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International Conference on Nuclear Data for Science and Technology 2007
DOI: 10.1051/ndata:07398
A new treatment of radiation behaviour beyond one-body observables
Koji Niita1,a, Yosuke Iwamoto2, Tatsuhiko Sato2, Hiroshi Iwase3, Norihiro Matsuda2,
Yukio Sakamoto2, and Hiroshi Nakashima2
1Reasearch Organization for Information Science & Technology (RIST), Tokai, Naka, Ibaraki 319-1106, Japan
2Japan Atomic Energy Agency (JAEA), Tokai, Naka, Ibaraki 319-1195, Japan
3High Energy Accelerator Research Organization (KEK), Oho, Tsukuba, Ibaraki 305-0801, Japan
Abstract. We propose a new treatment of radiation behaviour in transport calculations by introducing an event
generator model in which we combine the nuclear data and the reaction models so as to trace all correlations of
ejectiles keeping the energy and momentum conservation in a collision. By this new model, we can estimate the
fluctuations around the mean values of one-body observables, for example, the deposit energy distribution in a cell,
which cannot be obtained by the transport calculations based on the Boltzmann equation with the nuclear data.
1 Introduction
Nuclear data are extensively used in Monte Carlo transport
calculations to analyze the radiation behaviour in various
fields such as accelerator facilities, space radiation, and ra-
diotherapy. Most of the Monte Carlo transport calculations
are based on Boltzmann equation for one-body phase space
distribution of the transport particles. In such transport cal-
culations, one can obtain only the mean value of the one-
body observables in the phase space, e.g., heat, flux, and
dose, but not the fluctuations around the mean value, since the
Boltzmann equation, nor the nuclear data has information on
the two-body and higher order correlations which determine
the fluctuation around the mean value.
Recently, however, the higher order quantities, i.e., the
fluctuations around the mean values of the one-body ob-
servables are often required. A typical example for such a
correlated quantity is the deposit energy distribution in a
cell, which is necessary to estimate the response function of
detectors, the single event upset probability of semiconductor
memory cells and the radiation effects in a micro-dosimetric
treatment. The solution of the Boltzmann equation cannot
describethedistributionbutonlythemeanvalue.Furthermore,
Monte Carlo calculations using the nuclear data cannot deal
with these quantities, since the nuclear data includes only the
inclusive one-body cross sections but no information of the
correlations.
We have therefore developed a new treatment of radiation
behaviour in the transport calculations by introducing an event
generator model, in which we have combined the nuclear data
and the reaction models so as to trace all higher correlations of
ejectiles keeping the energy and momentum conservation in a
collision.
2 Boltzmann equation vs. event generator
For high energy transport calculations, the nuclear reaction
models are commonly used instead of the evaluated nuclear
data to describe the ejectiles from each nuclear reaction,
since there is not enough evaluated nuclear data for the high
energy reactions. The reaction models usually generate each
event keeping the energy and momentum by the Monte Carlo
method. In this sense, the reaction model is called as “Event
Generator”. Therefore we can extract any information from
the transport calculations with such reaction models. On the
other hand, the transport calculations based on the Boltzmann
equation with the nuclear data, e.g., MCNP-type calculations,
have no such concept of “Event”. For the actual numerical
solution of the Boltzmann equation, one usually employs the
test particle method where the one-body phase-space distri-
bution function is evaluated by integrating the test particle
tracks in the phase-space. In this numerical calculation, things
are going on in a very similar manner as in the high energy
transport calculation with the event generator. However, there
is no “Event” in this type of calculations. One history in this
type of calculation has no physical meaning but gives us only a
statistical weight. The observables are obtained after averaged
out the statistical weight. There is no physical meaning in
the distribution around the mean value but only the statistical
variance. However, the distribution around the mean value
calculated in the high energy transport code with the event
generator mode is a real physical quantity, which is often
required as mentioned above.
3 Reaction models in PHITS
We have developed a particle and heavy ion transport
Monte Carlo code system, PHITS [1], for general purposes.
PHITS has three important ingredients which enable us to
simulate various nuclear reactions, hadron-nucleus reactions
with energy up to 200GeV, nucleus-nucleus collisions from
10MeV/u up to 100GeV/u and reactions of low energy
neutron down to 10−5eV. For this, PHITS employs three
reactionmodels,ahadroncascademodelJAM[2],amolecular
dynamics model JQMD [3] for nucleus-nucleus collisions,
and a reaction model based on the evaluated nuclear data for
low energy neutrons and photons in the same manner as in
MCNP4C [4]. JAM and JQMD are reaction models which
satisfy the event generator mode but the MCNP part for low
energy neutron is not an event generator mode. Thus two fields
©2008 CEA, published by EDP Sciences
Article available at http://nd2007.edpsciences.org or http://dx.doi.org/10.1051/ndata:07398
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1168 International Conference on Nuclear Data for Science and Technology 2007
are mixed up in PHITS. In order to estimate the higher order
quantities such as the deposit energy distribution for a whole
energy range in PHITS, we have developed a new treatment of
collisional processes for low energy neutrons.
