Generalized projection operators for intrinsic rotation groups and nuclear collective models

Abstract

A general collective orthogonal basis combining the zero-phonon and one-phonon excitations in the quadrupole and octupole modes together with rotational motion is constructed in order to allow diagonalization of quadrupole-octupole-rotational collective Hamiltonians in the future. Such a collective approach would enable one to search for the fingerprints of the high-rank symmetries (e.g. octahedral, tetrahedral, …) in nuclear bands. This task could be performed by considering, e.g., the inter-band and intra-band electromagnetic reduced transition probabilities λ ( )B E within the eigensolutions of these Hamiltonians.

Finite Element Method for Solving the Collective Nuclear Model with Tetrahedral Symmetry

“…A realistic collective Hamiltonian with variable mass-parameter tensor and potential obtained through the macroscopic-microscopic Strutinsky-like method with particle-number-projected BCS approach in full vibrational and rotational, nine-dimensional collective space was diagonalized in the basis of projected harmonic oscillator eigensolutions. In this approach the symmetrized orthogonal basis of zero-, one-, two-and three-phonon oscillatorlike functions in vibrational part, coupled with the corresponding Wigner function [3] has been applied for solving the boundary value problem (BVP) in 6D domain. The algorithms for construction the symmetrized basis was considered in [4,5] w.r.t.…”