11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
Heavy Ion Collision Event Generator for the 3D Monte Carlo
Transport Code HETC
Thomas M. Miller and Lawrence W. Townsend
Department of Nuclear Engineering, University of Tennessee
Knoxville, TN 37996-2300, USA
Tony A. Gabriel
Scientific Investigation & Development, Knoxville, TN 37922, USA
Abstract
In order to perform 3-dimensional analyses of space radiation shielding requirements for future missions
in deep space, the Monte Carlo radiation transport code HETC has been extended to include transport of
energetic heavy ions, such as are found in the galactic cosmic ray spectrum in space. To carry out this
extension, a heavy ion collision event generator capable of providing the necessary nuclear interaction
data for use in HETC has been developed and incorporated into the transport code. The event generator
predicts the interaction product yields, production angles, and energies using nuclear models and Monte
Carlo techniques. Testing, modification, and validation of the event generator and extended transport
code, now called HETC-HEDS (High Energy Transport Code – Human Exploration and Development of
Space), is being carried out. In this work the current status of the heavy ion collision event generator is
described. Also, sample results from comparisons of code validation, benchmarking, and testing against
available laboratory beam data for energetic heavy ions interacting in various targets are presented.
Introduction
One of the hazards faced by future crews of spacecraft on missions in deep space is exposure to ionizing
radiation in the space environment. The main sources of these radiations are the galactic cosmic ray
(GCR) background, composed of all naturally occurring elements, and solar energetic particles, produced
by events, such as coronal mass ejections and associated phenomena on the Sun. Solar energetic particle
events (SPE) are composed of protons and some multiple-charged ions, with protons being the main
source of concern for human exposures.
As these radiations pass through spacecraft or habitat shielding, their particle fields are altered by
interactions with the shielding. Critical body organs, such as the central nervous system and bone
marrow, are also shielded by any overlying body tissue. Thus, the radiation fields that produce biological
damage may be substantially different than the external space environment impinging on the spacecraft.
Modification of the radiation fields result from atomic processes whereby the charged particles lose
energy in collisions (~ 108 cm-1 of travel) with orbital electrons and occasionally have nuclear collisions
(with mean free paths ~ several cm), which can result in identity changes because of breakup processes.
These fragmentation (breakup) processes produce heavy ions that are lighter than the fragmenting
nucleus, and also produce large numbers of light ions and neutrons. Transport of the radiation fields, as
they pass through spacecraft shielding and body tissue can be simulated using Monte Carlo techniques, or
described by numerical solutions of the Boltzmann Equation obtained by balancing changes in particle
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
fluxes as they traverse a small volume of material with the gains and losses caused by atomic and nuclear
collisions.
In 2003, NASA established a consortium involving the University of Tennessee (lead institution), the
University of Houston, Roanoke College, SID Inc., and various U.S. government and national
laboratories to accelerate the development of a standard set of radiation transport computer codes for
NASA human exploration applications. These efforts involve further improvements of the Monte Carlo
codes HETC and FLUKA and the deterministic code HZETRN, including developing nuclear reaction
databases necessary to extend the Monte Carlo codes to carry out heavy ion transport and extending
HZETRN to three dimensions. The FLUKA work is carried out in a collaborative effort involving INFN,
CERN and the University of Houston.
To carry out this extension to include heavy ion transport, a heavy ion collision event generator capable of
providing the necessary nuclear interaction data for use in HETC has been developed and incorporated
into the transport code [1 - 3]. The event generator predicts the interaction product yields, production
angles, and energies using nuclear models and Monte Carlo techniques. Testing, modification, and
validation of the event generator and extended transport code [4], now called HETC-HEDS (High Energy
Transport Code – Human Exploration and Development of Space), is being carried out.
Brief Overview of the HETC-HEDS Transport Code
HETC-HEDS simulates particle cascades by using Monte Carlo methods to compute the trajectories of
the primary particle and all the secondary particles produced in nuclear collisions. The particles
considered by HETC-HEDS (protons, neutrons, +, -, +, or -, light ions and heavy ions) can be
arbitrarily distributed in angle, energy, and space. Each particle in the cascade is followed until it
disappears by escaping from the boundaries of the system, undergoes a nuclear collision or absorption,
comes to rest due to energy losses from ionization and excitation of atomic electrons in the target
medium, or, in the case of pions and muons, decays. Neutrons produced below a specified cutoff, usually
20 MeV, and photons produced in the cascade from  decays or from deexcitation are not transported.
Information regarding the neutrons and photons is stored for transport by other codes such as MORSE
[5], MCNP [6], and EGS [7]. HETC-HEDS provides a complete history tape of all cascades so that
analyses of specific problems can be performed.
The energy loss of protons, light and heavy ions, charged pions, and muons due to the excitation and
ionization of target atomic electrons is treated using the Bethe-Bloch stopping power formula [8] based
on the continuous slowing-down approximation. Range straggling is taken into account. Range-energy
tables for each material in the system are computed for protons. These same tables are used for nuclei
with mass numbers A > 1, and for charged pions and muons by making use of scaling relations. HETCHEDS currently allows multiple Coulomb scattering only for the primary charged particles.
Pion production is based on the isobar model of Sternheimer and Lindenbaum [9]. Only single- and
double-pion production in nucleon-hydrogen collisions and single-pion production in pion-nucleon
collisions are accounted for. This model is used for energies up to 3.5 GeV for neutrons and protons and
up to 2.5 GeV for charged pions. Nonelastic nucleon collisions and charged-pion collisions with
hydrogen nuclei at energies above 3.5 GeV and 2.5 GeV, respectively, are treated by using the
calculational methods of Ref. [10]. Special provisions are made to insure that energy and nucleons are
conserved for each collision. Efforts are underway to incorporate pion production channels for collisions
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
involving light and heavy ions. Charged-pion decay is taken into account using the known pion lifetime.
The neutrino produced in the decay is ignored. The neutral pion is assumed to decay into two photons at
its point of origin. HETC-HEDS does not transport neutral pions. However, the energy, direction, and
spatial location of the neutral pions produced are included as part of the output. Muon decay in flight is
taken into account using the known muon lifetime. Muons that come to rest are assumed to decay
immediately. No information about the electrons, positrons, or neutrinos produced from muon decay is
calculated.
Elastic collisions of protons and pions with all nuclei other than hydrogen are neglected at all energies.
Elastic collisions of light and heavy ions with target nuclei are treated using cross sections obtained from
an optical potential model derived from quantum multiple scattering theory. The angular dependence is
obtained using a Fraunhofer approximation. Details are provided in Ref. [3]. Elastic collisions by
neutrons with nuclei other than hydrogen at energies above the neutron cutoff energy (usually 20 MeV) is
optional, and if the option is chosen, requires the input of elastic scattering cross section data (s and
ds/d).
The intranuclear-cascade evaporation concept of particle-nucleus interaction, as modeled by Bertini [11],
is used to model the particle-nucleus collisions below 3.5 GeV for nucleons and below 2.5 GeV for
charged pions. Following the intranuclear-cascade, the residual excitation energy is treated using an
evaporation model [12]. The particles allowed to evaporate are protons, neutrons, d, 3H, 3He, and . An
extrapolation model determines the energy, angle, and multiplicity of the products from inelastic nucleonnucleus and pion-nucleus collisions at higher energies (3-15 GeV) [13]. Heavy ion interactions are
modeled using the new event generator described in the next section. In this event generator, nucleusnucleus collision total cross sections are based upon an optical potential approximation of a nucleusnucleus multiple scattering formalism [14, 15]. Nucleus-nucleus reaction cross sections are described
using the parameterization due to Tripathi [16]. Breakup of light ions (Z < 2) is divided into 3 pieces,
which are (1) deuteron breakup, (2) alpha fragmentation, and (3) 3H and 3He breakup. These are
described in detail in the next section and in Ref. [17]. Finally, breakup of heavy ions (Z > 2) is described
using the semiempirical fragmentation model NUCFRG2 developed at NASA Langley Research Center
[18].
