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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
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montant
RELEASE FOR ANNOUNCEMENT
IN NUCLEAR SCIENCE ABSTRACTS

NOY 2 91966
Calculation of Radiation Dose Due to High-Energy Protons
Harvel Wright, E. E. Branstetter, Jacob Neufela. Con 7-660920-17
: J. E. Turner, and W. S. Snyder . He 1.00 103.59
Health Physics Division, Oak Ridge National Laboratory . .
Oak Ridge, Tennessee
...

The work reported here represents some of the results obtained in a
continuing program of the study of the dosimetry of high-energy protons and
neutrons, Studies in high-energy proton dosimetry are of interest in assessing
the potential radiation hazards for manned space flight ard are also of interest
for radiological protection in the vicinity of high-energy accelerators and for
biological irradiation experiments,
The present calculations consider the dose deposited in tissue by protons
with energies from 400 MeV to 2 BeV. Some of the results dealing with the dose
due to protons with energies up to 400 MeV have been reported previously. 50
For proton energies below 400 MeV, the production of pions in the cascade process.
was not sufficiently common to be considered significant. However, in the
present calculations it is necessary to take pions into account.
The basic quantity of interest in dosimetry is the absorbed dose, defined in
units of the rad where 1 rad is equal to 100 ergs/gram. In order to calcula te
the dose equivalent, one specifies a quality factor (QF) which is often related
to the values of linear energy transfer (LET) at which the energy deposition
takes place. This QF-LET relationship is then used to determine the dose
equivalent.
"Research sponsored by the U. S. Atomic Energy Commission under contract
with Union Carbide Corporation.
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The tissue phantom is the same as used previously and has the form of it
slab 30 cm. thick and infinite in lateral extent. The protons are assumed to be
normally incident on one surface of the tissue slab. The slab is divided into
:
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30 sub-slabs, each of which is 1 cm thick and the dose and dose equivalent in
each of the sub-slabs is calculated.
The Monte Carlo technique has been used in writing a code for the CDC 1604
computer to obtain the present estimates of absorbed dose and dose equivalent.
The calculations have been simplified considerably by using a simpler model for
the nuclear interactions than was used in the calculations up to 400 MeV. The
straight-ahead approximation is used in this report (i.e., the nucleons emitted
in the cascade process are assured to have the same direction as the incident
nucleon which initiates the cascade.) The validity of the straight-ahead approxi-
mation has been considered at 400 MeV by Alsmiller et al. Y and found to give
good agreement with more refined methods. It is expected that the straight-
ahead approximation is even better at higher energies. Much of the statistical
. information concerning products of the cascade such as the average number and
energy distribution of emitted protons, neutrons, and pions, excitation of the
residual nucleus, etc. is obtained from Metropolis et al.* The details of the
calculations will be described further in Part II of this investigation. The code
has čeen designed so that all statistical information is read in as input. Thus,
as new statistical information becomes available, it can easily be incorporated
into the program. The estimates of dose equivalent are made on the basis of the
QF-LET relationship endorsed by the International Commission on Radiological
Protection (ICRP) for long-term occupational exposure.
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LEGAL NOTICE
This report was prepared as an account of Government sponsored work. Nelther the United
Butos, oor the Commission, nor way parnoq ucung on behalf of the Commission:
A, Makes any warranty or representation, expressed or implied, with rosport to the accu-
racy, completeness, or wofulness of the information contained in this report, or that the use
of any information, paratus, mothod, or procesu disclosed in this roport may not infringe
privately owaad ridhuo; or
B. Assumes any llbluties with respect to the use of, or for damages resulting from the
use of any laformation, apparatus, method, or process dlaclosed in this report.
