Journal of Statistical Physics

, Volume 25, Issue 2, pp 321–360 | Cite as

The incoherent scattering function and related correlation functions in hard sphere fluids at short times

  • I. M. de Schepper
  • M. H. Ernst
  • E. G. D. Cohen
Articles

Abstract

For a classical fluid of hard spheres and hard disks exact expressions for all densities and wave vectors are derived for the coefficients oft n in the short-time expansion of the incoherent intermediate scattering function (n = 0, 1,..., 4) and the velocity correlation function (n=0,1,2). Similarly, we obtain the coefficient of the leading term in the short-time behavior of the cumulants of the displacements. Furthermore,S(k, ω) has a high-frequency tail ∼ω−4, characteristic for the hard-sphere fluid, which leads to a modification of the standard sum rules. We present estimates for the frequency range, in which this tail may be observed in neutron scattering off noble gases. The results are also compared with Enskog's theory and molecular dynamics calculations.

Key words

Incoherent scattering function velocity correlation function cumulants of displacement hard-sphere fluid short-time expansions 

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Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • I. M. de Schepper
    • 1
  • M. H. Ernst
    • 1
  • E. G. D. Cohen
    • 2
  1. 1.Institute for Theoretical PhysicsUniversity of UtrechtTA UtrechtThe Netherlands
  2. 2.The Rockefeller UniversityNew York

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