Self-Consistent Perturbation of Hartree-Fock-Bogoliubov Equations and Nuclear Rotational Spectra. I

Abstract

The effect of a single-particle perturbation on the Hartree-Fock-Bogoliubov equations is considered. Corrections to the ground-state wave function, density matrix, and pairing tensor are obtained through third order, thus determining the energy through fourth order. The results are applied to rotational spectra of even-even atomic nuclei, in which the nucleons interact via pairing and quadrupole forces, and the single-particle perturbation is the Coriolis force in a rotating frame of reference. The energy levels of the ground-state band are obtained to order $I^2{\mathrm{}(I+1\mathrm{})\mathrm{}}^2$ in the angular momentum. It is shown that the coefficient of the $I^2{\mathrm{}(I+1\mathrm{})\mathrm{}}^2$ term contains contributions arising from centrifugal stretching of the self-consistent quadrupole field, and having the expected form of a rotation-vibration interaction. In addition, however, the coefficient contains terms arising from the Coriolis unpairing effect and also terms arising from the influence of the Coriolis force on independent quasiparticle motion. Approximate numerical estimates indicate that the contribution from the Coriolis unpairing is far greater than from the beta vibration-rotation interaction.