As used in the above, "pornod acting on behall of the Commission" includes any on-
ployco or contractor of the Commission, or employee of such contractor, to the extent that
such amployo. or coatrictor of the Commission, or omployee of such coatractor preparos,
disseminates, or provides access to, way faformadoa pursuant to his employment or contract
The information regarding nuclear interactions that is currently available
is very incomplete and it has been necessary to make several assumptions and
compromises due to the lack of sufficient experimental data. Therefore, the
results presented here are preliminary and are expected to be refined when new
data are available. The program runs rapidly and can process 1000 incident
particles in approximately 3 minutes on the CDC-1604 computer.
II. DESCRIPTION OF THE CALCULATIONS
The slowing down of protons and pions is calculated by means of the stopping
power formula, 5
IN
fin 2my2
(1)
(1-B2
In this expression, e and mare the electron charge and mass, respectively; v is
.
the proton or pion velocity; B = V/c where c is the velocity of light; N, is the
number of atoms with atomic number 2 per cm”; and I, is the mean excitation
energy of atoms of type i. The tissue phantom considered in these calculations
is assumed to be a 30-cm thick homogeneous infinite slab composed of hydrogen,
carbon, nitrogen, and oxygen in the same proportions as they occur in a standard
man. 6
.,.
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Equation (!) is used to calculate the slowing down of a proton or pion until
the energy reaches 1 MeV at which point the proton or pion is assumed to be
absorbed locally and thus the 1 MeV of energy is deposited at that point.
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(b) Transport of particles
An incident proton is allowed to enter and slow down through the tissue slab
. and a distance to a collision point is selected using geometric cross sections
for carbon, nitrogen, and oxygen and using the cross section for hydrogen given
in Fig. 1 of Metropolis. If the distance to the point of the collision is greater
than the thickness of the tissue slab, then Eq. (1) is used to allow the proton
to slow down until it either escapes from the tissue phantom or its energy
reaches 1 MeV at which point the 1 MeV of energy is assumed to be absorbed
locally. If the distance to the collision point is less than the thickness of the
tissue phantom, then Eq. (1) is used to allow the proton to slow down until its
energy is 50 MeV or until it reaches the collision point. It is assumed that no
nuclear collisions occur for energies below 50 MeV and, therefore, if the energy
reaches 50 MeV before it reaches the collision site, it is allowed to slow down to
1 MeV. The energy of the proton at the collision point is thus determined. The
type of tissue element with wiich the collision occurs is then determined on the
basis of the relative contribution to the total cross section that is made by each
element for the energy that the particle has at the collision site,
(c) Cascade process
If the collision is determined to be with hydrogen, then the information given
in Table II of Metropolis et al. is used to determine whether zero, one, or two
.
pions are produced. If one or more pions are prcduced, then the kinetic energy
and charge of each pion is selected from information given by Melissinos et al.'
:
and by Bugg et al.° The kinetic energy plus the rest energy of the pions is
then subtracted from the energy of the incident nucleon and half of the remaining
energy is assigred to each of the two nucleons. Each of these two nucleons is
assumed to travel in the same direction as the incident nucleon.
.. If the collision is determine, to be with an element other than hydrogen,
Fig. 5 of Metropolis et al. is used to determine whether zero, one, or two pions
are produced. If one or more pions are produced, a charge and kinetic energy is
assigned to each pion from information given in Tables XI and IX of Metropolis
et al. The information for aluminum in Fig. 4 and Table VIII of Metropolis et al.
is then used to select the number of cascade protons and neutrons which result
from the nuclear interaction. The kinetic energy of each of these particles is
then assigned by using Figs. 12 and 13 of Metropolis et al. Each of the nucleons
thus produced are assumed to travel in the same direction as the nucleon which
initiated the cascade.
. .
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(a) Excitation of the residual nucleus
The excitation energy of the residual nucleus is selected from Fig. 14 of
Metropolis et al. Experience with the calculations of the evaporation process
used in the calculations of dose due to protons and neutrons with energies up to
400 MeV“, has shown that approxima tely one-half of the excitation energy gets
absorbed in the tissue as dose with a quality factor of approximately 8. The
excitation energy will be somewhat higher at higher incident energies, but the
evaporation products will be of the same type, and it is expected that the fraction
of the energy deposited will be approximately the same. Therefore, one-half.
of the excitation energy is deposited locally with a quality factor of 8.
