Magnetic form factors of rare earth ions

Abstract

The magnetic scattering of neutrons by atoms has been investigated by exploiting its similarity to the radiation problem in spectroscopy. Expressions for the magnetic scattering amplitude have been developed for cases in which an atom in the l/sup n/ electronic configuration is described by a Hamiltonian. For each case, the magnetic scattering amplitude can be expressed in terms of matrix elements of magnetic and electric multipole operators. For a nonrelativistic atom, the calculation of these matrix elements has been separated into evaluating radial matrix elements and matrix elements of Racah tensors W/sup (0,k)k/ and W/sup (1,k')k/. For a relativistic atom the effective operator approach has been used to define effective multipole operators so that a relativistic result is obtained by taking matrix elements of these effective operators between nonrelativistic states of the atom. The calculation of matrix elements of these effective operators has been reduced to evaluating relativistic radial integrals and matrix elements of the Racah tensors taken between nonrelativistic states of the atom. It is shown that for the case of elastic scattering by either a relativistic or nonrelativistic atom in single Russell-Saunders state, the magnetic scattering amplitude can be written in the conventional form p(vector q)vector q/sub m/ . vector sigma. General expressions for p(vector q) as well as elastic magnetic form factors have been obtained. The formalism has been illustrated throughout by applying it to the case of scattering by rare earth ions. Detailed calculations for the form factors of Er and Gd ions are presented.