Secondary Electron Production and Transport Induced by
Fast Protons in Thin Foils
L.H. Toburen*, W. Friedland#, M. Dingfelder#, N. Ozturk*, C. Christou*,
R.D. DuBois**, G. Lapicki*, J.L. Shinpaugh*, C.G. Drexler##, E.L.B Justiniano*,
and H.G. Paretzke#
*
Department of Physics
East Carolina University
Greenville, NC
#
Institute of Radiation Protection
GSF-National Research Center for Health and Environment
Neuherberg, Germany
**
Department of Physics
University of Missouri-Rolla
##
Städtisches Krankenhaus München-Schwabing
Institut für Medizinische Physik und Strahlenschutz
Munich, Germany
Abstract. Monte Carlo (MC) simulation of charged particle track structure has become an important tool in radiation
biology. MC calculations provide detailed spatial information on the production of radiation damage to DNA and other
cellular structures. To test the physical parameters used in these models and to explore details of electron transport in
condensed matter we have initiated a comparison of MC results to measured doubly differential yields of electrons
emitted from thin foils by the passage of fast charged particles. Our initial studies focus on the calculation of differential
electron yields resulting from passage of 1-2 MeV protons through thin carbon foils using the MC code PARTRAC
developed at the Institute of Radiation Protection – GSF, Neuherberg, Germany. Preliminary calculations are in
relatively good agreement with spectra measured for secondary electrons with energies larger than about 50 eV, however
large variations are observed for smaller energies. The effects of changes in such parameters as electron mean free path,
elastic and inelastic electron scattering cross sections, and foil thickness are illustrated.
secondary electrons, with the target material.
Unfortunately the reliability of these codes for the
study of low-energy electron transport can be
questioned because of the lack of experimentally
tested and verified cross sections for interactions with
condensed phase material. With recent advances in
radiobiology reaching molecular resolution [6], it is
important that the reliability of codes using the current
physical input data be tested to determine the
reliability of calculations at this level. One means for
gaining confidence in the physics used in these codes,
and at the same time gaining a better understanding of
condensed phase electron production and transport
INTRODUCTION
The use of Monte Carlo (MC) codes for event-byevent calculations of the spatial structure of charged
particle tracks has become a common tool in the study
of radiation damage in radiobiology [1-5]. This
technique has been successful in predicting the yields
of such quantities as DNA strand breaks and the
spectra of DNA fragment sizes produced by absorption
of radiation of different types. These MC codes make
use of experimental and theoretical cross sections for
excitation, ionization, and charge transfer for
interactions of protons and alpha particles, and their
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28
phenomena, is to compare calculated spectra of
electrons emitted from thin films with measured
spectra. This comparison also tests the sensitivity of
the MC results to different, and presumably more
reliable, interaction cross sections.
Most Monte Carlo track structure codes used in
radiobiology incorporate elastic and inelastic cross
sections either from measurements for charged particle
interactions with isolated “gas” atoms and molecules
or from various theoretical methods. When gas phase
cross sections are used, the gas results are simply
scaled to unit density to approximate tissue.
Unfortunately this scaling does not incorporate
condensed phase characteristics. The PARTRAC code
developed at GSF [3,4] uses elastic and inelastic cross
sections based on the plane wave Born approximation
(PWBA).
Within the approximations used, the
properties of the medium enter via the generalized
oscillator strength (GOS) that is related to the
dielectric response function, a macroscopic quantity
known from classical electrodynamics.
This
approximation allows one to model the cross sections
for condensed phase materials, i.e., liquid water [7,8].
Unfortunately, these cross sections cannot be
confirmed experimentally because single collision
cross sections are generally unavailable, or
measurements infeasible, in condensed phase material.
In addition, since the theoretical approach is based on
a perturbation method, the validity is in question for
interactions involving very-low-energy electrons.
FIGURE 1. Total elastic and inelastic cross sections for
electrons in water used in PARTRAC are shown for electron
impact energies greater than 10 eV. The cross sections
shown for energies below 10 eV are from a simple
extrapolation of the elastic cross sections (···) and inelastic
cross sections measured by Michand and Sanche [9] ( ).
The spectra of electrons ejected by fast protons
from the surface of a clean foil is expected to provide a
sensitive test of MC calculations of electron transport.
This is illustrated in Figure 2 where we show
differential electron yields measured at 45o from the
surfaces of different frozen hydrocarbons following
the passage of 2 MeV protons[10]. For electrons with
energies less than about 50 eV we observe significant
differences between the spectra of electrons ejected
from different surface materials.
