Bohr Hamiltonian with a deformation-dependent mass term: physical meaning of the free parameter

TL;DR

This paper explores how the deformation-dependent mass in the Bohr Hamiltonian relates to the curvature of the underlying 5D space and connects this to the classical limits of the interacting boson model, revealing the physical meaning of the free parameter.

Contribution

It establishes a geometric interpretation of the deformation-dependent mass parameter as the curvature of the 5D space and links it to specific nuclear interactions in the IBM.

Findings

The free parameter is linked to the curvature of the 5D space.

The DDM parameter correlates with pairing and quadrupole interactions in IBM.

Curved 5D space arises from nuclear interactions, contrasting with flat space in the original model.

Abstract

Embedding of the 5-dimensional (5D) space of the Bohr Hamiltonian with a deformation-dependent mass (DDM) into a 6-dimensional (6D) space shows that the free parameter in the dependence of the mass on the deformation is connected to the curvature of the 5D space, with the special case of constant mass corresponding to a flat 5D space. Comparison of the DDM Bohr Hamiltonian to the 5D classical limit of Hamiltonians of the 6D interacting boson model (IBM), shows that the DDM parameter is proportional to the strength of the pairing interaction in the U(5) (vibrational) symmetry limit, while it is proportional to the quadrupole-quadrupole interaction in the SU(3) (rotational) symmetry limit, and to the difference of the pairing interactions among s, d bosons and d bosons alone in the O(6) (gamma-soft) limit. The presence of these interactions leads to a curved 5D space in the classical limit of IBM, in contrast to the flat 5D space of the original Bohr Hamiltonian, which is made curved by the introduction of the deformation-dependent mass.