Hartree-Fock contribution, three-body

For polar systems, the Hartree-Fock three-body contribution, Pf[3], may give a reasonable approximation of the total nonadditive effect. This quantity can be decomposed as... 

An overview of the salient features of the relativistic many-body perturbation theory is given here concentrating on those features which differ from the familiar non-relativistic formulation and to its relation with quantum electrodynamics. Three aspects of the relativistic many-body perturbation theory are considered in more detail below the representation of the Dirac spectrum in the algebraic approximation is discussed the non-additivity of relativistic and electron correlation effects is considered and the use of the Dirac-Hartree-Fock-Coulomb-Breit reference Hamiltonian demonstrated effects which go beyond the no virtual pair approximation and the contribution made by the negative energy states are discussed. 

The final form of the Born-Handy formula consists of three terms The first one represents the electron-vibrational interaction. I will not present the numerical details for H2, HD and D2 molecules here, it can be found in our previous work. The most important result here is that the electron-vibrational Hamiltonian is totally inadequate for the description of the adiabatic correction to the molecular groundstates its contribution differs almost in one decimal place from the real values acquired from the Born-Handy formula. In the case of concrete examples -H2, HD and D2 molecules - the first term contributes only with ca 20% of the total value. The dominant rest - 80% of the total contribution - depends of the electron-translational and electron-rotational interaction [22]. This interesting effect occurs on the one-particle level, and it justifies the use of one-determinant expansion of the wave function (28.2). Of course, we can calculate the corrections beyond the Hartree-Fock approximation by means of many-body perturbation theory, as it was done in our work [22], but at this moment it is irrelevant to further considerations. 

For ns - vacancies in outer shells of noble gas atoms F g is prominently less than one, g1 and the excitation energy is shifted from its Hartree-Fock value. The cross section in the vicinity of the ns">-(n+l)p level is described in RPAE badly. Let us include "two electron-two hole" excitations of the same type that interact with ns strongly, i.e. np, np nd. As an example we shall take the 3s- 4p level in Ar 6 and include the photoexcitation vertex, given in Fig. 8. It is implied that the insertions of Z in the s-hole line (see Fig. 5) are also included. All these corrections are of "two electron-two hole type". To take them into account rigorously is impossible because even the motion of two electrons in an ion field is a three-body problem. However to Z33. the main contribution comes from 3d excitation. Therefore it is natural to take into account just the same states in Fig. 8 corrections. 

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