(0) Energy deposited by pions
Pions produced in the cascade process are treated in the following manner.“
The T° decays almost immediately into two photons and is not assumed to con-
tribute to dose. A 1" or cr7 pion is assumed to lose energy by ionization according
to formula (1) untü it escapes from the tissue phantom or its energy reaches
1 MeV where the remaining 1 MeV is deposited locally. The rº is usually absorbed
by a nucleus giving rise to two 70-MCV nucleons within the nucleus. One-half of
the rest energy of the pion is deposited locally with a quality factor of one at
the point where the ti stops. The * decays into a 4-MeV ut and a neutrino.
The ut then decays into a positron and two rieütcinns. The average energy of the
positron is assumed to be 45 Mev." Therefore, when a ot stops, 50 MeV of
energy with a quality factor of 1 is deposited locally.
A history is calculated for each nucleon produced in the cascade process. The
incident nucleon is absorbed in the nucleus and since its identity is then lost it is
considered as one of the cascade products. Each cascade nucleon is considered to
be born at the point of the collision, a flight distance to a collision site is chosen,
and the process described above is followed. After the history of each of the cascade
nucleons has been calculated, another incident proton is started and the process is
repeated.
Dose equivalent has also been estimated. For this purpose the energy deposited
in the tissue during the slowing-down process has been recorded separately for
various ranges of linear energy transfer (LET). The quality factor assigned to
each range of LET in this investigation is based on the recommendations of
the National Comnuittee on Radiation Protection and Measurements (NCRP) for
12
application to cases of long-term occupational exposure."
The absorbed energy in each of the chosen ranges of LET has been recorded
separately and quality factors other than those used here could be substituted
for the purpose of a specific application such as, for example, a manned space
flight to the moon. The particular quality factors used here for the LET ranges
35 or less, 35-70, 70-230, 230-530, and 530-1750 are, respectively, 1, 1.35,
3.04, 7.15, and 11.39.
III. RESULTS
The calcula. tions have been performed for protons with the five incident
energies 400, 600, 1000, 1500, and 2000 MeV. For each of these energies a
total of 10, 000. incident protons were used and the absorbed dose and dose equivalent
were calcula ted. The results thus obtained are presented in Figs. 1 through 5.
Each of these figures shows the absorbed dose and dose equivalent plotted as a
function of depth within the tissue slab.
It is noted that both absorbed dose and dose equivalent increase with depth
within the tissue phanto”. There is a rapid buildup of absorbed dose within the
first few centimeters and then a more gradual increase throughout the remainder
of the slab. The absorbed dose increases about 30% in the first five centimeters
and then gradually increases another 30 to 40% in the remaining 25 cm, reaching
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its largest value near the back of the tissue slab. The dose near the back of the
tissue slab for 2000-MeV incident protons is approximately 30% more than that
from 400-MeV protons. The increase in dose results from the contribution of
secondary particles. The number of secondary particles given off during a
cascade caused by a high-energy proton increases with the energy of the proton
Kre
causing the cascade. Also, the excitation energy increases with the incident
particle energy.
Figure 6 gives a breakdown of the absorbed dose for 2000-MeV incident
protons into components due to ionization by primary protons, ionization by
secondary protons, excitation, ionization by pions, and dose deposited by pions
that stop. Near the surface the most important contribution to dose results
from ionization by primary protons while near the back of the slab the most
important contribution results from ionization by secondary protons. Figure 7
gives a corresponding breakdown of dose equivalent. The largest contribution to
dose equivalent results from the excitation energy.
