Spurious rotational states in deformed nuclear shell models

Abstract

A method for projecting spurious rotational states from many-particle nuclear wavefunctions is extended to wavefunctions generated by a deformed shell model of axial symmetry. For completeness, the projection procedure is reviewed [19]. According to this method the deformed shell model (SM) Hamiltonian is altered by a correction term such that the new Hamiltonian H = H SM − H corr is translation- and rotation-invariant, i.e., it depends only on intrinsic coordinates when it is transformed to a body-fixed system. The eigenfunction of H which are obtained by diagonalizing this Hamiltonian in the shell model basis separate into an intrinsic function and a collective factor depending on the center of mass coordinates and Euler angles. By identifying the spurious rotational states this set of functions can be made nonredundant so that the functions are a complete substitute for a set of realistic intrinsic functions. For shell models with axial symmetry we introduce only two Euler angles. It turns out that the intrinsic function is characterized by a good projection of the total angular momentum on the symmetry axis of the nucleus. Applications for the Ω π = 0 + , T = 0 bandheads of 20Ne are given and good agreement with the experimental spectrum is obtained. A study of the potential energy surface leads to the conclusion that it contains spurious rotational energies.