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The following article appeared as:
Fuss, M., Munoz, A., Oller, J., Blanco, F.G., Almeida, D.,
Limao-Vieira, P., Do, T.P., Brunger, M.J., & Garcia, G., 2009.
Electron-scattering cross sections for collisions with
tetrahydrofuran from 50 to 5000 eV. Physical Review A,
80(5), 052709-1-052709-6.
and may be found at:
http://link.aps.org/doi/10.1103/PhysRevA.80.052709
DOI: 10.1103/PhysRevA.80.052709
Copyright (2009) The American Physical Society. This article
may be downloaded for personal use only. Any other use
requires prior permission of the author and The American
Physical Society.
Electron-scattering cross sections for collisions with tetrahydrofuran from 50 to 5000 eV
M. Fuss,
1
A. Muñoz,
2
J. C. Oller,
2
F. Blanco,
3
D. Almeida,
4
P. Limão-Vieira,
4
T. P. D. Do,
5
M. J. Brunger,
5
and G. García
1,6
1
Instituto de Matemáticas y Física Fundamental, Consejo Superior de Investigaciones Científicas (CSIC),
Serrano 113-bis, 28006 Madrid, Spain
2
Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 22, 28040 Madrid, Spain
3
Departamento de Física Atómica, Molecular y Nuclear, Universidad Complutense de Madrid, Avenida Complutense s.n.,
28040 Madrid, Spain
4
Departamento de Física, CEFITEC, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal
5
ARC Centre for Antimatter-Matter Studies, School of Chemistry, Physics and Earth Sciences, Flinders University, G.P.O. Box 2100,
Adelaide, South Australia 5001, Australia
6
Departamento de Física de los Materiales, UNED, Senda de Rey 9, 28040 Madrid, Spain
共Received 16 September 2009; published 19 November 2009
兲
In this paper, we report on total electron tetrahydrofuran 共C
4
H
8
O兲 scattering cross-section measurements for
energies in the range from 50 to 5000 eV with experimental errors of about 5%. In addition, integral elastic and
inelastic cross sections have been calculated over a broad energy range 共1– 10 000 eV兲, with an optical
potential method assuming a screening-corrected independent atom representation. Partial and total ionization
cross sections have been also obtained by combining simultaneous electron and ion measurements with a
time-of-flight analysis of the ionic induced fragmentation. Finally, an average energy distribution of secondary
electrons has been derived from these measurements in order to provide data for modeling electron-induced
damage in biomolecular systems.
DOI: 10.1103/PhysRevA.80.052709 PACS number共s兲: 34.80.Bm, 34.80.Gs, 34.50.Bw
I. INTRODUCTION
Radiation damage in biomolecular systems has been ex-
tensively studied in the last decade, paying special attention
to the role of secondary electrons 关1–3兴 in radiation induced
effects. The main purpose for some of these studies is to
provide radiation interaction models to be used in biomedical
applications, both for diagnosis and therapy. These models
require electron-scattering cross sections over a wide energy
range, in principle, from the high energy of the primary ra-
diation slowing down to thermal energies. Although these
parameters have been widely studied for different atomic and
molecular targets 关4–6兴, most of the works have been re-
stricted to the low energy domain. Indeed, from the experi-
mental point of view, electron-scattering cross-section data
for energies above 500 eV are scarce. Concerning calcula-
tions, a complete scattering treatment is not affordable at all
these energies and so some approximations are required. For
high energies, it is customary to use the first Born approxi-
mation to calculate cross-section data, both for elastic and
inelastic scatterings. However, we have previously shown
关7–10兴 that this approximation overestimates cross-section
values for simple life-relevant molecules even at a 5000 eV
incident electron energy. At intermediate and high energies
共50–5000 eV兲, optical potential calculations, assuming an in-
dependent atom configuration, have proven to be a simple
and powerful tool 关11–13兴 applicable to different-sized mol-
ecules, from diatomic molecules to complex biomolecules
共DNA and RNA bases 关14兴 or DNA dodecamer complex
关15兴兲 when appropriate corrections are included 关15兴.
