Gamow vectors as solutions of a non-hermitian eigenvalue problem

Abstract

Gamow vectors have been extensively used for describing resonance phenomena, but they do not belong to the usual Hilbert space. They can be obtained for a single channel potential by solving the Schrödinger equation with out-going boundary conditions. A new method for calculating Gamow vectors through the solution of a matrix eigenvalue problem is presented. The matrix to be diagonalized is real and non-symmetric, allowing the treatment of bound states and resonances on the same footing. The advantage of the method is to be equally applicable to the coupled channel problem when the standard procedure of solving the set of radial differential equations have the problem of denning the regular solution at the origin. Furthermore, the solution of the eigenvalue problem gives directly the Gamow momenta and vectors, thus avoiding the usual search in the complex momentum plane which can be rather cumbersome. Applications to single as well as coupled channel cases, both for model potentials and realistic nucleon-nucleon interaction, show great accuracy of the method.