P. Gulshani | Searcharxiv

arXiv2017

A microscopic rotational cranking model and its connection to conventional cranking and other collective rotational models

A microscopic time-reversal invariant cranking model (MCRM) for nuclear collective rotation about a single axis and its coupling to intrinsic motion is derived. The MCRM is derived by transforming the stationary nuclear Schrodinger equation using a collective rotation-intrinsic product wavefunction, imposing no constraints on the wavefunction and the nucleon coordinates, and using no relative co-ordinates. The derivatives of the collective-rotation angle are defined in terms of a combination of rigid and irrotational collective flows of the nucleons. The collective wavefunction is chosen to be an eigenstate of the angular momentum, yielding a MCRM Schrodinger equation for the intrinsic wavefunction that contains a cranking Coriolis energy term that is linear in the angular momentum and shear operators, a collective centrifugal energy term, and a rotation-fluctuation energy term. In absence of the irrotational-flow component and fluctuation energy term, the MCRM equation reduces to that of the conventional cranking model (CCRM), but with a dynamic rigid-flow angular velocity and rigid-flow centrifugal-energy term. The expectation of the angular momentum operator, which is the sum of the collective rotation angular momentum and the expectation of the angular momentum in the intrinsic state, would reduce to that in the CCRM if the collective rotation angular momentum were small. However, it is shown that, even for the simple case of the anisotropic harmonic oscillator mean-field potential in , the collective rotation angular momentum is not small in the current version of the MCRM, and that this problem needs further study. It is also shown that the MCRM Schrodinger equation is reducible to the equations of the particle-plus-rotor, phenomenological and microscopic collective rotation-vibration, and two-fluid semi-classical collective models.

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arXiv2014

Quantal self-consistent cranking model for monopole excitations in even-even light nuclei

In this article, we derive a quantal self-consistent time-reversal invariant parameter-free cranking model for isoscalar monopole excitation coupled to intrinsic motion in even-even light nuclei. The model uses a wavefunction that is a product of monopole and intrinsic wavefunctions and a constrained variational method to derive, from a many-particle Schrodinger equation, a pair of coupled self-consistent cranking-type Schrodinger equations for the monopole and intrinsic systems. The monopole co-ordinate used is the trace of the quadrupole tensor and hence describes the overall deformation of the nucleus. The monopole and intrinsic wavefunctions are coupled to each other by the two cranking equations and their associated parameters and by two constraints imposed on the intrinsic system. For an isotropic Nilsson shell model and an effective residual two-body interaction, the two coupled cranking equations are solved in the Tamm Dancoff approximation. The strength of the interaction is determined from a Hartree-Fock self-consistency argument. The excitation energy of the first excited state is determined and found to agree closely with those observed in the nuclei He-4, Be-8, C-12, O-16 , Ne-20, Mg-24, and Si-28. The variation of the model parameters are explained. In particular, it is found that the monopole excitation energy as a function of the mass number undergoes an increase whenever the nucleons begin to occupy a new sub-shell state with non-zero orbital angular momentum as a consequence of suppressing or constraining the resulting spurious monopole excitation in the intrinsic system.

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