Magnetic scattering of neutrons

The magnetic scattering of neutrons by an arbitrary system of particles has been examined by exploiting its similarity to the radiation problem in spectroscopy. It has been shown, in fact, that the magnetic scattering amplitude can be expressed in terms of the multipole moments of the scattering system. The number of multipoles, which contribute to the scattering amplitude, is limited by selection rules based on the symmetry properties of the states of the system, in particular, parity and angular momentum conservation. The formalism has been applied to the magnetic scattering of neutrons by an atom in the $l^n$ electronic configuration. If the spin—other-orbit and orbit-orbit interactions in the atomic Hamiltonian can be neglected, only even-order electric and odd-order magnetic multipoles, whose order of multipolarity is less than or equal to $2l+1$, contribute to the scattering amplitude. In this case the calculation of the magnetic scattering amplitude is reduced to evaluating matrix elements of the Racah double tensors $W^{\mathrm{}(0,k)\mathrm{}}$ and $W^{(1,k^{\prime })}\left(k^{\prime } \mathrm{even}\right)$. The former tensors are associated with the convection current and the latter with the spin magnetization contribution to the magnetic scattering amplitude. The calculation of the maxtrix elements of these tensors is simplified by selection rules based on the groups Sp($4l+2$), R($2l+1$), R(3), ${\mathrm{G}}_2$ used in the classification of the atomic states. The contribution to the magnetic scattering amplitude of the convection current, associated with the spin-orbit and mass correction terms of the atomic Hamiltonian, has been examined in some detail.