## Abstract

The probability of finding a nearest neighbor at some given distance from a reference point in a many-body system of interacting particles is of importance in a host of problems in the physical as well as biological sciences. We develop a formalism to obtain two different types of nearest-neighbor probability density functions (void and particle probability densities) and closely related quantities, such as their associated cumulative distributions and conditional pair distributions, for many-body systems of D-dimensional spheres. For the special case of impenetrable (hard) spheres, we compute low-density expansions of each of these quantities and obtain analytical expressions for them that are accurate for a wide range of sphere concentrations. Using these results, we are able to calculate the mean nearest-neighbor distance for distributions of D-dimensional impenetrable spheres. Our theoretical results are found to be in excellent agreement with computer-simulation data.

Original language | English (US) |
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Pages (from-to) | 2059-2075 |

Number of pages | 17 |

Journal | Physical Review A |

Volume | 41 |

Issue number | 4 |

DOIs | |

State | Published - 1990 |

## All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics