IFISUR   23398
INSTITUTO DE FISICA DEL SUR
Unidad Ejecutora - UE
congresos y reuniones científicas
Título:
Three-body break-up model problem in hyperspherical coordinates: analytical and numerical solution
Autor/es:
ANCARANI L U, GASANEO G AND MITNIK D M,
Lugar:
Metz
Reunión:
Conferencia; French National Conference; 2012
Resumen:
An analytically solvable S?wave model for three particles break?up processes is presented.
The scattering process is represented by a non-homogeneous Coulombic Schr¨odinger equation
where the driven term is given by a Coulomb-like interaction multiplied by the
product of a continuum wave function and a bound state in the particles coordinates.
The closed form solution is derived in hyperspherical coordinates leading to an analytic
expression for the associated scattering transition amplitude. The proposed scattering
model contains most of the difficulties encountered in real three-body scattering problem,
e.g., non-separability in the electrons? spherical coordinates and Coulombic asymptotic
behavior. The knowledge of the analytical solution provides an interesting benchmark to
test numerical methods dealing with the double continuum, in particular in the asymptotic
regions.
An hyperspherical Sturmian approach recently developed [1, 2] for three?body
collisional problems is used to reproduce to high accuracy the analytical results.
In addition to this, we generalized the model generating an approximate wave function
possessing the correct radial asymptotic behavior corresponding to an S-wave three-body
Coulomb problem. The model allows us to explore the typical structure of the solution of
a three-body driven equation, to identify three regions (the driven, the Coulombic and the
asymptotic), and to analyze how far one has to go to extract the transition amplitude.