fig. 1. The slight break at
450 g/cm (dashed line) in the calculated 1-GeV curve arises because the
primary protons at this depth fall below 32 MeV and thus no longer con-
tribute to
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02
ORNL-DWG 65 - 7558
12
23-GeV PROTONS ON IRON
-GeV PROTONS ON IRON
{mb/ proton)
! -50
w on õio a on
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0,• EXPERIMENTAL
- CALCULATED
0
100
200
500
600
700

300 400
r(g/cm2)
Fig. 1. Op vs Depth.
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-.-
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In the 3-GeV case the calculation gives a much smaller buildup than
thai obtained experimentally and is higher than the experimental curve at
large depths. It is significant that the calculated and experimental points
do not agree at r = 0. This means, if the cross sections which are being
used are correct, that a reasonable number of high-energy particles are
moving in the backward direction and consequently the one-dimensional ap-
proximation will always underestimate the buildup at the beginning of the
shield. For the same reason the one-dimensional approximation will give.
an overestimate at the end of the shield. Also in the experiment some
particles are escaping through the sides of the target and this will tend
to make the measured values too small at large depths. These latter two
explanations are perhaps adequate to explain the discrepancy between the
calculated and experimental curves at the large dilstances. On the other
hand, the nuclear data being used is quite crude and this could very well
be the reason for some of the discrepancy.
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In the l-GeV case the calculation reproduces the experimentally mea-
sured buildup reasonably well but does not at all reproduce the experi-
mentally measured attenuation. The calculated and experimental points
are in agreement at = 0. so there is no albedo in evidence in this case.
The poor agreement at large distances is probably due to experimental side
losses and the lack of albedo at the end of the shield. This explanation,
however, in the present case is made somewhat dubious by the lack of
albedo at r = 0. It is of some interest to know how much each kind of
particle contributes to Mr. This is shown in Fig. 2 where P, and Pe
refer to primary and secondary protons, respectively. .
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C
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ORNL-DWG 65-9617

ⓇF, N
BF; (mb/proton).
,
F.
©
200
600
700
300 400
p (g/cm ).
500
in
11
Fig. 2. O,
VB r for 3-GeV Protons on Iron.
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Before a comparison can be made with the 24 Na activation data it is
necessary to estimate the neutron intensity at energies below 32 MeV. To
do this we introduce the ad hoc assumption, which was used in 1, that the
low-energy equilibrium neutron spectrum in a thick shirld has the same
shape as the equilibrium cosmic-ray neutron rpectrum in the atmosphere.
This 18, of course, a very far reaching assumption. There are many reasons
why the two spectra might be different; differences in nuclear properties,
differences in density, differences in the nature of the incident radia-
tion, etc.
Having made the asswmption, the measured cosmic-ray spectrum 18
normalized to the calculated spectrum, at each r, and at some energy r.
The energy r 18 chosen to be such that the measured and calculated spectra
join together smoothly at r. The calculated and renormalized cosmic-ray
spectrum for r = 496 g/cmr for l- and 3-GeV incident protons are shown in
F1g. 3. In all cases considered here, as in the previous calculations,
I was taken to be 109 MeV. The fit of the cosmic-ray spectrum to the
calculated intensities at other r values 18 roughly the same as that shown
in Fig. 3.
.
In the calculetion of ya from Eq. 2 the renormalized cosmic-ray
spectrum is used to represent the neutron spectra below I and the calcu-
lated intensity 18 used above r. The cross section one is taken from
measurements,* and it is assumed thet Ona, N and one., are equal to One, P
above 32 MeV. Below 32 MeV only one has an appreciable value and for
this cross section measured values are used.?
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ORNL-DWG 65-9618
9

in
• COSMIC-RAY NEUTRON
SPECTRUM (NORMALIZED
TO CALCULATED CURVES
AT 109 MeV)
N
---CALCULATED
(r = 496 gm/cm2)
Ns (E, r) [(No./MeV)/proton]
:
--3- GeV
PROTONS
1-GeV PROTONS-
10-4 L
10'
2
5
102
2
E (MeV)
5
103
2
5x108

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Fig. 3. N. (E,r) vs E.
bo'.......
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The calculated and experimental values of ® are compared in Fig. 4 :
and the individual contributions to @ for the 3-GeV incident beam are:
shown in Fig. 5. In Fig. 4 the calculated curves are shown only for dis-
tances greater than 123 g/cm? because for 'smaller distances equilibrium
cannot be assumed. In Fig. 5 the neutron contribution to co is obtained
by adding air (E < 109 MeV) and @na. (E > 109 MeV). The comparison
in Fig. 4 cannot, of course, be expected to be any better than that shown
in Fig. 1 and is in fact somewhat worse at the larger distances, parti- ;
cularly in the l-GeV case.
The significant point is that a very large
contribution to comes from the low-energy neutrons and a not entirely
unreasonable estimate of this contribution can be obtained by using the
cosmic-ray spectrum to estimate the low-energy neutron intensity.
The comparisons presented here obviously leave a great deal to be
:
desired. However, in all cases the calculations are conservative and thus
it seems likely that the results given in 1 are also conservative.
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ORNL-DWG 65-9619R
܀

ܝ
[3-GeV PROTONS ON IRON -
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ܕܽ
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i l-GeV PROTONS
E ON IRON
®No (mb/proton)
ܘ ܘ̄
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%
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5
2x10-1
0
100
200
500
600
700
..
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300 400
r (g/cm2)
24Na Activation
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2125
ORNL-DWG 65-9620

N (E>109)
=
No. N (E<109)
Na, Ps
No, ; (mb/proton)
un
-
Na, Pi
o
0.
100
200
__
300 400
p (g/cm2)
500
600
700
T
--
Fig. 5. ONA 4 vs r for 3-GeV Protons on Iron.
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REFERENCES
L.
R. G. Alsmiller, Jr., F. S. Alsmiller, and J. E. Murphy, Nucleon-Meson
Cascade Calculations: Transverse Shielding for a 45-GeV Electron
Accelerator (Part I), ORNL-3289 (1962); (Part II), ORNL-3365 (1962);
(Part III), ORNL-3412 (1963); and (Part IV), ORNL-3734 (1965).
.
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.
ni .....
2. R. G. Alsmiller, Jr. and J. Barish, Calculation of the Nuclear Cascade
in Steel Initiated by 10- and 19.2-GeV/c Protons and Comparison with
Experiment, ORNL TM-1072 (1965).
....-.
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.
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3. S. P. Shen, Passage of High-Energy Particles in Matter: Nuclear Cas-
cades Induced in Dense Media by l- and 3-GeV Protons, BNL-8721 (1964).
4. J. B. Cumings, Ann. Rev. of Nucl. Sci. 13, 261 (1963).
5. A. M. Poskanzer and L. P. Remsberg, Phys. Rev. 134, B779 (1964).
6. W. N. Hess, H. W. Patterson, and R. Wallace, Phys. Rev. 116, 445
(1959). :
7. J. P. Butler and D. C. Santry, Canadian J. of Phys. 41, 372 (1963).
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END

DATE FILMED
12/ 22 / 65
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