By using the evaluated nuclear data, if it could include all
cross sections of the ejectiles, we cannot construct an event
by the Monte Carlo method except for the elastic channel,
since the evaluated nuclear data has no information about
correlation between ejectiles of a collision. Let us consider a
typical example of this, i.e., neutron induced (n,2n) reaction
channel. In the MCNP-type calculation, the momentum of the
first outgoing neutron is determined according to the nuclear
data for the inclusive neutron spectra. The momentum of the
second outgoing neutron is also determined in the same pro-
cedure independently of the first neutron. Thus, for example,
the following situation can be happened; a neutron with the
incident energy 19MeV hits a nucleus and produces the first
neutron with energy of 12MeV and the second with 15MeV.
In this case, the total energy and momentum is violated in this
event. This is due to a lack of information about the correlation
in the evaluated nuclear data. In the MCNP-type calculation,
however,thetotalenergyandmomentumisconservedinterms
of the expectation values obtained by the integration with the
one-body phase-space distributions, which is realized after
averaging out the observables by the test particle tracks in the
actual numerical simulation.
One possibility to construct an event for low energy
neutron collision might be to make a pure theoretical model to
describe the collision. However, it is almost hopeless since the
cross section of neutron in the low energy below 20MeV has a
lot of resonance structure and all of the resonances cannot be
described purely by a theoretical model. Therefore, we have
developed a new treatment of collisional processes for low
energy neutrons by combining the evaluated nuclear data and
a reaction model in the following way.
4 Event generator mode in PHITS
The evaluated nuclear data for the low energy neutron includes
the information of the total cross section, the channel cross
sections of capture, elastic, inelastic, and (n,Nn?) the inclusive
double differential cross section of outgoing neutrons. From
this information, the energy and momentum of all ejectiles
including the residual nucleus are not determined uniquely,
since in particular the information on the correlation is not
available. Therefore, we have developed a model to determine
the energy and momentum of all ejectiles, event by event, by
using the information of the nuclear data and combining a
special statistical decay model.
At first, we use the total cross section and the channel
cross sections from the evaluated nuclear data to choose a
channel of the collision. We categorize the channels by the
number of outgoing neutrons. For the channel which does
not produce neutrons, that we call “capture” channel, the
excitation energy and momentum of the captured nucleus is
determined uniquely from the incident energy of neutron and
target nucleus. For the decay process of this excited nucleus,
we apply a special statistical decay model, in which the decay
width of neutron is assumed to be zero for the capture channel.
Considering the charged particle decay and photon decay in a
statistical way, we can determine all energy and momentum of
ejectiles and residual nucleus for the capture channel.
For the elastic channel, which is one of the channels
categorized by one outgoing neutron, we choose the scatter-
ing angle of outgoing neutron by the Monte Carlo method
accordingtotheevaluatednucleardata.Wecanthendetermine
the neutron energy and the momentum of the recoil nucleus
uniquely by the kinematics of the elastic collision.
For the inelastic channel (n,n?), which is also a channel
with one outgoing neutron, we first choose the momentum of
the outgoing neutron according to the double differential cross
sections of the evaluated nuclear data by Monte Carlo method.
Using the kinematics of this emission, we can uniquely deter-
mine the excitation energy and the momentum of the residual
nucleus. We then apply the same statistical decay procedure as
in the capture channel without neutron decay width since there
is no more neutron emission after the first neutron emission for
this channel.
Finally for (n,Nn?) channel, which is a channel with N
outgoing neutrons, we choose the momentum of the first
outgoing neutron in the same way as in the (n,n?) case. After
one nucleon emission, we apply only neutron decay procedure
to the excited nucleus until N nucleons are emitted. Once
N neutrons are emitted, the special decay procedure without
neutron decay width is applied.
Using the above procedure, we can treat a low energy
neutron collision as an “Event”, keeping the energy and
momentum conservation and preserving the channel cross
sections and the inclusive neutron double differential cross
sections, which are given by the evaluated nuclear data. The
validation of the event generator mode in the PHITS code is
presented in the other paper of these proceedings [5].