One of the most important molecules for biological sys-
tems is water. Consequently, electrons interacting with H
2
O
molecules have been studied, both theoretically and experi-
mentally, by means of many different techniques. We
have recently published a detailed study of electron-
scattering cross sections from water molecules 关16兴, includ-
ing comparisons to previous results and available review pa-
pers 关17,18兴. Going to more complex biomolecules,
tetrahydrofuran-C
4
H
8
O 共THF兲 reveals great interest due to
its similar structure to that of the sugar components of DNA
and RNA 关19兴. As a consequence, electron-scattering cross
sections by THF have been measured and calculated in the
last few years for intermediate and low energies 关19–30兴.
However, for energies above 500 eV, experimental and the-
oretical electron interaction data are almost nonexistent for
this molecule.
These considerations partly motivated the present study,
in which absolute experimental electron-scattering total cross
sections 共TCSs兲 have been determined by measuring the at-
tenuation of an electron beam through a sample of THF for
energies between 50 and 5000 eV. Differential and integral
electron-scattering cross sections have also been calculated
by using an optical potential method, based on an indepen-
dent atom representation but including screening corrections
in order to emulate the molecular structure. In addition, par-
tial and total electron-impact ionization cross sections have
been measured with a pulsed crossed-beam technique in
combination with a time-of-flight analysis of the induced
molecular fragmentation.
Other important information in simulations to define
single-particle tracks includes the energy-loss distribution
function and the energy distribution of the secondary elec-
trons. As a complement of the abovementioned experiments,
we will provide these distribution functions as derived from
direct measurements of the primary electron energy-loss
spectra or energy analysis of the produced secondary elec-
trons, respectively.
PHYSICAL REVIEW A 80, 052709 共2009兲
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II. MEASUREMENTS
The experimental configuration to measure TCS and
energy-loss spectra was based on that previously reported
关16兴. However, in contrast with the procedure used in 关16兴,
ionization cross sections have now also been measured in an
independent system. Here, we will only thus describe briefly
the original apparatus, giving more details about the system
which was used to determine the partial and total ionization
cross sections and the energy distribution of the secondary
electrons.
A schematic diagram of the first system is shown in Fig.
1. The primary electron beam was produced by an emitting
filament. Thereafter, a combination of magnetic and electro-
static fields controls the direction of the beam and reduces
the energy spread to ⬃100 meV. The collision chamber con-
taining the gas target was a stainless-steel tube delineated by
two apertures. The entrance aperture was always 0.5 mm in
diameter, whereas different exit apertures with 1, 2, or 3 mm
diameter, as well as two different lengths of the collision
chamber of 10 and 50 mm, respectively, were used according
to the experimental requirements. The gas pressure in the
chamber was measured with an absolute capacitance gauge
共MKS Baratron 127A兲 and it was varied from 0.1 to 10
mTorr according to the experimental conditions. Electrons
emerging from the collision chamber were deflected by a
quadrupole electrostatic system to select the angle of analy-
sis. The energy analyzer was a hemispherical electrostatic
spectrometer in combination with a retarding field. In these
conditions, the energy resolution of the spectrometer was
about 0.5 eV 共full width at half maximum, FWHM兲 for the
whole energy range considered here. Transmitted electrons
through the analyzer were finally detected by a channel elec-
tron multiplier operating in single pulse counting mode.
Count rates were typically on the order of 10
3
s
−1
for the
total cross-section measurements and up to 10
4
s
−1
through
the energy-loss spectra determination. Note that he maxi-
mum angular acceptance of the energy analyzer was 1.9
⫻ 10
−5
sr. The whole system was differentially pumped by
two turbo pumps of 80 and 250 l/s, respectively, reaching a
background pressure of ⬃10
−8
Torr. On the other hand, the
pressure in the electron gun and energy analyzer region was
maintained lower than 10
−6
Torr during the measurements.
TCSs have been measured for energies between 50 and
5000 eV, while energy-loss spectra were measured in the
same energy range but for different scattering angles. These
angles were selected by deflecting the scattered beam with a
quadrupole electrostatic plate system. A typical energy-loss
spectrum for 1000 eV incident energy, 10 mTorr pressure in
the gas cell, and an analysis angle around 10° is shown in
Fig. 2.
The second experimental system is schematically shown
in Fig. 3. The electron gun consists of an emitting filament,
extractive and focusing electrodes, and an electrostatic quad-
rupole system to drive the beam into the collision chamber.
The collision chamber is a gas cell which is limited along the
direction of the electron beam by two apertures of 0.5 and 2
mm diameter, respectively, separated by 30 mm. Another two
apertures of 2 mm diameter are placed perpendicular to both
12 3 54678
9
10
12
11
12
FIG. 1. 共Color online兲 Present experimental apparatus: 1, elec-
tron gun; 2, transverse magnetic field; 3 and 7, quadrupole electro-
static plates; 4, 6, and 8, decelerating and accelerating lenses; 5,
scattering chamber; 9, hemispherical electrostatic energy analyzer;
10, channel electron multiplier; 11 and 12 vacuum turbo molecular
pumps.
04080
Ener
gy
loss
(
eV
)
0
100
200
300
400
El
ectron
i
ntens
i
ty
(
ar
bi
trary un
i
ts
)
x4
FIG. 2. 共Color online兲 Typical measured electron energy-loss
spectrum for a 1000 eV incident energy electron beam. In this case,
there was 10 mTorr pressure in the gas cell and a 10° analysis angle.
FIG. 3. 共Color online兲 Experimental system to determine total
and partial ionization cross sections by electron impact: 1, electron
gun 共filament, control electrode focusing lens, and deflecting
plates兲; 2, gas cell; 3, ion drift tube 共extracting electrode, focusing
lens, and deflecting plates兲; 4, electron drift tube; 5, magnetic coils;
6, microchannel plate detectors; 7, Faraday cup.
FUSS et al. PHYSICAL REVIEW A 80, 052709 共2009兲
052709-2
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sides of the incident beam and are separated by 3 mm. These
four apertures define the geometry of the collision region, in
which the target gas is introduced by a needle valve at a
well-known pressure controlled by a MKS Baratron capaci-
tance gauge. Note that each perpendicular aperture defines
the entrance of a differentially pumped drift tube. The larger
drift tube 共1.5 m length兲 drives the collected ion beam by
means of two additional apertures, 3 mm in diameter, and an
electrostatic quadrupole system which controls the ion direc-
tion. These ions are finally detected by a two-stage micro-
channel plate assembly operating in a single pulse mode. The
other drift tube, with a geometrical length of 0.5 m, trans-
ports and detects the extracted secondary electrons. A vari-
able parallel magnetic field 共0–0.01 T兲 is externally applied
to increase the actual length of these electron trajectories. As
for the ions, the secondary electrons are detected by a two-
stage microchannel detector in single-pulse operation mode.
The primary electron beam in this second system was
pulsed by applying a +10 V train of pulses to the gun con-
trol electrode, each of 10
−5
s duration and having a repeti-
tion rate of 10
4
Hz. Extractive bipolar pulses of variable
amplitude, up to ⫾400 V, in synchronism with the electron-
beam pulses, were applied to the perpendicular apertures.
Under these conditions, ions and secondary electrons are ex-
tracted in opposite directions toward the respective drift
tubes. The secondary electron and ion signals were indepen-
dently stored as a function of time by a two-channel Tek-
tronix TDS3032C digital scope. Primary electrons, transmit-
ted through the gas cell, are detected by a Faraday cup. Note
that the average electron currents in the cup, typically on the
order of 10
−8
A, were measured with a Keithley 6517A elec-
trometer. Total ion intensity measurements, normalized by
the primary electron currents at each measured electron en-
ergy, provided relative total ionization cross sections as a
function of electron energies from 50 to 5000 eV. For a given
energy, partial cross sections 共corresponding to the different
observed ion fragmentation channels兲 were determined from
the consequent time-of-flight spectra provided by the ion
drift tube. These relative values were put on an absolute
scale by normalizing to the electron-impact ionization cross
section for N
2
at 1000 eV, which was assumed to be
共0.85⫾ 0.05兲 ⫻ 10
−16
cm
2
in accordance with previous mea-
surements available in the literature 关31–35兴. Similarly, sec-
ondary electron distribution energies were derived from
time-of-flight measurements given by the electron drift tube.
