NONINTEGRAL EXPANSION METHOD OF F(R)Y-L(M)(THETA,PHI) FUNCTIONS ABOUTA DISPLACED CENTER

The transformation properties of f(R)Y-M(M)(Theta,Phi) functions under translation of the reference system along the z axis, apart from thos e in relation to rotation of the system, have to be known to formulate the effective one-electron crystal held hamiltonian. The classical so lution of the problem for a general radial function f(R) in the form o f expansion into the spherical harmonic series has been given by Sharm a in 1976. Another method avoiding integration but making use of the s imple translational behaviour of the multipole functions R(-(L+1))Y-L( M)(Theta,Phi), and reduction of the Kronecker products of spherical ha rmonics, is presented. The method allows one to find the expansion of the f(R)Y-L(M)(Theta,Phi) function by means of the 3-j symbols only. T he method is applicable to a wide class of radial functions which can be expanded into a power series. Moreover, in the case of crystal fiel d potential, it gives a clear survey of the contributions of each loca l potential moment to the crystal field parameters.