Complete Numerical Solution of Bohr's Collective Hamiltonian

摘要

The general form of Bohr's collective Hamiltonian for quadrupole deformations is reviewed. It contains seven largely arbitrary functions of beta and gamma, 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 Schrodinger equation. A purely numerical method involving a finite mesh is developed for solving this Schrodinger 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 beta and gamma. 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. (Author)