III. CALCULATIONS
The optical potential method described in previous papers
关10–12兴 has been used to calculate differential and integral
elastic, as well as integral inelastic, electron-THF scattering
cross sections. This calculation includes the recent adjust-
ments we have introduced in the potential which signifi-
cantly improved results for many molecular targets, both for
the integral 关12兴 and differential 关13兴 cross sections, espe-
cially in the low energy region. Processes involving nuclear
motion are neglected in this calculation. The present method
considers inelastic scattering as being due to electron-
electron interaction processes; only those arising from elec-
tronic excitation are considered, thus rotational and vibra-
tional excitations are ignored. This restriction is not thought
to be significant in general for the relatively high energies
considered in this study.
Following the above procedures, we present calculated
integral electron-scattering cross sections 共elastic, inelastic,
and total兲 from 1 to 10 000 eV. The reliability of these re-
sults, in comparison to the experimental data, is discussed in
the next section.
IV. RESULTS AND DISCUSSION
TCSs measured in this study, from 50 to 5000 eV, are
shown in Table I and plotted in Fig. 4. The estimated experi-
mental errors on these data are less than 5% 共see Ref. 关36兴
for a detailed analysis of the main error sources兲. Previous
TABLE I. Experimental and theoretical electron-scattering cross
sections 共10
−16
cm
2
兲 for THF as obtained in this study.
Energy
共eV兲
Calculation
共10
−16
cm
2
兲
Experiment
共10
−16
cm
2
兲
Elastic
共
el
兲
Inelastic
共
inel
兲
Total
共
tot
兲
Ionization
共
ion
兲
Total
共
tot
兲
1 79.5 79.5
1.5 74.2 74.2
2 68.6 68.6
3 58.5 58.5
4 54.6 54.6
5 51.8 51.8
7 47.3 47.3
10 43.1 0.07 43.2
15 37.2 2.97 40.3
20 31.1 7.84 38.9
30 23.0 14.2 37.2
40 19.2 16.2 37.2
50 16.8 16.6 33.3 11.2 44.2
70 13.9 16.2 30.2 36.5
100 11.5 14.8 26.3 12.5 31.4
150 9.27 12.7 22.0 12.0 26.3
200 7.90 11.1 19.1 9.89 22.0
300 6.19 9.04 15.2 7.90 16.6
400 5.15 7.59 12.8 6.57 13.7
500 4.45 6.61 11.1 5.64 11.8
700 3.53 5.24 8.76 9.08
1000 2.70 4.03 6.72 3.39 6.96
1500 1.95 2.91 4.86 2.49 5.11
2000 1.54 2.30 3.84 1.99 3.90
3000 1.09 1.63 2.72 1.46 2.84
4000 0.851 1.27 2.12 1.16 2.17
5000 0.700 1.04 1.74 0.978 1.78
7000 0.518 0.770 1.29
10000 0.378 0.557 0.932
ELECTRON-SCATTERING CROSS SECTIONS FOR… PHYSICAL REVIEW A 80, 052709 共2009兲
052709-3
Archived at Flinders University: dspace.flinders.edu.au
measurements available in the literature 关21,22兴 are also in-
cluded in this figure for comparison. As shown in Fig. 4,
there is good agreement, within experimental error, between
the present data and those of Ref. 关22兴, reaching a maximum
difference of 9% at 400 eV. Low energy data from 关21兴 are
systematically lower than those of 关22兴, but showing a simi-
lar energy dependence. This discrepancy is due to the poorer
angular resolution of the apparatus used in 关21兴 compared to
that of 关22兴. Correcting for this effect, by using the differen-
tial cross sections measured in 关23兴, the data of Ref. 关21兴
increase by up to about 40% being therefore now in satisfac-
tory agreement with those of 关22兴.
Regarding the theoretical data, Table I also includes our
calculated integral elastic and integral inelastic 共absorption
potential contribution兲 cross sections. As may be seen in Fig.
