The need for a velocity-dependent basis in microscopic heavy ion dynamics

Abstract

The inadequacy of the usally employed static basis for the expansion of the time-dependent wave function is demonstrated for heavy ion collisions and fisson beyond the scisson point. In a microscopic treatment of the kinetic energy of relative motion this energy is subject to large errors, which are due to the inevitable truncation of the static basis for the solution of the time-dependent Schrödinger equation. For moderate kinetic energies errors of about 50 % are found in a 1p 1h basis, corresponding to a first order (adiabatic) cranking approach. It is shown that the enlargement of the basis by an inclusion of higher excitations 2p2h,3p,3h etc.) does not offer a way out of these problems. Instead, the use of a “travelling” basis would remove the kinetic energy problem at large internuclear separations by proper plane wave translation factors. The problems arising from the use of this basis at smaller separations are discussed and possible solutions are proposed.