5 Example of event generator mode
Thanks to the event generator mode in PHITS for low energy
neutron transport phenomena, we can calculate many new
quantities which cannot be obtained by MCNP-type calcula-
tion, e.g., kinetic energy distribution of residual nuclei and
charged particles, two-particle correlation, and so on. Here
we show an example of the event generator mode in PHITS,
i.e., deposit energy distribution in a cell, which is a typical
quantity beyond one-body observable. This quantity is well
known as a pulse height tally in MCNP. However, this is a
conceptually wrong quantity to be treated in the MCNP-type
calculation as discussed before. As mentioned in the MCNP
manual, this tally is very restricted to use for neutron transport
in MCNP. Namely, this tally does not work if a collision
produces multiple neutrons.
Figure 1 shows the deposit energy distribution in a thin
Si tip irradiated by 19MeV mono energetic neutrons. The
thickness of the Si tip is 3µm. If we calculate the deposit
energy by using the Kerma factor in MCNP-type calculation,
we get a delta-function-like single peak at 100eV with almost
no distribution. However, figure 1 shows broad distribution
obtained by the event generator mode in PHITS, where the
deposit energy is estimated from the ionization losses of the
charged particles and the recoil nuclei. This distribution is
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Koji Niita et al: A new treatment of radiation behaviour beyond one-body observables 1169
Fig. 1. Deposit energy distribution in a thin (3 µm) Si tip irradiated by
mono energetic neutron at 19MeV. The solid (red) line is the result
of the event generator mode of PHITS with nucleus transport, and the
dashed (blue) line is the result of a local approximation, i.e., without
nucleus transport.
not a statistical fluctuation in the Monte Carlo numerical
calculation but a physical quantity to be considered. This
distribution is also very important to estimate the single event
upset probability of semiconductor memory cells, since only
the events which induce the deposit energy greater than a
certain threshold energy contribute to the error.
In figure 1, we have plotted two distributions, solid line
and dashed line. The dashed line was obtained by the local
approximation (Kerma approximation), in which all charged
particles and recoil nuclei produced in neutron induced re-
actions are assumed to be stopped and deposit their kinetic
energy at the collision point. This approximation is valid under
the condition that the range of charged particles is much
smaller than the size of the system. For this example, both
are comparable since the range of charged particles is of the
order of µm, while the thickness of Si is 3µm. Therefore we
transported the charged particles and the recoil nuclei in the
PHITS calculation without the local approximation. The result
is shown by the solid line in figure 1. This shows that the
highest peak of the dashed line has disappeared. This means
that some part of the charged particles or the recoil nuclei
(mainly alpha particles for this case) can escape from Si tip
to the outside.
This example indicates two important points. The first is
that the deposit energy distribution in a cell is well described
by the event generator mode in PHITS even for low energy
neutron transport below 20MeV. The second is that the local
approximation is not valid for the system whose size is
comparable to the range of the transport charged particles and
recoil nuclei.
6 Conclusion
We have proposed a new treatment of radiation behaviour in
the particle and heavy ion transport code system PHITS by
introducing an event generator model. In the event generator
mode of PHITS, we combine the evaluated nuclear data and
the reaction models to describe all the ejectiles of a collision
keeping the energy and momentum conservation. Using this
new model, we can estimate new quantities which are related
to the higher order correlations beyond one-body observable.
We have shown an example of such observable, the deposit
energy distribution in a cell, which cannot be obtained by
the MCNP-type transport calculation based on the Boltzmann
equation with the evaluated nuclear data.
The existing nuclear data bases include many cross sec-
tions such as total cross section, channel cross section, double
differential cross section of ejectile, and so on. These are
all one-body inclusive data, while there is almost no data
for the correlations between ejectiles. One reason of this is
that huge storage is necessary to compile the correlation data
particularly for higher energy, since the combination of the
ejectiles is drastically growing up as energy is increasing.
Another is that there is no need for the correlation data as
far as one treats one-body observables such as heat, flux,
and dose in the transport calculations with the nuclear data.
However, as stressed in this paper, the quantities beyond one-
body observable are often required in many new fields. The
treatment of the event generator mode in PHITS proposed
in this paper might be a direction to fulfil the new fields
requirements.
References
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61, 024901 (2000).
3. K. Niita, S. Chiba, T. Maruyama, H. Takada, T. Fukahori, Y.
Nakahara, A. Iwamoto, Phys. Rev. C 52, 2620 (1995).
4. J.F. Briesmeister et al., MCNP: General Monte Carlo N-Particle
Transport Code, LANL Report, LA-12625-M (1997).
5. Y. Iwamoto, K. Niita, Y. Sakamoto, T. Sato, N. Matsuda (these
proceedings).