A common optical algorithm for the evaluation of specular spin polarized neutron and M\"ossbauer reflectivities

Using the general approach of Lax for multiple scattering of waves a 2x2 covariant expression for the reflectivity of polarized slow neutrons of a magnetic layer structure of arbitrary complexity is given including polarization effects of the external magnetic field. The present formalism is identical to the earlier published one for the (nuclear) resonant X-ray (Mossbauer) reflectivity and properly takes the effect of the external magnetic field of arbitrary direction on the neutron beam into account. The form of the reflectivity matrix allows for an efficient numerical calculation.