Heavy Ion Event Generator
The HETC-HEDS heavy ion event generator incorporates elastic and nonelastic scattering interaction
models for incident heavy ions. The event generator provides total cross sections for the selection of
interaction points, the type of interaction (elastic or nonelastic), and the interaction products (species,
energy and direction of motion) for each collision between a propagating particle and stationary nuclei in
the target. Because of the needs of the U.S. space program for developing methods to analyze and design
complex shielding configurations for human crews, the emphasis in the development of this event
generator is on computational speed and accuracy, specifically for the deep space radiation environment,
especially the high energy heavy ion component of the galactic cosmic ray spectrum. Hence, some
features that one would expect to see in a general purpose code are incomplete or missing in the current
version of the event generator. For example, it does not yet include meson production in heavy ion
collisions, nor does it include a heavy ion fission channel for very heavy nuclei.
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
Nucleus-Nucleus Total and Reaction Cross Sections
The nucleus-nucleus cross sections include the total, total reaction, and elastic scattering. The total
reaction cross section is assumed to be the cross section for all nuclear interactions that are not elastic.
The elastic scattering cross section is the difference between the total cross section and the total reaction
cross section. The model used to calculate the total reaction cross section was developed by Tripathi and
collaborators [16], and is valid for any colliding system of nuclei from a few MeV per nucleon to a few
GeV per nucleon. The total cross section is obtained using a combination of three different models. The
total and reaction cross sections calculated using an optical potential approximation have a reasonably
correct energy dependence, but tend to underestimate the magnitudes at energies below ~100
MeV/nucleon [14, 15]. At energies ~ 1 GeV/nucleon the error is ~3%. At energies ~25 MeV/nucleon the
error is ~20%. The errors in the ratio of these two quantities are smaller than the error in either. Hence,
the decision was made to obtain the total cross section by scaling Tripathi’s total reaction cross section,
which agrees better with data, by the ratio of the total cross section to the total reaction cross section
obtained from the optical potential model using
 total 
optical
 total
optical
 reaction
Tripathi
*  reaction
The total cross section is converted to a mean free path and used in HETC-HEDS to determine the
location of the next interaction point. The total and reaction cross sections are also used to determine if a
collision is elastic or nonelastic. Because of limitations in the optical model used in Ref. [14, 15],
projectiles must currently have a charge number less than 27 and targets must have a charge number less
than 83. Tripathi’s total reaction cross section has no restriction on the projectile target pair charge
numbers, but kinetic energies must be greater than or equal to 1 MeV per nucleon.
Elastic Scattering Cross Sections
The elastic scattering cross section is the difference between the total cross section and the total reaction
cross section. In the event that an elastic scattering interaction occurs, particle kinematics is used to
determine the new energy and direction of travel of the projectile and target. This simply involves
applying conservation of energy and momentum before and after the collision. To find the scattering
angles in the center of mass system the Fraunhofer approximation is used [19]. This distribution is
sampled to select a center of mass scattering angle for the projectile. Transformations between the center
of mass system and the laboratory system are applied as appropriate [20].
Double Differential Fragmentation/Spallation Production Cross Sections
If the interaction is nonelastic, it is assumed that it is a fragmentation event. Note that this assumption
will require modification when meson production is added for these collisions.
Heavy Ion (Z > 2) Fragmentation Cross Sections
Breakup of heavy ions is modeled using the NUCFRG2 code developed at NASA Langley Research
Center in the late 1980’s and early 1990’s [18]. NUCFRG2 calculates yields of all light ion and heavy ion
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
fragments produced by a nucleus-nucleus collision, with a projectile charge number greater than 2. Given
a particular nucleus-nucleus pair and beam energy, NUCFRG2 calculates the cross sections for each
possible fragment/spallation product. For light ion production from heavy ion breakup, corrections for
particle multiplicity were made. Sample results for 1 GeV/nucleon 12C colliding with 12C are displayed in
Table 1. The neutron production cross section, which is not calculated in NUCFRG2, is obtained by
scaling the proton production cross section using
 neutron 
AP  Z P
 proton
ZP
For the example shown in Table 1, the neutron production cross section is 718 mb. Particle yields from
the fragmentation event are obtained by sampling this distribution. Methods of selecting the particle
energies and trajectories will be described below.
