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Journal ArticleDOI

Excitation of electronic states in tetrahydrofuran by electron impact.

08 Apr 2011-Journal of Chemical Physics (American Institute of Physics)-Vol. 134, Iss: 14, pp 144302-144302

TL;DR: The important effects of the long-range target dipole moment and the target dipoles polarizability, on the scattering dynamics of this system, are evident from the present results.
Abstract: We report on differential and integral cross section measurements for the electron impact excitation of the three lowest lying Rydberg bands of electronic states in tetrahydrofuran. The energy range of the present experiments was 15–50 eV with the angular range of the differential cross section measurements being 15°–90°. The important effects of the long-range target dipole moment and the target dipole polarizability, on the scattering dynamics of this system, are evident from the present results. To the best of our knowledge, there are no other theoretical or experimental data against which we can compare the cross section results from this study.
Topics: Dipole (58%), Polarizability (55%), Cross section (physics) (54%), Rydberg formula (52%), Excitation (50%)

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Excitation of electronic states in tetrahydrofuran by electron impact
T. P. T. Do, M. Leung, M. Fuss, G. Garcia, F. Blanco et al.
Citation: J. Chem. Phys. 134, 144302 (2011); doi: 10.1063/1.3575454
View online: http://dx.doi.org/10.1063/1.3575454
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THE JOURNAL OF CHEMICAL PHYSICS 134, 144302 (2011)
Excitation of electronic states in tetrahydrofuran by electron impact
T. P. T. Do,
1,a)
M. Leung,
1
M. Fuss,
2
G. Garcia,
2
F. Blanco,
3
K. Ratnavelu,
4
and M. J. Brunger
4,b)
1
ARC Centre for Antimatter-Matter Studies, School of Chemical and Physical Sciences, Flinders University,
GPO Box 2100, Adelaide, SA 5001, Australia
2
Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Madrid 28006, Spain
3
Departamento de Fisica Atómica, Molecular y Nuclear, Universidad Complutense de Madrid,
Madrid 28040, Spain
4
Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia
(Received 7 February 2011; accepted 21 March 2011; published online 8 April 2011)
We report on differential and integral cross section measurements for the electron impact excitation
of the three lowest lying Rydberg bands of electronic states in tetrahydrofuran. The energy range
of the present experiments was 15–50 eV with the angular range of the differential cross section
measurements being 15
–90
. The important effects of the long-range target dipole moment and the
target dipole polarizability, on the scattering dynamics of this system, are evident from the present
results. To the best of our knowledge, there are no other theoretical or experimental data against
which we can compare the cross section results from this study. © 2011 American Institute of Physics.
[doi:10.1063/1.3575454]
I. INTRODUCTION
Single-track simulation procedures
14
for photons and
electrons (including secondary electrons produced through
ionization), for modeling radiation damage in matter, with
clear applications to the fields of radiotherapy
58
and radiodi-
agnosis, require interaction probabilities (cross sections) over
a broad energy range for all accessible processes as well as the
corresponding energy loss patterns.
9
These studies are partic-
ularly useful in attempting to achieve good therapeutic out-
comes, where irradiated areas are reduced with the absorbed
dose in surrounding healthy tissue minimized. For the partic-
ular case of DNA-damage, this requires a capacity for spa-
tial resolutions of the order of a nanometre or better.
9
Such
a level of description in turn requires a detailed knowledge
of the atomic and molecular properties of the target for the
simulation.
It is well known
10
that high-energy radiation produces
abundant secondary electrons (4 × 10
4
per MeV of energy
deposited), which are the main source of the energy trans-
fer map and radiation damage. However it is only relatively
recently, thanks to the work of Sanche and colleagues,
1113
that we began to understand that even electrons with subion-
ization energies could produce damage, in terms of DNA
strand breaks and molecular dissociation, more efficiently
than the traditionally considered way of direct ionization
of the medium. Unfortunately, DNA is not itself readily
amenable for the sort of studies needed to determine all of the
input data for the modeling work. As a consequence, moieties
a)
Present address: Physics Department, School of Education, Cantho Univer-
sity, Vietnam.
b)
Electronic mail: Michael.Brunger@flinders.edu.au. Permanent address:
ARC Centre for Antimatter-Matter Studies, School of Chemical and Phys-
ical Sciences, Flinders University, GPO Box 2100, Adelaide, SA 5001,
Australia.
of DNA like tetrahydrofuran (THF), as well as water, have
become the biomolecules of choice for attempting to build up
the requisite data bases for track simulations in matter.
14
Of
course these gas phase cross sections are an approximation to
what actually might be the case in soft matter, although the
recent work of White and Robson,
15
in which the collective
behavior of soft matter is taken into account through “struc-
ture factors,” suggests that they will have a continued utility.
Previous gas phase studies into electron scattering from
THF have been quite limited, and we now summarize them
briefly below. At the total cross section (TCS) level there are
measurements from the work of Zecca et al.,
16
Fuss et al.,
14
and Možejko et al.
17
Differences between their cross sections
can be understood in terms of the different angular-resolution
correction effects of their apparatus, with the results from the
work of Fuss et al. and Možejko et al. being closer to the
true physical value because of their superior angular resolu-
tion. Absolute elastic differential cross sections (DCSs) for
energies (E
0
) above and equal to 20 eV were reported by
Milosavljevi
´
c et al.,
18
while Colyer et al.
19
reported elastic
DCS data for energies between 6.5–50 eV and for scattering
angles (θ) between 10
–130
. At about the same time Dampc
et al.,
20
for E
0
= 6 20 eV and θ = 20
180
, reported
corresponding elastic measurements. Most recently, a detailed
study (absolute) of both elastic excitation functions and angu-
lar distributions was reported by Allan
21
who, where a com-
parison could be made, found good agreement with the results
of Colyer et al.
19
We note that some of the above groups also
derived elastic integral cross section (ICS) values from their
DCS measurements. Vibrational excitation function measure-
ments have been reported by Dampc et al.,
22
with a compre-
hensive series of excitation functions, for six of the normal
modes of THF, at θ = 135
and for E
0
=
threshold 16 eV,
also being given by Allan.
21
Significant resonance effects in
the vibrational excitation functions were observed by Allan.
0021-9606/2011/134(14)/144302/8/$30.00 © 2011 American Institute of Physics134, 144302-1
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144302-2 Do
et al.
J. Chem. Phys. 134, 144302 (2011)
With respect to the electron impact excitation of the electronic
states of THF, we know of only two measurements, a single
energy loss measurement at E
0
= 100 eV and θ = 10
from
the work of Giuliani et al.,
23
and a more complete study by
Bremner et al.
24
Some “bandlike” structure was apparent in
the spectrum of Giuliani et al., although it was not nearly as
pronounced as that found in those same authors’ photoabsorp-
tion studies.
From a theoretical perspective, several detailed electron
scattering calculations on THF have been reported. Trevisan
et al.
25
published results from an ab initio calculation of
the elastic differential and momentum transfer cross sec-
tions using the complex Kohn variational method. A similar
study was undertaken by Winstead and McKoy,
26
although in
this case the cross sections were obtained from a Schwinger
multichannel method. A detailed series of independent atom
model (IAM)-screened additivity rule (SCAR) calculations,
for grand total cross sections, integral elastic cross sections,
and the sum of all the integral cross sections for inelastic pro-
cesses (except rotations and vibrations), can be found in the
work of Fuss et al.
14
Bouchiha et al.
27
used an R-matrix ap-
proach, with a Born correction, to calculate elastic and some
inelastic (electronic-state) ICSs and the energies of a number
of core-excited or Feshbach resonances. Finally, Tonzani and
Greene
28
calculated some integral elastic cross sections and
were able to provide additional insight into resonance effects
on this channel.
In Sec. II of the paper, we present some information on
the spectroscopy of THF, followed by a precis of our experi-
mental methods and analysis details. Thereafter (Sec. IV), we
provide our results and a discussion of those results before
finishing with some conclusions.
II. SPECTROSCOPY OF THF (C
4
H
8
O)
The first hurdle to overcome, in attempting to under-
stand the spectroscopy of THF, is to determine precisely what
is the point-group symmetry of its global energy-minimum
conformer and also its next nearest (in energy) conformers.
The literature suggests several possibilities, with some work
(Refs. 25 and 29 and references therein) suggesting that its
ground-state equilibrium geometry belongs to the planar C
