## Abstract

The Feenberg-Jastrow Euler-Lagrange theory for inhomogeneous quantum liquids is developed to study many-electron atomic systems. We describe the ground state of the atoms by the Jastrow-Feenberg ansatz for the wave function. The generalized Born-Green-Yvon and Fermi-hypernetted-chain equations are used to relate the wave function to reduced distribution functions. The variational wave function is optimized by a generalized Hartree-Fock equation for the single-particle orbitals and an Euler-Lagrange equation for the two-body correlations. We calculate the electron correlation energies for various atoms and ions with four and ten electrons. Our theoretical results for the correlation energy of the ten-electron systems are within 93% of the experimental data. We discuss the behavior of the exchange-correlation holes in the atomic systems and analyze the qualitative difference of the correlations between the localized and extended states. The theory does not depend on any input parameters and only involves the Coulomb interaction among electrons and the nuclear charge. The relationship of this theory to density functional theory and configuration interaction theory is discussed.

Original language | English (US) |
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Pages (from-to) | 1-42 |

Number of pages | 42 |

Journal | Physics Reports |

Volume | 223 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1992 |

### Bibliographical note

Funding Information:This work was supported in part by National Science Foundation grants No. DMR-8406553 (to CEC), PHY-8806265 and PHY-9l08O66 (to EK), R.A. Welch Foundation grant No. A-l 111 and Texas Advanced Research Program grant No. 010366-12 (to EK), the Department of Energy, the Associated Western Universities; and the Graduate School, the Theoretical Physics Institute and the Supercomputer Institute of the University of Minnesota. EK would like to thank the Theoretical Physics Institute of the University of Minnesota for warm hospitality during a time when much of this work was done. CEC would like to express his gratitude to Group T-11 of the Theoretical Division, the Center for Nonlinear Studies, and the Center for Materials Science of Los Alamos National Laboratory for support and hospitality during the completion of this work. We would like to acknowledge helpful discussions with J. Almlöf, M. Idrees, U. Kaldor, J.F. Reading, and K. Schmidt, and to acknowledge Xiaoqian Wang for rerunning the corrected code to remove the error which appeared in ref. \[17\].We are indebted to K. Schmidt for providing us with an early copy of