Microscopic description of high-spin states: Quantum-number projections of the cranked Hartree-Fock-Bogoliubov self-consistent solution

Quantum-number projection is applied to generate exact eigenstates of angular momentum or of particle numbers from the self-consistent solution of the angular-momentum- and particle-number-constrained Hartree-Fock-Bogoliubov (CHFB) equation. Calculations are based on the symmetry-conserving microscopic Hamiltonian and the large single-particle space spanned by spherical Nilsson bases covering about 1.5 major shells for both protons and neutrons in the case of the yrast bands for ${}^{158,164,168}\mathrm{Er}$ and almost three major shells in the case of the superdeformed bands as well as g and s bands for ${}^{132}\mathrm{Ce}.$ The residual interaction is given by the monopole- and quadrupole-pairing interactions plus the quadrupole-quadrupole interaction. Symmetry properties of the Hamiltonian are fully taken into account through both stages of solving the CHFB equation and projections to reduce computational time substantially. A great mixture of angular momentum components requires the projection while particle-number projections become less important at high spins, especially along superdeformed bands with vanishingly small static gaps. It is shown that the angular momentum projection is effective to reproduce $K=0\mathrm{}$ superdeformed levels appearing in the yrast band together with the g and s bands.