Original scientific paper

Gram Detereminantal Inequalities with Elements <rm> Obtained from Hylleraas Wave Functions for the 2S States of the Three-Electron Systems Li, Be+, B2+, C3+,N4+, O5+, F6+, and Ne7+

P. Csavinszky ; Department of Physics and Astronomy, University of Maine; Orano, Maine 04469-5709, USA

Abstract

The present work considers 2 x 2, 3 x 3, 4 x 4, 5 x 5, and 6 x 6
Gram determinants whose elements are expection values of r,
where r is the distance from the nucleus of a three-electron system.
The «r":» values considered are those of King and Dressesl, who
evaluated the radi al electronic density function in closed form for
the 28 states of three-electron systems that are described by
Hylleraas-type wave functions. (The number of terms in the wave
functions are the following:233 for Li, 164 for Be", 201 for B2+, and
213 for C3+, N4+, 05+, F6+, and Ne7+). In the present work it is assumed, for purposes of illustration, that is unknown. It is
found that lower bounds to , calculated from the 2 x 2, 3 x 3,
4 x 4, 5 x 5, and 6 x 6 Gram determinantal inequalities converge
to the literature values obtained in King and DresseL (The literature
values are those that have been obtained with wave functions
more involved than those of King and Dressel).

Keywords

Hrčak ID:

177121

URI

https://hrcak.srce.hr/177121

Publication date:

1.11.1996.

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