Relativistic theory of neutron form factors

Abstract

We derive, for the first time, an expression for the generalized susceptibility χ(G+q,q) of a metal by using a relativistic treatment based on the Dirac equation and linear response theory (q is the wave vector and G is a reciprocal-lattice vector). The induced-moment form factor is calculated in the q→0 limit and is expressed as a sum of three terms, χ(G,0)=${\mathrm{\chi }}_{\mathrm{o}}$(G,0)+${\mathrm{\chi }}_{\mathrm{s}}$(G,0)+${\mathrm{\chi }}_{\mathrm{so}}$(G,0). ${\chi }_o$(G,0) and ${\chi }_s$(G,0), which also contain spin-orbit effects, reduce to the induced orbital and spin form factors obtained earlier in the nonrelativistic limit provided we use the same approximations. ${\chi }_{\mathrm{so}}$(G,0) is an explicit spin-orbit contribution which has no analog in the nonrelativistic limit. Our theory for neutron form factor is valid for G to be in any arbitrary direction while in the earlier (nonrelativistic) theories, G was restricted to be perpendicular to the magnetic field. Our expressions for ${\chi }_o$(G,0) and ${\chi }_{\mathrm{so}}$(G,0) are also free from any divergences, while in the earlier theories each of these expressions contained divergent terms in the q→0 limit which cancel only for a finite crystal. Our theory for induced magnetic form factor should be important in the analysis of the neutron scattering data of heavy transition metals in which spin-orbit interactions are important.