A closer look at pseudo space-spin symmetry in atomic nuclei

A. L. Blokhin, Louisiana State University
T. Beuschel, Louisiana State University
J. P. Draayer, Louisiana State University


A procedure for applications of the pseudospin transformation within the framework of nuclear oscillator shell model is developed. It is valid for operators expressed in terms of single-particle variables and is based on permutation rules for special rotational invariants. The procedure is applied to a number of physical operators including several rotational scalars, the spin and orbital momenta, and the quadrupole moment. The validity of the pseudo-spin concept for triaxially deformed nuclei is also investigated by calculating the correlation coefficient of a generalized Nilsson model Hamiltonian and the pseudo spin-orbit interaction. This correlation coefficient, which is a normalized measure for the goodness of pseudo-spin symmetry, indicates that even though the near level degeneracy of pseudo spin-orbit partners for axially symmetric geometries (prolate and oblate) is lost in triaxial systems, the symmetry itself remains good.