Einzelteilchen-Berechnungen zur Kernspaltung

Abstract

We use an axial symmetric, energy-, spin-, and isospin-dependent shell model Hamiltonian to describe heavy deformed nuclei, where the equipotential surfaces are taken to be spheroids, corrected towards a more realistic nuclear shape by means of Legendre polynomials of maximal order four, and the potential is assumed to depend on the modified radial coordinate like a Fermi function. The eigenvalue problem is solved by a perturbation treatment which starts with the eigensolutions for purely spheroidal deformations as a first approximation. By analysis of an expression which involves the single particle energies for a given deformation, the sets of deformation parameters for the ground state and the transition point of a fissioning nucleus are found, and from them the total energy at the transition point is obtained. For Th²³¹, Th²³³, U²³⁵, U²³⁶ and U²³⁷ we give our results and compare them with measurements and liquid drop model calculations.