On The Theory of the Forward Scattering of Neutrons by Paramagnetic Media

Experiments on the scattering of neutrons by paramagnetic media may have two possible goals: ($a$) determination of the magnetic moment of the neutron, and ($b$) investigation of exchange forces. In ($a$), materials of negligible exchange coupling should be used, while in ($b$) the reverse is true. The present paper is concerned with ($b$). It is shown that the exchange interaction between the paramagnetic ions tends to make the scattering inelastic, and reduces the form factor for forward scattering, so that it is no longer unity. An attempt is made to calculate the amount of this reduction. The distribution of energy changes in the inelastic processes is estimated by calculating the mean square and mean fourth power absorption frequencies, as well as the exact frequency distribution spectrum for an over-simplified "cluster" model. A Gaussian distribution appears to be the best feasible approximation. If this is used, it is estimated that in MnS, a typical material with appreciable exchange coupling, the form factor reduces the scattering of monochromatic liquid-air and room-temperature neutrons near the forward direction by about 75 and 50 percent, respectively.