2v
point group so that the oxygen and four carbon atoms lie in
a single plane. However, other studies (Refs. 27, 30, and 31
and references therein) have suggested that there are in fact
lower symmetries, including the twisted C
2
and envelope C
s
structures, which have even lower absolute energies. In addi-
tion to these three conformers, a couple of measurements
32, 33
have also reported the possibility that C
1
is the ground-state
symmetry of THF. However, most work
23, 30, 3437
does seem
to support the notion that the nonplanar symmetrical C
2
point
group symmetry is the global minimum (energy) conformer,
with another local minimum conformer of the C
s
symmetry.
In any event, Bouchiha et al.
27
and Trevisan et al.
25
noted that
the structural bond-lengths and bond angles for three of the
different configurations (C
2
,C
s
, and C
2v
) are very similar and
so are their target properties. For example, the energy differ-
ences between their various ground-state structures are small
(< 0.2 eV), while their permanent dipole moments change by
only0.02D.
The theoretical work contained in the recent study of
Giuliani et al.
23
took into account what are generally consid-
ered to be the three most common conformers in THF (C
2v
,
C
2
, and C
s
). They conducted a Boltzmann analysis at 298 K
that indicated that both the C
2
and C
s
forms were present
with relative populations of 55.5% and 44.5%. The C
2v
ge-
ometry, however, was found from their computations to be
a saddle point with two imaginary frequencies and so is not
expected to be present. It is therefore quite clear that the effu-
sive, room temperature, THF molecular beam, which we em-
ploy in our scattering measurements (see Sec. III), will con-
tain at least two conformational forms each with their own
set of electronic-state configurations.
23
This already suggests
some of the complexity involved in interpreting our measured
energy-loss spectra.
One of the first studies into the excited electronic-state
spectroscopy of gas-phase THF was performed by Pickett
et al.
38
This investigation employed a vacuum ultraviolet
(VUV) photoabsorption spectrometer, and reported two no-
ticeable electronic bands with peaks at 6.378 and 6.899 eV,
respectively (see also Ref. 23 and references therein). Subse-
quently, Hernandez
39
similarly worked on the VUV absorp-
tion spectra of THF. Those results also indicated the presence
of the two bands, at around 6.377 and 6.899 eV, thereby con-
firming the work of Pickett et al. In addition, Hernandez noted
the presence of a region consisting of several doublet bands
beginning at 7.634 eV. This region ended with a very broad fi-
nal band with a peak at around 7.978 eV. Thereafter, the spec-
tra became increasingly complicated with a large number of
closely spaced bands. Indeed, the energy differences between
these groups gradually decrease as you go to even higher en-
ergies, until beyond 9.237 eV where the states significantly
overlap.
In 1991, Bremner et al.
24
reported electron energy loss
spectra (EELS) for THF that showed broad “absorption”
bands. They suggested that the observed transitions may in-
volve a nonbonding electron (n
0
) from the oxygen atom oc-
cupying the highest occupied molecular orbital (HOMO).
Bremner et al. and Tam and Brion
40
assigned the three lowest
bands to being Rydberg in nature, the
1
n
0
3s,
1
n
0
3p,
and
1
n
0
3d bands, with respective vertical excitation en-
ergies of 6.6, 7.2, and 7.8 eV. Interestingly, Bremner et al.
also suggested that these lower-lying excited states of THF
may also contain valence excitations. Three other Rydberg
states were also found by these authors
24, 40
at 8.57 eV (
1
n
0
4p), 8.89 eV (
1
n
0
5p), and 8.1 eV [
1
n
0
1 (or HOMO-
1) 3s], with all these data being summarized in the work
of Bouchiha et al.
27
Excitation thresholds for the various electronic states
were calculated by using pseudonatural orbitals from two
models, by Bouchiha et al. (see this paper for full details). Un-
fortunately although the model, which employed equal abun-
dances for the ground electronic states that result from the
C
2
and C
s
symmetries, gave fair agreement with experiment
in some cases, in others the excitation threshold agreement
between experiment and theory was quite poor. Bouchiha
et al. suggested that using larger basis sets and more exact
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144302-3 Electron excitation of tetrahydrofuran J. Chem. Phys. 134, 144302 (2011)
configuration interaction models would correct these prob-
lems, but at the cost of having a much more computationally
expensive calculation to run.
Giuliani et al.
23
published a detailed study of the ground
and excited electronic states of both neutral THF and its
cation. We note that this work employed state-of-the-art theo-
retical and experimental methods. In particular, their photoab-
sorption spectra, which may be the highest resolution spectra
currently available (0.075 nm), showed excellent agreement
with their ab initio calculations and with some of the previ-
ously published data. In addition, they were able to resolve
several controversies in regard to the spectroscopy of THF.
Of particular importance to this study, they clearly observed
the lowest-energy excited electronic states distributing them-
selves into three distinct bands, which we now discuss in more
detail. Note that this result was in excellent agreement with
the work of Bremner et al.
24
The first band, covering the energy range of 6.04–
6.88 eV, was also found to be in very good agreement with
the results from the Davidson et al.
41
study. This band, peak-
ing at around 6.6 eV, appears to contain significant struc-
ture at high resolution and was assigned by Giuliani et al.
as being primarily due to the excitation of 3s-type Rydberg
states. The transitions giving rise to this band were assigned
by them
23
for both the C
2
and C
s
conformers, with the ver-
tical excitation energy for the lowest 3s (C
s
) transition being
estimated to be at 6.353 eV. The second band, with a peak at
7.15 eV, contains features that originate mainly from the
excitation of the 3p Rydberg terms. This band also, at high
resolution, contains numerous structures in the photoabsorp-
tion spectrum due to the excitation of the 3p states and their
associated vibrational sublevels. Note that here the vertical
excitation energy for the lowest 3p (C
s
) transition is at around
7.154 eV. The 3d Rydberg terms, spanning from about 7.40–
8.15 eV, contribute to both the second and third bands. For
instance, a prominent feature in the measured photoabsorp-
tion spectrum at 7.483 eV, i.e., in the second band, is in fair
agreement with the theoretical value (7.474 eV) for the excita-
tion of the lowest 3d (C
2
) state.
23
The third band also contains
many structures when measured at high resolution, with sharp
features observed at 7.730, 7.813, and 7.973 eV. The two most
intense of these features, at 7.730 and 7.813 eV, match quite
well with the predicted transition energies for the excitation of
two 3d (C
2
) states at 7.715 and 7.754 eV. For a more complete
description of the states in each band, and also for their entire
experimental and theoretical findings, please consult Giuliani
et al.
We consider that the study of Giuliani et al.
23
currently
provides the most thorough description for the electronic-
state spectroscopy of THF. This work clearly illustrates why
it would be folly for us, with our energy resolution (see
Sec. III), to try and assign flux and ultimately cross sections
to any individual excited electronic state. Rather, we follow
their lead and attempt to interpret our EELS results in terms
of three bands (which we call band 1, band 2, and band 3)
of Rydberg excited states. The first band is composed of 3s
Rydberg terms, while the second and third bands contain a
mixture of 3p and 3d type Rydberg terms. These bands are
illustrated on a series of typical energy-loss spectra, from the
present investigation, in Fig. 1. Plots such as this are very im-
portant in charged-particle-track studies,
14
as they determine
the energy deposition for the kinematical conditions specified.
Using the results of Giuliani et al. we perform a spectral de-
convolution on each of our measured energy-loss spectra, see
Sec. III for those details, from which the DCSs for the band
1, band 2, and band 3 of Rydberg states are ultimately de-
termined. Those results are presented and discussed later in
Sec. IV.
III. EXPERIMENTAL METHODS AND ANALYSIS
DETAILS
A high-resolution electron monochromator, described
originally by Brunger and Teubner,
42
was employed to make
the measurements. Here a beam of high-purity THF (Aldrich,
stated purity >99.99%), effusing from a molybdenum tube of
0.6 mm internal diameter, is crossed with a beam of pseu-
domonoenergetic electrons of desired energy E
0
. Elastically
and inelastically scattered electrons at a particular scattering
angle are energy analyzed and detected. The overall energy
resolution of the monochromator for these experiments was
50–60 meV (full width at half maximum) and, under nor-
mal operating conditions, incident electron beam currents of
2nA were obtained in the interaction region for the energy
range of these measurements. As in previous work,
42
the true
zero scattering angle was determined as that about which the
elastic scattering intensity was symmetric. The estimated er-
ror in this determination was ±1
