Energies of N equivalent electrons expressed in terms of two-electron energies and independent three-electron parameters: a new complete set of orthogonal operators. I. Theory

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Abstract
The lN configuration is described as a collection of 1/2N(N-1) electron pairs, with the angular momenta of the electrons of each pair being coupled to the (2l+1) SL terms of l2. In this way, a set of parameters is defined which can be visualised as the energies of these particular SL terms. The parameters represent the effects of two-particle excitations on the lN configuration to second order. Moreover, they turn out, after a minor modification, to form an orthogonal set. The number of pairs multiplied by the average pair energy proves to be equal to the average energy of the full lN configuration. Inner products of general two-particle operators are calculated and conditions for their orthogonality are derived. For the dN configurations, two orthogonal three-body operators are added in order to obtain a complete set of electrostatic parameters. A simple general procedure is sketched that allows for the determination of the contributions of physical excitations to the various orthogonal parameters. This is illustrated by the s to d case. Values of all the matrix elements used are given.