Inertial Parameters for Collective Nuclear Oscillations

Abstract

Inertial parameters for nuclear rotation and quadrupole shape oscillation are known to be several times as large as the values assuming irrotational flow. These parameters may be calculated by using a method due to Inglis and applied in recent work by Bohr and Mottelson. The nucleus is assumed to be mainly in the lowest possible intrinsic state, but slightly perturbed by the time-dependence of the nuclear shape. It is convenient to separate the nuclear Hamiltonian into interactions of the individual nucleons with an average potential of the anisotropic harmonic oscillator type and residual interactions independent of deformation. Then the intrinsic motions of the nucleons must satisfy, at least approximately, self-consistency conditions between the potential and nuclear density. The nucleons outside closed shells are seen to contribute about half of the nuclear deformation. The excess of the inertial parameters over the irrotational values is related directly to the spread in energy of admixed excited states of the intrinsic motion, an essential consequence of the approximately independent motions of the nucleons.