Eigenfunctions for Integer and Half-Odd Integer Values of <i>J</i> Symmetrized According to the Icosahedral Group and the Group <i>C</i>3<i>v</i>

Abstract

Eigenfunctions of J2 for J=0, ½, 1···8, have been obtained and tabulated which are symmetrized according to the icosahedral group and the group C3v, in terms of eigenfunctions of J2 and Jz, referred to a fivefold axis of rotation as the z axis. The functions are symmetrized according to C3v in such a way that the symmetry operation of a 2π/3 rotation is represented by a diagonal matrix. The results have been applied to calculate the anisotropic magnetic splitting factors for the doublet states arising from the above symmetry.