Charge
6
6
6
6
5
5
5
5
5
4
4
4
4
4
Mass
11
10
9
8
11
10
9
8
6
10
9
8
7
6
Cross
section
(mb)
52.9027
0.353754
2.73E-03
2.30E-06
53.11982
54.56862
3.07356
1.60E-02
3.75E-06
3.299027
13.15494
3.452457
18.95178
7.85E-02
Charge
3
3
3
3
3
2
2
2
2
2
1
1
1
1
Mass
10
9
8
7
6
9
8
6
4
3
6
3
2
1
Cross
section
(mb)
2.52E-03
3.42E-02
0.106091
20.5311
28.61594
4.61E-06
3.35E-05
0.36744
25.80074
8.24591
3.33E-05
16.49329
23.06178
717.6099
Table 1: Production Cross Sections for 12C on 12C at 1 GeV per Nucleon
Light Ion (Z  2) Fragmentation Cross Sections
The model of Cucinotta and collaborators [17] is used to determine the products from the breakup of
alpha particles. For alpha breakup the products of the reaction will actually be determined by choosing
the entire reaction channel of the alpha breakup. Representative cross sections as a function of energy for
the 5 possible breakup channels are displayed in Figure 1 for alphas colliding with 12C targets.
The cross section for breakup of deuterons is simply the total reaction cross section since the deuteron has
no excited states and only one breakup channel.
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
The fragmentation models for 3He and 3H are very similar. Since there are only two fragmentation
channels for each ion, one involving production of a deuteron and the other involving only nucleon
production, the cross sections are used to pick the specific channels not just the individual fragments. The
deuteron production cross section for triton and 3He fragmentation is 35 percent of the total reaction cross
section [17]. Hence, if either ion undergoes an inelastic collision one merely samples whether a deuteron
was produced or not. This determines which fragmentation channel has resulted from the collision.
Figure 2 shows the fragmentation channel cross sections for a triton on 12C as a function of projectile
kinetic energy.
450
400
350
Cross Section (mb)
300
pickup
t+p
he3+n
d+d
d+p+n
p+p+n+n
250
200
150
100
50
0
10
100
1000
10000
100000
Kinetic Energy (MeV per Nucleon)
Figure 1. Alpha-12C Fragmentation Channel Cross Sections
Fragment Kinetic Energy and Angular Distributions
In order to choose the kinetic energies of fragments resulting from nucleus-nucleus collisions, a
microscopic model for the estimation of energy degradation in nucleus-nucleus collisions developed at
the Naval Research Laboratory by Tsao and collaborators is used [21]. This model assumes that the
kinetic energy distributions of fragmentation/spallation products in the fragmenting nucleus rest frame are
Gaussian distributed, as suggested by experimental data. The momentum or energy downshift due to the
collision is accounted for. Using the mean and standard deviation obtained from the model, a Gaussian
distribution is sampled in order to pick a kinetic energy for the fragment.
The production angles are selected based upon the reported systematics of momentum distributions
observed during experiments by Morrissey [22], who noted that longitudinal momentum distributions of
projectile-like particles are roughly isotropic in a rest frame moving with nearly the beam velocity.
Therefore, the event generator samples scattering angles of particles emitted by the projectile isotropically
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
in the projectile rest frame. Second, Morrissey stated that target-like particles’ momentum distributions
are essentially isotropic in a frame nearly at rest. Therefore, the event generator samples scattering angles
of particles emitted by the target isotropically in the target rest frame, which is equivalent to the
laboratory frame.