. The electron energy scale
was calibrated against the well-known helium
2
S resonance
at 19.367 eV (Ref. 43) and is estimated to be accurate to less
than 50 meV.
At each incident energy in the range E
0
= 15 50 eV,
energy-loss spectra, at each scattering angle in the range
θ = 15 90
, were recorded over the range of 0.5 11 eV.
Typical spectra (with the background having already been
subtracted) are shown in Fig. 1, where the three bands of Ry-
dberg states we wish to study are also denoted. It is inter-
esting that these three bands become somewhat less distinct
as the scattered electron angle increases, possibly suggest-
ing that the excitation of some triplet valence states is also
occurring. While this hypothesis, in the absence of theory,
remains speculative, it is consistent to some extent with the
work of Bremner et al.
24
who suggested that valence states
might exist in this energy-loss region. The energy-loss spec-
tra were obtained by ramping the analyzer in an energy-loss
mode in conjunction with a multichannel scalar (TN-7200),
which stored the scattered signal as a function of energy loss.
The data were then transferred to a 433 MHz workstation for
analysis. Each spectrum was then analyzed (deconvolved) by
a computer least squares fitting technique that is similar in
detail to that outlined by Nickel et al.,
44
although adapted to
accommodate the particular spectroscopy of THF.
23, 24
In par-
ticular, the Rydberg band profiles’ shapes and widths, as well
as the energy-loss value of the respective band maxima, were
all gleaned and fixed as much as possible from the work of
Giuliani et al.
23
In practice, the fitting procedure yielded the
ratio (R) of the DCS for the Rydberg band of interest (band
1, band 2, or band 3, n
in general), σ
n
(E
0
), to that for the
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144302-4 Do
et al.
J. Chem. Phys. 134, 144302 (2011)
0
2 10
4
4 10
4
6 10
4
8 10
4
1 10
5
1.2 10
5
1.4 10
5
1.6 10
5
024681012
E
o
= 20eV,
θ
= 20
o
Intensity (arb. units)
Electron energy loss (eV)
Elastic peak
0
50
100
246810
0
2 10
4
4 10
4
6 10
4
8 10
4
1 10
5
024681012
E
o
= 20eV,
θ
= 50
o
Intensity (arb. units)
Electron energy loss (eV)
Elastic peak
Vibrational peaks
0
20
40
60
80
100
120
140
160
246810
0
1 10
4
2 10
4
3 10
4
4 10
4
5 10
4
6 10
4
7 10
4
8 10
4
024681012
E
o
= 20eV,
θ
= 80
o
Intensity (arb. units)
Electron ener
g
y loss (eV)
Elastic peak
Vibrational peaks
0
20
40
60
80
100
120
140
160
246810
Band 1
Band 2
Band 3
Band 1
Band 2
Band 3
Band 1
Band 2
Band 3
FIG. 1. Typical electron energy loss spectra for 20 eV electrons scattering from THF, obtained at a variety of kinematical conditions as denoted on the plots.
The spectra are very complicated with many overlapping Rydberg terms. Different scales were employed to highlight the differences in the peak heights, of the
various components in these spectra, which vary with the kinematical conditions under study. The three main bands of Rydberg terms that we study are also
denoted on this figure.
elastic DCS, σ
0
(E
0
). That is,
R
n
(E
0
) =
σ
n
(E
0
)
σ
0
(E
0
)
. (1)
It is immediately apparent from Eq. (1) that the product
R
n
(E
0
) × σ
0
(E
0
) then gives the required Rydberg elec-
tronic band DCS provided σ
0
(E
0
) is known. In the present
study our preferred elastic THF differential cross sections are
those obtained by Colyer et al.
19
Equation (1) is only valid if
the transmission efficiency of the analyzer remains constant
over the energy loss and the angular range studied, or is at
least well characterized. In this work we determine the behav-
ior of the analyzer response function following the philosophy
outlined by Allan.
45
Particular attention to the identification and quantifica-
tion of all possible sources of error has been made through-
out these measurements, with a general discussion of these
sources of error being found in the work of Brunger and
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Abstract: This work provides the first cross section data set of DNA constituents for an impact of electrons in the energy range between about 10 eV and 1 keV on a DNA target. The data set is designed for an implementation in Monte Carlo simulations and consists of model functions, taking into account elastic scattering, ionization and excitation interactions with the DNA constituents tetrahydrofuran, trimethylphosphate, pyrimidine and purine. It was developed on the basis of experimentally determined absolute differential and total scattering cross sections in accordance with the available literature data. The data set will be available in the Geant4-DNA toolkit to allow secondary electron transport in a DNA-like medium down to the ionization threshold.

