A semiclassical, microscopic model for nuclear collective rotation

Abstract

In this article, a semiclassical, microscopic model (dubbed SMRM) is derived to describe collective rotation in deformed nuclei. The SMRM is derived by transforming the time-dependent, multiparticle Schrodinger equation to a rotating frame whose axes are chosen to coincide with the principal axes of the expectation value of an arbitrary, second-rank, symmetric, tensor (nuclear shape) operator [Formula: see text]. This transformation circumvents the difficulty associated with the introduction of redundant particle coordinates in the Villars' transformation. The SMRM Schrodinger equation, which resembles the cranking model (CM) equation, is a time-dependent, time-reversal-invariant, nonlinear integro-differential equation. In this equation, the angular velocity is determined by the wave function and deformation–rotation shear operators, and this introduces the nonlinearity in the equation. A variational method is proposed and justified to obtain: a stationary solution of the SMRM Schrodinger equation in the Rayleigh–Ritz Hartree–Fock particle–hole formalism, the rotational energy increment, and the associated moment of inertia. When exchange interaction terms are neglected or a separable interaction is used, the SMRM moment of inertia is shown to reduce to that given by the CM provided that a certain relationship exists between the moment of inertia and the expectation value of [Formula: see text]. However, the SMRM and CM wave functions are not the same (SMRM preserves and CM violates time-reversal invariance) implying that the calculated values of other parameters, including the moment of inertia at higher values of the angular momentum, may not be the same in the two models. In any case, the SMRM derives the CM moment of inertia from a microscopic, time-reversal invariant, nonlinear theory.PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz