Inertial Parameters for Collective Nuclear Oscillations

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.The inertial parameters are determined mainly by excitation of nucleons outside closed shells and they are inversely proportional to the square of the average excitation energy within a major shell. In summary, the nuclear collective motion appears to resemble the shell model situation more than was thought previously, especially as regards the dominant role of the nucleons outside filled shells.Empirical values of the inertial parameters are discussed in the light of these results, and a comparison is made with the recent analysis of Bohr and Mottelson. Anomalies in the empirical gyromagnetic ratios of rotational motion for odd-A nuclei result from the important role of the unpaired nucleon. With the aid of a simplified model in which the unfilled shell is assumed to be a p shell, it is possible to account qualitatively for a number of the observed features.