It is of interest to compare the results given here with the results given
in the report of Committee NV (1953-1959) of the International Commission on
Radiological Protection." The estimates of Committee IV, based on the work
of Neary and Mulvey, '4 indicate that the dose equivalent for 1000-MeV incident
protons is almost twice the value of dose equivalent for 400-MeV incident protons,
whereas the results obtained here indicate an increase of only approximately 20%.
It is also of interest to compare the results obtained here with the results
from the more detailed calculations that were reported by Turner et al.' It is
seen by comparing Fig. 13 of Turner et al. with Fig. 1 of this study that at
400 MeV the absorbed dose agrees within only a few percent and the dose equivalent
obtained by Turner et al. is approximately 10 to 15% higher than that obtained
here. In view of the approximation made here in this less detailed calculation the
agreement is considered to be quite good.
.
10
References
J. E. Turner, C. D. Zerby, R. L. Woodyard, H. A. Wright, W. E. Kinney,
W. S. Snyder, and J. Neufeld, Health Phys. 10, 783 (1964).
Jacob Neufeld, W. S. Snyder, J. E. Turner, and Harvel Wright, Health Phys.
12, 227 (1966).
PR. G. Alsmiller, Jr., D. C. Irving, W. E. Kinney, and H. S. Moran, Proc.
Second Symposium on Protection Against Radiations in Space, Gatlinburg, 1964.
NASA SP-71, p. 177 (1965).
*N. Metropolis, K. Bivins, M. Storm, J. M. Miller, G. Friedlander, and Anthony
Turkevich, Phys. Rev. 110, 204 (1958).
Cf. V. Fano, Ann. Rev. Nucl. Sci. 13, 1 (1963).
Protection Against Neutron Radiation up to 30 MeV, National Bureau of Standards
Handbook 63, p. 8 (1957).
'A. C. Melissinos, T. Yamanouchi, G. G. Fazio, S. J. Lindenbaum, and
L. C. L. Yuan, Phys. Rev. 128, 2372 (1962).
3%. V. Bugg.. A. J. Oxley, J. A. Zoll, J. G. Rushbrooke, V. E. Barnes, J. B. Kinson,
W. P. Dodd, G. . Doran, and L. Riddiford, Phys. Rev. 133, B1017 (1964).
'L. Dresner, EVAP - A Fortran Program for Calculating the Evaporation of
Various Particles from Excited Compound Nuclei, Oak Ridge National Laboratory
Report ORNL CF-61-12-30 (1961).
J. E. Turner, Proc. USAEC First Symposium on Accelerator Radiation Dosimetry
and Experience, Conf. 651109, U. S. Dept. of Commerce, p. 346 (1965).
10
"T. D. Lee and C. S. Wu, Ann. Rev. Nucl. Sci. 15, 381 (1965).
Recommendations of the International Commission on Radiological Protection,
ICRP Publication 9, p. 3 (Pergamon Press, Oxford, 1966).
11
.
13.
Recommendations of the ICRP Report of Committee IV (1953-1959) or.
Protection Against Electromagnetic Radiation Above 3 MeV and Electrons,
Neutrons and Protons, ICRP Publication 4, p. 3 (Pergamon Press, Oxford, 1964).
"*G. J. Neary and J. Mulvey, Maximum Permissible Fluxes of High-Energy
Neutrons and Protons in the Range 40 to 1000 MeV, Report of the Medical Research
Council, Radiological Research Unit, AERE, Harwell, 1957, unpublished.
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HDOSE EQUIVALENT (rem) 1
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ORNL DWG 66-8445
- POSE EQUIVALENT (rem)
ABSORBED POSE (rad)
DOSE / PROTON/cm
INCIDENT ENERGY 1000 MeV
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ORNL-DWG. 66-8442
DOSE EQUIVALENT (dem)
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DOSE EQUIVALENT (tem)
107
ABOSORBED DOSE (rád )
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INCIDENT ENERGY 2000 MeV
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SECONDARY, PROTON IONIZATION
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END
DATE FILMED
12/ 22 / 66
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