A Nilsson model for deformed phonons

Abstract

Vibrations of deformed even nuclei are treated as vibrations in the intrinsic system projected out into rotational bands in the laboratory. A vibrational quantum is viewed as a quantized surface ripple, with a good K but not J, in analogy to a nucleon in the Nilsson well. The intrinsic Hamiltonian is taken to be of the Bohr-Mottelson type, with the parameters B lm , C tm and β 0 defining the deformed field. The intrinsic problem is solved in terms of the phonons of the spherical field, first in perturbation theory and then exactly. The Bogoyubov-Valatin transformation for bosons is used in the latter. By the Peierls-Yoccoz projection method, the physical states are found as certain superpositions of spherical-phonon states with various phonon numbers. The present model reproduces the usual results of the Bohr-Mottelson model; in addition, it suggest a K = 1 quadrupole-vibrational band. Finally, the coherence, or collectivity, of the projected states is discussed in terms of the B(E2) value between the two lowest states. The expected qualitative behaviour is established. The B(E2) value increases as deformation sets in; slow convergence encumbers the study of large deformations. Altogether, the present work continues work continue the phonon descriptiopn of spherical nuclei to the permanently deformed ones; it forms a rather detailed examination of the long-alleged equivalence of deformation and vibration.