Schrödinger equation for neutron optics

It is usually assumed that neutron optical phenomena are adequately described by a one-body Schrödinger equation containing a complex optical potential that is given by the average value of the Fermi pseudopotential. The main problem with this elementary approach is that it only includes the attenuation of the neutron wave function in the medium resulting from absorption, and neglects the often more important contribution to the attenuation from diffuse scattering which is also present in reality. The purpose of this paper is to show how the rigorous theory of dispersion overcomes the above problem by taking properly into account the local field effects and a correction to the scattering amplitude that are neglected in the elementary theory. The importance of the local field correction in some current measurements of neutron scattering lengths by neutron optical experiments is also indicated.