Non-Gaussian Corrections to Van Hove's Gs(r, t) for a Monatomic Gas

Abstract

Non-Gaussian corrections to Van Hove's self-correlation function, Gs(r, t), are studied for real monatomic gases. Gs(r, t) is identified with the motion of a tagged atom in a dilute gas, where the motion is determined entirely by free streaming and random binary collisions with the untagged atoms. In this description, Gs(r, t) is the velocity integral of a distribution function f(r, v, t) which is initially Maxwellian, localized at the origin, and which satisfies a linearized Boltzmann equation. Spatial moments of Gs(r, t) are calculated using the Lennard-Jones (12–6) potential and the modified Buckingham exp (14–6) potential as interatomic potentials. Results are compared with those using a rigid-sphere potential and with those of Rahman from a high-density molecular-dynamics calculation. It is found that (i) the behavior of non-Gaussian corrections is qualitatively similar in all the cases, (ii) the corrections are larger for higher densities, and (iii) at low densities, the corrections increase almost by a factor of 2 when attractive forces are included. It is also shown that the moments approach (through space-dependent BE) and the velocity correlation-function approach (through velocity—space BE) in calculating the non-Gaussian corrections are equivalent.