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A microscopic time-reversal invariant cranking model (MCRM) for nuclearcollective rotation about a single axis and its coupling to intrinsic motion isderived. The MCRM is derived by transforming the stationary nuclear Schrodingerequation using a collective rotation-intrinsic product wavefunction, imposingno constraints on the wavefunction and the nucleon coordinates, and using norelative co-ordinates. The derivatives of the collective-rotation angle aredefined in terms of a combination of rigid and irrotational collective flows ofthe nucleons. The collective wavefunction is chosen to be an eigenstate of theangular momentum, yielding a MCRM Schrodinger equation for the intrinsicwavefunction that contains a cranking Coriolis energy term that is linear inthe angular momentum and shear operators, a collective centrifugal energy term,and a rotation-fluctuation energy term. In absence of the irrotational-flowcomponent and fluctuation energy term, the MCRM equation reduces to that of theconventional cranking model (CCRM), but with a dynamic rigid-flow angularvelocity and rigid-flow centrifugal-energy term. The expectation of the angularmomentum operator, which is the sum of the collective rotation angular momentumand the expectation of the angular momentum in the intrinsic state, wouldreduce to that in the CCRM if the collective rotation angular momentum weresmall. However, it is shown that, even for the simple case of the anisotropicharmonic oscillator mean-field potential in , the collective rotation angularmomentum is not small in the current version of the MCRM, and that this problemneeds further study. It is also shown that the MCRM Schrodinger equation isreducible to the equations of the particle-plus-rotor, phenomenological andmicroscopic collective rotation-vibration, and two-fluid semi-classicalcollective models.

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