Theory of thermal neutron scattering from crystals containing ions with impaired f electrons

The problem of calculating the magnetic contribution to the cross section for the scattering of polarized thermal neutrons by crystals containing ions with unpaired f electrons is reduced to the evaluation of simple expressions that involve spherical harmonics and certain functions characteristic of the ion in question. These 'characteristic' functions (at most four per ion) are tabulated for tripositive rare earth ions. For the particular case of saturated ions the magnetic contribution to the elastic cross section is shown to be contained in a generalized atomic form factor. Three numerical samples are given, namely Pr 3+ , Sm 3+ and Er 3+ , and it is shown that the form factor for Sm 3+ possesses a maximum at a non-zero value of the scattering vector.