## Abstract

The Mori memory-function formalism is used to derive systematically a hierarchy of approximations relating the dynamic structure factor S(k,ω) of a dense classical fluid to its self-part Ss(k,ω). The formalism is applied to a column vector of dynamical variables whose components include the self and distinct parts, ρs and ρd, of the fluctuating density plus N time derivatives of these variables. Increasing N is analogous to a continued-fraction expansion of the memory functions, and builds in more short-time information about the correlation functions. In this manner approximations generated earlier by Vineyard, by Kerr, and by Ortoleva and Nelkin are concisely stated, and a new approximation which gives the first six frequency moments of S(k,ω) correctly is obtained. Since the sixth frequency moment of S(k,ω) is not known from molecular-dynamics calculations, it is used as a parameter to fit these calculations. Agreement for S(k,ω) to within a few percent is obtained for several k values and two thermo-dynamic states. The deduced value of the sixth frequency moment has a reasonable dependence on k, and may give useful information about the three-particle static correlation function.

Original language | English (US) |
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Pages (from-to) | 2065-2075 |

Number of pages | 11 |

Journal | Physical Review A |

Volume | 4 |

Issue number | 5 |

DOIs | |

State | Published - 1971 |

Externally published | Yes |

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics