The calculation of time-correlation functions for molecular collisions

Selective adsorption resonances: Quantum and stochastic approaches

“…In this section we will extent the CTCF formalism to particle-surface scattering following a parallel theoretical treatment as that developed in Refs. [254,255].…”

“…If L s is the corresponding Liouvillian operator, Eq. (221) can be rewritten [254,255] as (222) or, in terms of its Fourier transform, as…”

“…This short-time approximation, valid whenever the collision time (over which the energy transfer takes place) is short compared to the timescales associated with the internal motion, leads to a Gaussian distribution of the transferred energy; a more detailed discussion can be found in Refs. [254,255]. Furthermore, for quasi-elastic scattering the rate of energy transfer is expressed in terms of what is called the dynamic structure factor, which is the Fourier transform of a TCF of the particle density [263].…”

“…The time-correlation function (TCF) formalism for molecular collisions [254,255] is also an alternative theoretical framework to study atom surface scattering. Though it is based on the CC formalism, in the TCF formalism a rigorous time-dependent treatment is considered.…”

“…Furthermore, if surface temperature effects and inelastic events are considered, the numerical computation of such a set of CC equations becomes prohibitive. An alternative formalism to the scattering theory is the so-called collision time-correlation function (CTCF) [254,255], based on the calculations of time-correlation functions of the transition operator of scattering theory. The corresponding formalism is very similar, but more exact than that found in molecular spectroscopy [262], or the van Hove TCF related to neutron inelastic scattering by surfaces [263].…”