Abstract
Upper bounds are derived to the many-electron density () of an -electron atomic or molecular wave function. The derivation is based on former results on the decay of the one-electron density and on the "Schrödinger inequality" for which, by means of a comparison theorem, allows the deduction of upper bounds for in the region , being a constant and , provided an upper bound to is available on the boundary . The latter can be obtained from bounds to . A recurrence procedure leads to the final result which for the case of an atom is given by ( is a constant, acts as a symmetrizer, denotes the nuclear charge, and the () denote the successive ionization potentials of the state under consideration). We further report an improved bound for which depends explicitly on the interelectronic distance.
- Received 9 March 1978
DOI:https://doi.org/10.1103/PhysRevA.18.328
©1978 American Physical Society