Abstract
The matrix elements which determine the magnetic inelastic neutron cross section for scattering by localised electronic states are calculated for the transition lmsms to l'm'sm's. Use of the formulae is illustrated in a calculation of the neutron cross-section for scattering from thallium-activated potassium chloride (when the thallium ion changes its configuration from 6s2 to 6s6p) and the associated atomic structure factors are estimated on the basis of free-atom wavefunctions.