Foundations of self-consistent particle-rotor models and of self-consistent cranking models

Abstract

The Kerman-Klein formulation of the equations of motion for a nuclear shell model and its associated variational principle are reviewed briefly. It is then applied to the derivation of the self-consistent particle-rotor model and of the self-consistent cranking model, for both axially symmetric and triaxial nuclei. Two derivations of the particle-rotor model are given. One of these is of a form that lends itself to an expansion of the result in powers of the ratio of single-particle angular momentum to collective angular momentum, that is essentual to reach the cranking limit. The derivation also requires a distinct, angular-momentum violating, step. The structure of the result implies the possibility of tilted-axis cranking for the axial case and full three-dimensional cranking for the triaxial one. The final equations remain number conserving. In an appendix, the Kerman-Klein method is developed in more detail, and the outlines of several algorithms for obtaining solutions of the associated non-linear formalism are suggested.

29 pages

References in corpus (8)

• Generalized quantum dynamics
• Calculation of the properties of the rotational bands of ${}^{155,157}$Gd
• Possible solution of the Coriolis attenuation problem
• From Heisenberg matrix mechanics to EBK quantization: theory and first applications
• Further application of a semi-microscopic core-particle coupling method to the properties of Gd155,157, and Dy159
• Derivation and assessment of strong coupling core-particle model from the Kerman-Klein-Dönau-Frauendorf theory
• Application of a semi-microscopic core-particle coupling method to the backbending in odd deformed nuclei
• Application of the Kerman-Klein method to the solution of a spherical shell model for a deformed rare-earth nucleus

Cited by in corpus (6)

• Chiral bands for quasi-proton and quasi-neutron coupling with a triaxial rotor
• Open Problems in Understanding the Nuclear Chirality
• Specific features and symmetries for magnetic and chiral bands in nuclei
• Microscopic core-quasiparticle coupling model for spectroscopy of odd-mass nuclei
• Triaxiality explored by an odd quasi-particle
• Kerman-Klein-Donau-Frauendorf model for odd-odd nuclei: formal theory