In Figure 3 we compare data for
measurements of the ejected electron spectra from a
carbon foil using a time-of-flight (TOF) technique that
RESULTS
The total elastic and inelastic cross sections used in
the PARTRAC code [7,8] along with measured
inelastic cross sections of Michand and Sanche [9] are
shown in Figure 1. The dotted line representing the
low-energy portion of the elastic scattering cross
sections is a simple extrapolation; the PARTRAC code
was not designed to follow electron transport for
energies below 10 eV. For such low energies,
following electrons in an event-by-event manner
requires an inordinate amount of computer time. The
code does, however, account for the production of
low-energy electrons in ionizing collisions; it assumes
each electron with energy less than 10 eV is
thermalized and its energy deposited in the local
region of production. This methodology is appropriate
for many calculations of interest in radiobiology, but
when detailed spatial information is required on a
microscopic scale, e.g., DNA cluster damage, the
transport of sub 10 eV electrons can be of importance.
FIGURE 2. The yield of ejected electrons observed at 45o
to the forward direction of a 2 MeV proton passing through a
thin foil of frozen hydrocarbons. The foil is “thick” relative
to the range of the electrons, but “thin” relative to the
protons range.
29
little effect because the 3 µg/cm2 foil is thicker than
the range of all but the most energetic electrons
produced by the proton. To check the potential effects
of uncertainty on the foil thickness we have made MC
calculations for foils of relatively large differences in
thickness. The result of calculations for electron
yields for two emission angles for foils differing in
thickness by nearly a factor of seven are shown in
Figure 4. Only at the highest energy, ejected electron
energies greater than about 1 keV, is there evidence of
an effect of foil thickness. Such high-energy electrons
FIGURE 3. The yields of electrons emitted at 45o from a
3 µg/cm2 carbon foil following the passage of 1 MeV
protons. The MC calculation was made with the PARTRAC
code using “water” cross sections for electron transport. The
two measured spectra were obtained using different
experimental techniques.
is optimized for the study of low-energy electrons
along with data from electrostatic energy analysis
appropriate for the measurement of high-energy
electrons and a Monte Carlo calculation using the
PARTRAC code. The MC code uses water cross
sections for electron transport and cannot be expected
to accurately reproduce the low energy electron yields
for carbon. For electron energies greater than about 50
eV the MC calculation is in excellent agreement with
the measurements although there is some evidence that
the MC calculation might overestimate the yield of the
highest energy electrons. To confirm the cause of this
discrepancy will require additional study to determine
if it reflects an overestimation of collision cross
sections involving large energy loss in PARTRAC or
results from some experimental inaccuracy.
FIGURE 4. Electron yields calculated for different foil
thickness and emission angles.
interact only weakly with the thin foil, therefore their
yield is related to the number of target electrons; this
parameter is proportional to target thickness. There is
no dependence on thickness observed for the yield of
low-energy electrons confirming our assumption that
the foil is thick relative to the range of these electrons.
The same trends are observed for electrons ejected
from the backside of the foil (not shown).
For low-energy ejected electrons we see
considerable differences between the different data
sets in Figure 3. The data obtained using the
electrostatic analysis technique were obtained without
the aid of ultra-high vacuum, thus one expects an
enhancement of the yield owing to the dirty carbon
surface [11]. The PARTRAC results were obtained
with water cross sections for electron production and
transport, thus we cannot expect the data to agree at
low energies where the electronic structure of the
target can influence the yield.
As noted above, the combination of relatively large
elastic cross sections and small inelastic cross sections
used in the PARTRAC code encouraged the use of a
low-energy cut-off for electron transport in order to
conserve computer time. Therefore, to study electron
transport for electrons with energies less than 10 eV
we were required to make modifications to the code.
Our first calculations for electron energies less than 10
eV are shown as the open circles in Figure 5. These
results were obtained by simply counting the yield of
electrons produced in the slowing down of secondary
electrons that, when randomized in direction, were
within one mean free path of the surface. For this
calculation, the mean free path for electrons with
energy less than 10 eV was chosen equal to that used
for the 10 eV electrons. Although the calculated yield
was found to agree with the measured yield, we
The differences between the shapes of the electron
spectra for high-energy electron emission can be either
a result of theoretical or experimental errors. One
possibility we have considered is that the thickness of
the measured foil might have been incorrectly stated.
Our intuition was that the foil thickness would have
30
electron emission from carbon foils. In addition,
appropriate interaction cross sections must be
incorporated into the MC codes for electron energies
below the current 10 eV limit.
ACKNOWLEDGMENTS
This research was supported in part by the Low
Dose Radiation Research Program, Office of
Biological and Environmental Research, US
Department of Energy Grant DE-FG02-01ER63233,
by NIH Grant RO1CA9335101A1, and by the
European Community Contract No. FIGH-CT199900005 Low-Dose Risk Models.
FIGURE 5. Comparison of the spectrum of electrons
emitted from a thin foil by the passage of a 1 MeV proton
calculated with PARTRAC using water cross sections to that
measured from a carbon foil. See text for methods used to
calculate spectra for electron energies less than 10 eV.
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