Predictions of microscopic and conventional CRMs for light nuclei

The conventional cranking model (CCRM3) uses a constant angular velocity. To study the effect of a microscopic angular velocity on the model-predicted results, a quantal, microscopic cranking model Hamiltonian for triaxial rotation (MSCRM3) is derived from the action of a microscopic rotation operator on a deformed nuclear state using Hartree-Fock method. This derivation is exact. MSCRM3 and CCRM3 Hamiltonians have identical forms (hence MSCRM3 and CCRM3 are equally easy to use), but MSCRM3 includes residual correction terms, and uses a dynamic angular velocity, hence it is time-reversal and D₂ invariant. For a self-consistent deformed harmonic oscillator potential, MSCRM3 and CCRM3 equations are determined in closed algebraic forms using Feynman’s theorem and solved iteratively. The two cranking models are used to investigate the stability of nuclear rotational states, nuclear shapes, rotation modes and their transitions, and the differences between these predictions in some light nuclei. The impact of spin-orbit and residuals of the square of the angular momentum and a two-body interaction is studied. It is shown that MSCRM3 predicts rotational relaxation of the intrinsic system, triaxial rotation, inherent instability of the cranked rotational states, rotational-band termination on spherical symmetry, the observed reduced rotational-energy-level spacing in ²⁰Ne, whereas CCRM3 does not. In some cases, MSCRM3 predicts rotations and band terminations whereas CCRM3 does not, and vice versa.