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

V Encuentro Sud Americano de Colisiones Inelásticas en la Materia
Ab-Initio Sturmian method for three-body quantum mechanical problems:
Scattering states and ionizing collisions
A. L. Frapiccini 1 , 5 , J. M. Randazzo 1 , 5 ,
G. Gasaneo 2 , 5 , F. D. Colavecchia 1 , 5 , D. M. Mitnik 3 , 5 and L. U. Ancarani 4
1 División de Colisiones Atómicas, Centro atómico Bariloche, San Carlos de Bariloche, Río Negro, Argentina.
2 Depto. de Física, Universidad Nacional del Sur, Bahía Blanca, Buenos Aires, Argentina
3 Instituto de Astronomía y Física del Espacio and Departamento de Física, Facultad de Ciencias Exactas y Naturales,
Universidad de Buenos Aires C.C. 67, Suc. 28, (C1428EGA) Buenos Aires, Argentina.
4 Laboratoire de Physique Moléculaire et des Collisions,Université Paul Verlaine-Metz, 57078 Metz, France.
5 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).
email address corresponding author: randazzo@cab.cnea.gov.ar
In this work we present the general theory to
compute scattering states with a novel abinitio
method[1] based on generalized Sturmians.
These functions are solutions of a
radial Schrödinger equation where the magnitude
of a generating potential is assumed
as the eigenvalue, while the energy is a parameter
of the calculation. These Sturmians
are versatile enough to include almost any
arbitrary (atomic) asymptotic conditions in
the radial electron coordinates, such as the
outgoing flux conditions for Coulomb potentials
which are the adequate ones for
atomic collisions. The full three body
Schrödinger equation is solved with a Configuration
Interaction expansion of the wave
function in these generalized Sturmians. The
basis set is used to expand the scattering
portion of the total wave function, which
evolves from a separable state composed by
a plane wave and the ground hydrogen state.
By means of the Galerkin method, a linear
system of equations is obtained for the expansion's
coefficients. We show that the
scattering wave function has the appropriate
outgoing behaviour in the radial hyper
spherical coordinate.
Single differential cross section for the simple
problem of atomic ionization by electronic
impact in the S-wave model is presented
(see Fig. 1). Our results of the cross
sections at 55 and 54.4 eV incident energy
present an excellent agreement compared to
Exterior Complex Scaling results[2] and
Time dependent calculations from M. S.
Pindzola and F. Robicheaux [3].
Figure 1. Single differential cross section for single
electron-atom ionization in the Temkin-Poet model
with different theoretical methods (E=54.4 eV).
Acknowledgements
This work has been supported by PICT 08/0934
of ANPCYT (Argentina), PIP 200901/552 of
Conicet (Argentina), and PGI 24/F049, Universidad
Nacional del Sur (Argentina).
References
[1] A. L. Frapiccini, J. M. Randazzo, F. D.
Colavecchia and G. Gasaneo, J. Phys. B: At.
Mol. Opt. Phys. 101001 43 (2010).
[2] C. W. McCurdy and T. N. Rescigno, Phys.
Rev. A 56, R4369 (1997).
[3] M. S. Pindzola and F. Robicheaux, Phys.
Rev. A 55, 4617 (1997).
84 Valparaíso, Chile