Properties of universal functions in the Wigner mass formula for nuclei

The properties of the empirical functions in the Wigner mass formula for nuclei, which is based on SU(4) spin-isospin symmetry, are considered. It is shown that the origin of the odd-even effect in nuclei can be explained on the basis of an explicit analytic form of the second-degree Casimir operator for even-even and odd-odd nuclides and for nuclei of odd mass number. Experimental data in support of the proposed Wigner origin of the odd-even effect are presented.