Spin symmetry and pseudospin symmetry in the relativistic mean field with a deformed potential

The equations for the pseudospin pair levels become of the same form as those of the spin pair levels at the limit where the derivatives of potentials are zero. However, the centrifugal terms of four amplitudes among eight components in the pseudospin pair levels have pseudo-l_z, while those in the spin pair-levels have natural l_z. When both of the pseudospin and spin symmetries are well satisfied, there appears a triple degeneracy. The relativistic mean-field calculation over ¹⁵⁴Sm gives [400]1/2, [402]3/2, and [402]5/2 levels as such a candidate. The relation between the deformed wave function and the spherical wave function are discussed at the spherical limit by using the transformation from the cylindrical coordinate into the polar coordinate.