Complete numerical solution of Bohr's collective Hamiltonian

Abstract

The general form of Bohr's collective Hamiltonian for quadrupole deformations is reviewed. It contains seven largely arbitrary functions of β and γ, the potential energy and six inertial functions. A thorough discussion is given of the symmetries of these seven functions and of the corresponding properties of the solutions of the Schrödinger equation. A purely numerical method involving a finite mesh is developed for solving this Schrödinger equation. The output of the calculation consists in the low-lying levels, the corresponding wave functions and the relevant E2 and M1 static and transition moments; the latter depend on the intrinsic quadrupole moments and intrinsic gyromagnetic ratios as functions of β and γ. The numerical method is tested on a number of examples and is found to be sufficiently accurate for application to spherical, transition and many deformed nuclei.