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Formal solution for the three body problem in helium theoretical chemistry

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Abstract

The theory of co-ordinates r a , r b , with r b = max(r 1 , r 2 ) and r a = min(r 1 ; r 2 ) is developed to yield formal solutions for Schroedinger equations of helium theoretical chemistry. The correction for nuclear motion is included. Four most significant sets of terms in the ground state for the radial equation give a good approximation for the radial limit independently of the variation theorem. Thirteen most significant terms from the four sets are the basis for accurate variation calculations. A new radial limit is obtained.

Zusammenfassung

Es wird eine Theorie für die Koordinaten r a und r b (r b =max(r 1 , r 2 ), r a =min(r 1 , r 2 ) entwickelt, um formale Lösungen der Schrödingergleichung von heliumartigen Systemen zu erhalten. Die Kernbewegung wird durch eine Korrektur berücksichtigt. Vier sehr wichtige Termgruppen des Grundzustandes ergeben im Falle der Radialgleichung eine gute Näherung für das Grenzverhalten, und zwar unabhängig vom Variationstheorem. Dreizehn sehr wichtige Terme aus den erwähnten vier Termgruppen bilden die Grundlage für exakte Variationsrechnungen.

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  1. Computing Centre, Trent Polytechnic, Nottingham, England

    F. T. Newman

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  1. F. T. Newman
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Newman, F.T. Formal solution for the three body problem in helium theoretical chemistry. Theoret. Chim. Acta 30, 95–113 (1973). https://doi.org/10.1007/BF00527637

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