800
700
n+d
n+n+p
Cross Section (mb)
600
500
400
300
200
100
0
1
10
100
1000
10000
100000
Kinetic Energy (MeV per Nucleon)
Figure 2. Triton on 12C Fragmentation Channel Cross Sections
After the event generator chooses the projectile fragments and their energies and angles the role of
projectile and target are reversed. Then with the actual target in the role of the projectile this same
process is repeated to choose the target fragments and their energies and directions. The target, now in
the role of the projectile, maintains the same kinetic energy per nucleon as the projectile. However, one
difference does exist. After the kinetic energies of the projectile fragments have been chosen they are
transformed from the projectile rest frame back to the laboratory frame. After the kinetic energy of the
target fragments have been chosen they are not transformed from the target rest frame to the laboratory
rather they are transformed from the target rest frame to the frame of the recoiling target.
Representative Results
Figure 3 displays calculated yields from HETC-HEDS compared with those from the PHITS code for 2
GeV/nucleon Fe-56 colliding with 10 g cm-2 of polyethylene. The agreement between the codes is fairly
good considering that the event generators are very different in the models used to treat the underlying
physics. Generating these results for HETC-HEDS took ~20-25 minutes on a personal computer.
Figure 4 displays results obtained with HETC-HEDS for fragment fluences obtained for 1037
MeV/nucleon Fe-56 colliding with ~ 2 g/cm2 aluminum alloy 6061 (International Space Station wall).
Also displayed are experimental results obtained by the NASA-funded group led by J. Miller at Lawrence
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
Berkeley National Laboratory using beams obtained from the AGS at Brookhaven National Laboratory
[23]. The agreement is good for fragments with charge numbers greater than 7. The larger discrepancies
Nuclide Yield/56Fe ion
10
HETC-HEDS
1
PHITS
0.1
0.01
0.001
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
Charge (Source Particle 56Fe listed at 27)
Figure 3. Fragment Fluences Calculated Using HETC-HEDS and PHITS for 2 GeV/nucleon 56Fe on 10
g/cm2 of Polyethylene
for fragments with charge numbers  7 are mainly the result of differences in the way the fragments are
tallied. The experiment measures “leading fragments only. Hence, the first fragment or fragments (if
simultaneous) to reach the detector triggers the circuitry and records the energy deposition(s), which are
then assigned an effective charge number. For example, if an event produces 3 alphas, only one will be
recorded unless multiple alphas arrive simultaneously, in which case the event would be recorded as a
single particle having an effective charge given by the square root of the sum of the squares of the
particles detected. Hence, the simultaneous arrival of 2 alphas would be reported as an event as having an
effective charge of 2.8, which would likely have been counted as a Li fragment. At the time that these
calculations were performed, we were unaware of the procedures being used to assign charge numbers to
the measured fragments. Hence, our predictions include contributions from all fragments with a specific
charge number, and not just contributions from “leading fragments”. Therefore, quantitative comparisons
with the data for low Z fragments are not definitive.
Concluding Remarks
The heavy ion event generator recently developed and incorporated into the HETC-HEDS transport code
has been briefly described, as has the current status of development of the HETC-HEDS radiation
transport computer code. Some details of the event generator treatment of heavy ions were presented.
Representative comparisons with the PHITS heavy ion transport code and with recent measurements
11th International Conference on Nuclear Reaction Mechanisms
Villa Monastero, Varenna, Italy, June 12-16, 2006
obtained for cosmic ray iron colliding with spacecraft shielding materials have been presented and
discussed. Several shortcomings of the present version of the event generator were also described.
0.009
0.008
Measurement
0.007
Fluence per Incident Ion
HETC-HEDS
0.006
0.005
0.004
0.003
0.002
0.001
0
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
Fragment Charge
Figure 4. Fragment Fluence Due to 1037 MeV per Nucleon 56Fe on 1.93 g/cm2 of Aluminum Alloy
Acknowledgements
Thomas Miller gratefully acknowledges research support for this work from a NASA Graduate Student
Researchers Program Fellowship. The other authors (LWT and TAG) gratefully acknowledge research
support provided under NASA Grant Nos. NAG8 –1669 and NAG8-1901.
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