INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS
J. Phys. B: At. Mol. Opt. Phys. 37 (2004) 801–807 PII: S0953-4075(04)70780-4
Low-energy electron collisions with water: elastic and
rotationally inelastic scattering
A Faure1, J D Gorfinkiel2 and Jonathan Tennyson2
1 Laboratoire d’Astrophysique, Observatoire de Grenoble, BP 53,
38041 Grenoble Cedex 09, France
2 Department of Physics and Astronomy, University College London,
Gower Street, London WC1E 6BT, UK
Received 17 October 2003, in final form 16 December 2003
Published 30 January 2004
Online at stacks.iop.org/JPhysB/37/801 (DOI: 10.1088/0953-4075/37/4/007)
Abstract
Differential, integral and momentum transfer cross sections for the vibrationally
elastic and rotationally inelastic scattering of electrons from water at low
collision energies (E < 7 eV) are reported. The R-matrix method is used
to compute the body-fixed T-matrices while the scattering calculations are
performed within the fixed-nuclei approximation corrected with the standard
Born-closure formula. Our calculations are compared with the very recent
experimental results of Cho et al (2003 Radiat. Phys. Chem. 68 115). The
differential and momentum transfer cross sections are in good agreement with
the experimental results. The relative contribution of the rotationally inelastic
processes is investigated in some detail. In particular, the importance of the
pure elastic process at very low energy is emphasized.
1. Introduction
Water is an extremely important molecule: it is ubiquitous in the universe and fundamental
to life. Collisions of electrons with water molecules thus play an important role in a
variety of research fields such as astrophysics and atmospheric physics, radiation biology
and plasma physics. In the last two decades, these collisions have been studied extensively,
both experimentally and theoretically (for a review, see Mason and Itikawa (in preparation)).
In particular, differential cross sections (DCS) for the vibrationally elastic scattering have been
computed and measured by several authors for collision energies below 50 eV. Elastic DCS
of water indeed provide crucial parameters for modelling the radiation effects on biological
matter (e.g. Champion (2003)). The recent experimental paper by Cho et al (2003) gives
absolute DCS at four incident energies between 4 and 50 eV and over scattering angles of
10–180◦ measured with an original device to extend the measurements to backward angles. A
detailed comparison of this data with previous measurements and calculations shows general
0953-4075/04/040801+07$30.00 © 2004 IOP Publishing Ltd Printed in the UK 801

802 A Faure et al
good agreement among the experimental data up to 100◦. At higher angles, however, the
available data show very different behaviours. In particular, the results of Cho et al (2003)
are consistently lower than previous experimental DCS in the backward direction. The elastic
integral cross section (ICS) and the momentum transfer cross section (MTCS) were also
derived by Cho et al (2003) by extrapolating the DCS at the forward scattering angles that
are difficult to measure experimentally. As discussed by Okamoto et al (1993), such an
extrapolation procedure introduces rather large uncertainties because the large dipole moment
of water leads to heavily forward peaked cross sections. Reliable theoretical DCS for the
forward scattering are therefore highly desirable, as we shall further discuss below.
In this paper, we report differential, integral and momentum transfer cross sections for
vibrationally elastic electron scattering from water at collision energies below 7 eV. The water
molecule is described by an ab initio multicentred wavefunction using the R-matrix method
while the scattering calculations are performed within the fixed-nuclei (FN) approximation.
A comparison with the most recent experimental results is presented. The theoretical and
computational treatment is briefly introduced in the next section. Results are discussed in
section 3. Conclusions are summarized in section 4.
2. Theory
All calculations were performed using the electron–H2O wavefunctions developed by
Gorfinkiel et al (2002) who calculated cross sections for different molecular geometries
(see paper for full details). In this paper, the R-matrix calculations were performed at the
equilibrium geometry of H2O (rOH = 1.81 a0 and ĤOH = 104.5◦) using an R-matrix sphere
of radius 10 a0. The total wavefunction takes the form

k =
∑
ij
aijkφi(x1, . . . , xN)uij (xN+1) +
∑
i
bikχi(x1, . . . , xN+1), (1)
where φi are target wavefunctions, uij (x) are continuum orbitals and χi are two-centre
quadrically integrable (L2) functions constructed from the target occupied and virtual
molecular orbitals. These last functions are important both for relaxing the enforced
orthogonality between the target and continuum orbitals, and for representing short-range
polarization effects not included in the truncated partial wave expansion. The present scattering
model includes the seven lowest electronic states of water generated using a complete active
space configuration interaction (CASCI) procedure and averaged natural orbitals. This model
gives a dipole moment of 1.864 D, which can be compared with the experimental value of
1.854 D (Suresh and Naik 2000). The continuum orbitals were represented using the Gaussian-
type orbitals basis set developed by Faure et al (2002) which includes all angular momentum
up to l = 4 and is optimized to span energies below 68 eV.
Cross sections were calculated following the procedure implemented in the program
POLYDCS (Sanna and Gianturco 1998). The general theory of the scattering of an electron
from a polyatomic molecule in the fixed-nuclei (FN) approximation has been presented many
times before (see, for example, the review by Gianturco and Jain (1986)). In this approach,
the cross section is expressed as a partial-wave expansion within the adiabatic–nuclei–rotation
(ANR) approximation which assumes that the initial and final target states are degenerate
(Lane 1980). For low partial waves (here l
4), the cross section is computed from the FN
T-matrices obtained via the R-matrix calculations. In the case of a polar molecule, the partial-
wave expansion does not converge in the FN approximation, owing to the very long-range