Testing the hyperspherical Sturmian approach for break up processes: an analytically solvable model

G. GASANEO, D.M. MITNIK, L.U. ANCARANI, F.D. COLAVECCHIA, A.L. FRAPICCINI, AND J.M. RANDAZZO

Salamanca

Conferencia; 10th European Conference on Atoms, Molecules and Photons; 2010

ECAMP

In this contribution we present a spectral method to study the dynamics of a three-body collision break up process. By expressing the wave function of the system as a sum of a scattered wave function and a known initial state, a non-homogeneous Schrödinger equation is derived [1,2]. The scattering term is expanded with a basis of Sturmian functions. Two types of basis sets are used: (i) product of functions of the interparticle coordinates [1] and (ii) product of hyperspherical Sturmians functions [2]. Both basis sets explicitly include continuum asymptotic boundary conditions, and are the eigenvectors of a two-body problem where the magnitude of a potential is taken as the eigenvalue [2,3]. The basis representation of the initial and scattering wave functions allow for a transformation of the non-homogeneous Schrödinger equation into an algebraic problem which is solved with standard matrix techniques.