4, the total theoretical electron-scattering cross sections, ob-
tained by adding those partial cross sections, show excellent
agreement with our experimental data in the overlapping en-
ergy region 共50–5000 eV兲. However, integral elastic cross-
section calculations from Mozejko and Sanche 关37兴, obtained
with an independent atom model, show important discrepan-
cies with the present results, being 23% higher than ours at
2000 eV and increasing up to 88% larger at 50 eV. The origin
of this discrepancy is unclear; we have shown that our
screening correction 关14兴 improves significantly the indepen-
dent atom calculation results for relatively low energies.
Nonetheless, this does not explain the ⬃20% discrepancy at
2000 eV.
Below 50 eV, we would expect our method to become less
reliable as energy further decreases. However, as may be
seen in Fig. 4, recent measurements carried out by Colyer et
al. 关23兴 and Dampc et al. 关24,25兴 show reasonable agreement
with our calculated integral elastic cross sections even at
energies as low as around 10 eV.
Concerning our ionization cross-section data, Fig. 5 rep-
resents a typical ion mass spectrum derived from the time-
of-flight spectrum
showing the ion fragmentation pattern for
an incident electron energy of 1000 eV. As can be seen, our
mass resolution is somewhat limited, so that fragments dif-
fering only by one mass unit are not fully resolved. Notwith-
standing that point, present partial and total ionization cross-
section results from our measurements between 50 and 5000
eV are shown in Fig. 6 and Table II. Experimental errors for
the total ionization data, including the accuracy of the
present normalizing procedure, have been estimated at about
7%. For the partial cross sections, the statistical uncertainties
tend to be higher for the less abundant fragments, reaching a
maximum value of ⬃15% for the H
n
+
共n =1,2兲 ionic frag-
ments. As can be seen in Fig. 6, our absolute total ionization
data show excellent agreement, to within 6%, with the cal-
culations of Ref. 关37兴 derived with the binary-encounter-
Bethe 共BEB兲 model.
When modeling radiation effects at the molecular level,
an energy distribution of the generated secondary electrons is
needed at each energy of the primary ionizing radiation. As
mentioned earlier, time-of-flight measurements of secondary
electrons produced by ionization of the target provide such
1 10 100 1000 1000
0
Electron ener
gy (
eV
)
0.1
1
10
100
Cross section (10
-16
cm
2
)
FIG. 4. 共Color online兲 Cross section for electron scattering by
THF: 䉱, present experimental total cross sections; 䊊, experimental
total cross-section data from Ref. 关22兴; 〫, experimental total cross
sections given in Ref. 关21兴; —, present total cross-section calcula-
tion; - · -, present inelastic cross-section calculation; —, present
elastic cross-section calculation; -· ·-, elastic cross section calcu-
lated in Ref. 关37兴; +, experimental elastic cross section from Ref.
关23兴; 쎲, experimental elastic cross sections from Ref. 关24兴.
0 102030405060708
0
Ion mass
(
atomic units
)
0
20
40
60
80
100
Ion intensity (arbitrary units)
H
n
+
CH
n
+
+H
n
O
+
C
2
H
n
+
+CH
n
O
+
C
3
H
n
+
+C
2
H
n
O
+
C
4
H
n
+
+C
3
H
n
O
+
C
4
H
n
O
+
FIG. 5. 共Color online兲 Ion fragment mass spectrum derived from
the time-of-flight spectrum for an incident electron energy of 1000
eV. Species detected are as labeled on the figure.
100 1000 1000
0
Ener
gy (
eV
)
0.001
0.01
0.1
1
10
100
Cross section (10
-16
cm
2
)
FIG. 6. Total and partial electron-impact ionization cross sec-
tions in THF. 䉱, present total ionization cross-section measure-
ments; —, total ionization cross sections calculated in Ref. 关37兴.
Present partial ionization cross sections corresponding to: 䉮,H
n
+
;
쎲,CH
n
+
+H
n
O
+
; 䊊,C
2
H
n
+
+CH
n
O
+
; 䉲,C
3
H
n
+
+C
2
H
n
O
+
; 〫,
C
4
H
n
+
+C
3
H
n
O
+
;+,C
4
H
n
O
+
.
FUSS et al. PHYSICAL REVIEW A 80, 052709 共2009兲
052709-4
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