Solution of Bohr Hamiltonian with Application to High Spin States

Abstract

<p>The structure of rare earth nuclei in high spin states is investigated using two collective models. The first model is a generalization of the Variable Moment of Inertia model to allow for axially asymmetric deformation. This model predicts that at sufficiently high spin, the nucleus will minimize its rotational energy by changing from an axially symmetric to an axially asymmetric shape. This sudden shape change can cause a phenomenon described as "backbending". This model also provides a natural explanation for the phenomenon of "forking" as observed in Ba^126 and Os^186.</p> <p>The second model investigated is the quadrupole collective model of Bohr and Mottelson. The Schroedinger equation with the Bohr-Mottelson Hamiltonian is solved numerically for states with angular momentum as high as 20 h. The method is valid for arbitrary collective potential energy and arbitrary inertial functions. The method involves converting the partial differential equation into a matrix eigenvalue equation using finite difference techniques. The resulting Hamiltonian matrix is diagonalized using the Lanczos algorithm. The results confirm the prediction of the previous model that backbending can result from a shape change. E2 transition rates are calculated and found to agree with rigid rotor estimates to within a factor of 2.</p> <p>The method of solution of the Bohr-Mottelson Hamiltonian is extended to add particle nuclei. It is found that the B representations of the D2 group are likely to be of physical importance in odd-even nuclei, a result which appears never to have been considered before.</p>