Aca - Departamento de Física - Universidad Técnica Federico Santa ...

V Encuentro Sud Americano de Colisiones Inelásticas en la Materia
LPA stopping power of swift ions in solids. Modeling the inhomogeneous
electron gas
J. M. Fernández-Varea 1 , C. D. Denton 2 , I. Abril 2 and R. Garcia-Molina 3
1
Facultat de Física (ECM and ICC), Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
2
Departament de Física Aplicada, Universitat d’Alacant, Apartat 99, E-03080 Alacant, Spain
3
Departamento de Física-CIOyN, Universidad de Murcia, Apartado 4021, E-30080 Murcia, Spain
email address corresponding author: jose@ecm.ub.es
The stopping of swift ions in solids is
still a subject of intense research in spite of
the many decades elapsed since the pioneering
works of Bohr, Bethe and others. There
are numerous theories that describe the energy
loss of a heavy charged particle (charge
Z 1 , velocity v) in a free-electron gas (FEG) of
uniform density ρ, such as the dielectric
formalism or non-linear methods [1,2]. If the
projectile penetrates a medium with a varying
local electron density, e.g. a crystalline solid,
the local-plasma approximation (LPA) lets us
express the stopping power as
where V is the volume of the unit cell.
We find it convenient to split ρ(r) into
contributions from atomic inner shells (cores)
and weakly-bound (valence) electrons, i.e.
difficult to implement. As an alternative, the ab
initio TB-LMTO method [4,5] has been used occasionally
to model the stopping of swift ions in
channeling conditions [6].
In the present work, Roothaan-Hartree-
Fock wave function [7] are employed to model
the electron density of the cores. In turn, the
program TB-LMTO-ASA [4,5] is adopted to
generate the 3D valence-electron densities.
These methods are used to calculate the electron
densities of solid Al, Si, Cu, Ag, and Au.
In order to avoid computing the LPA
stopping power due to valence electrons as a 3D
integral, the probability distribution function
p(ρ v ) is first extracted from ρ v (r) because then
Figure 1 shows the p(ρ v ) distributions of solid
Al, Si, and Cu.
Neglecting the overlap between the two electron
densities, the LPA stopping power may
be written as
Electrons in the cores are barely disturbed by the
solid-state environment. Hence, the corresponding
density is spherically symmetrical and can
be evaluated straightforwardly using atomic
wave functions. On the other hand, the spatial
distribution of valence electrons is strongly affected
by aggregation effects. and may display a
non-negligible anisotropy. The 3D electron
density can be calculated with the Dawson-
Stewart-Coppens formalism. However, so far
this method has found only limited application
(see e.g. reference [3]), possibly because it is
Figure 1. Probability distribution function
p(ρ v ) of solid Al, Si, and Cu, extracted from the
3D valence-electron densities calculated with the
TB-LMTO-ASA program.
44 Valparaíso, Chile