43 citations


References
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Journal ArticleDOI
Ranbir Singh1, B. M. Deb1Institutions (1)

2,761 citations


Journal ArticleDOI
03 Mar 2000-Science
TL;DR: It is shown that reactions of such electrons, even at energies well below ionization thresholds, induce substantial yields of single- and double-strand breaks in DNA, which are caused by rapid decays of transient molecular resonances localized on the DNA's basic components.
Abstract: Most of the energy deposited in cells by ionizing radiation is channeled into the production of abundant free secondary electrons with ballistic energies between 1 and 20 electron volts. Here it is shown that reactions of such electrons, even at energies well below ionization thresholds, induce substantial yields of single- and double-strand breaks in DNA, which are caused by rapid decays of transient molecular resonances localized on the DNA's basic components. This finding presents a fundamental challenge to the traditional notion that genotoxic damage by secondary electrons can only occur at energies above the onset of ionization, or upon solvation when they become a slowly reacting chemical species.

1,756 citations


Journal ArticleDOI
TL;DR: It is shown that below 15 eV such low-energy electrons induce single (SSB) and double (DSB) strand breaks in plasmid DNA exclusively via formation and decay of molecular resonances involving DNA components (base, sugar, hydration water, etc.).
Abstract: Nonthermal secondary electrons with initial kinetic energies below 100 eV are an abundant transient species created in irradiated cells and thermalize within picoseconds through successive multiple energy loss events. Here we show that below 15 eV such low-energy electrons induce single (SSB) and double (DSB) strand breaks in plasmid DNA exclusively via formation and decay of molecular resonances involving DNA components (base, sugar, hydration water, etc.). Furthermore, the strand break quantum yields (per incident electron) due to resonances occur with intensities similar to those that appear between 25 and 100 eV electron energy, where nonresonant mechanisms related to excitation/ionizations/dissociations are shown to dominate the yields, although with some contribution from multiple scattering electron energy loss events. We also present the first measurements of the electron energy dependence of multiple double strand breaks (MDSB) induced in DNA by electrons with energies below 100 eV. Unlike the SSB and DSB yields, which remain relatively constant above 25 eV, the MDSB yields show a strong monotonic increase above 30 eV, however with intensities at least 1 order of magnitude smaller than the combined SSB and DSB yields. The observation of MDSB above 30 eV is attributed to strand break clusters (nano-tracks) involving multiple successive interactions of one single electron at sites that are distant in primary sequence along the DNA double strand, but are in close contact; such regions exist in supercoiled DNA (as well as cellular DNA) where the double helix crosses itself or is in close proximity to another part of the same DNA molecule.

343 citations


Journal ArticleDOI
01 Nov 1992-Medical Physics
TL;DR: It is proposed to carry out radiotherapy and radiosurgery for brain lesions by crossfiring an array of parallel, closely spaced microbeams of synchrotron-generated x rays several times through an i-modelling system.
Abstract: It is proposed to carry out radiotherapy and radiosurgery for brain lesions by crossfiring an array of parallel, closely spaced microbeams of synchrotron-generated x rays several times through an isocentric target, each microbeam in the array having an approximately 25-microns-wide adjustable-height rectangular cross section. The following inferences from the known tissue sparing of 22-MeV deuteron microbeams in the mouse brain and the following exemplary Monte Carlo computations indicate that endothelial cells in the brain that are lethally irradiated by any microbeam in an array of adequately spaced microbeams outside an isocentric target will be replaced by endothelial cells regenerated from microscopically contiguous, minimally irradiated endothelium in intermicrobeam segments of brain vasculature. Endothelial regeneration will prevent necrosis of the nontargeted parenchymal tissue. However, neoplastic and/or nonneoplastic targeted tissues at the isocenter will be so severely depleted of potentially mitotic endothelial and parenchymal cells by multiple overlapping microbeams that necrosis will ensue. The Monte Carlo computations simulate microbeam irradiations of a 16-cm diameter, 16-cm-long cylindrical human head phantom using 50-, 100-, and 150-keV monochromatic x rays.

244 citations


Journal ArticleDOI
Abstract: Procedures and calibration techniques for measuring the absolute elastic and inelastic differential cross sections (DCS) for electron impact on molecular (atomic) species are described and illustrated by examples. The elastic DCS for the molecule under study is first determined by calibration against helium using the relative flow technique. The second step involves the production of energy-loss spectra for the instrument response function, the unfolding of overlapping inelastic structures and the normalization of inelastic intensities to the elastic cross sections. It is concluded that this method of determining absolute differential electron-molecule (atom) scattering cross sections is generally applicable and provides reliable results.

164 citations


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