The global element method applied to a discontinuous nuclear potential

Abstract

A new variational technique, the Global Element Method (GEM), is applied to a well-known nuclear physics problem. The GEM enables the solution region to be divided into physically meaningful subregions and appropriate expansion functions to be used in each of these subregions. The continuity of the trial functions (and their derivatives) at the subregion interfaces, together with the prescribed boundary conditions is enforced by the variational principle. It is demonstrated that for the bound-state and scattering problems for a typical discontinuous nuclear potential, the GEM obtains significantly faster convergence rates than previous variational methods. Moreover this new approach will enable the major components of existing computer programs, using conventional global variational methods, to be reused after suitable modification. The GEM, with the possibility of high convergence rates, should hopefully prove to be a useful computational tool in many areas of computational physics.