Influence of non-Markov effects in the thermal motion of particles on the intensity of incoherent scattering of slow neutrons in a liquid

To elucidate the part played by non-Markov effects in the incoherent scattering of slow neutrons on the basis of Bogolyubov's idea of a reduced description of many-particle systems, the fluctuation kinetics of the local density of an individual atom of a liquid is considered. Mori's method of projection operators is used to construct exact kinetic equations for the time correlation function of the fluctuations of the density and the memory function. Bogolyubov's other fundamental idea, of a hierarchy of relaxation times, is used to find approximate solutions of the obtained equations in the long-time approximation. These solutions provide the basis for the proposal of several methods for calculating the law of incoherent scattering $S_\mathrm{inc}(\mathbf k,\omega)$ for different regimes of molecular relaxation. It is shown that the relaxation processes responsible for incoherent scattering are essentially non-Markov. Numerical calculations have been made for the $S_\mathrm{inc}(\mathbf k,\omega)$ of liquid argon at temperature $T=85.2^\circ$K and values of the wave vector $\mathbf k$ from 1 to 3 Å$^{-1}$. In the approximation based on allowance for the second-order memory function good agreement is obtained between the theory and experiments on incoherent neutron scattering.