Many body perturbation theory relativistic

3 Relativistic Many-body Perturbation Theory. - Since the early 1980s, we have witnessed a growing interest in the effects of relativity on the electronic structure of atoms and molecules. Over the past decade the theoretical and computational machinery has been put in place for a relativistic many-body perturbation theory of atomic and molecular electronic structure.29,32-36,38 

Pyykko104 has surveyed the influence of relativity on periodic trends and provided a concise summary of previous reviews of relativistic electronic structure theory. This development can be seen, on the one hand, as a result of a growing awareness of the importance of relativity in accounting for the properties of heavy atoms and molecules containing them. The inadequacy of 

In a report presented by the author at the 1988 Symposium on Many-body methods in quantum chemistry held at Tel Aviv University,34 we suggested that 

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 theoretical description of any many body system is usually approached in two distinct stages. First, the solution of some independent particle model yielding a set of quasi-particles, or dressed particles, which are then used to formulate a systematic scheme for describing the corrections to the model. Perturbation theory, when developed with respect to a suitable reference model, affords the most systematic approach to the correlation problem which today, because it is non-iterative and, therefore, computationally very efficient, forms the basis of the most widely used approaches in contemporary electronic structure calculations, particularly when developed with respect to a Moller-Plesset zero order Hamiltonian. 

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We refer the interested reader to our previous report1 for a review of the literature on many-body perturbation theory studies of relativistic effects molecules upto 1999. Here the background to the relativistic many-body problem in molecules was given in Section 2.1 and a review of the relativistic many-body perturbation theory was given in Section 2.3. 

RMBPT-relativistic many-body perturbation theory differs from the full QED cal-... 

The all-orders relativistic many-body perturbation theory approach [82], [83], the combination of this approach with the multiconfiguration Dirac - Fock method [84] or the relativistic coupled-cluster approach [85] allow for the evaluation of the energy levels for valence electrons with accuracy of the order of... 

Early non-relativistic many-body perturbation theory studies of correlation energies in molecules established that the error associated with truncation of the finite basis set is most often much more significant than that resulting from truncation of the perturbation expansion.15 The chosen basis set is required to support not only an accurate description of the occupied Hartree-Fock orbitals but also a representation of the virtual spectrum. Over the past twenty years significant progress has been reported on the systematic design of basis sets for electron correlation studies in general and many-body perturbation theory calculations in particular.18... 

We now have a well defined prescription for the calculation of the properties of atoms and molecules within a relativistic formulation. As in the non-relativistic case, the relativistic many-body perturbation theory becomes increasingly complicated in higher orders and in practice it is possible to take the expansion to about fourth order with the size of basis set that is required for calculations of useful accuracy. Sapirstein82 has recently re-iterated the view that... 

Abstract A consistent relativistic energy approach to the calculation of probabilities of cooperative electron-gamma-nuclear processes is developed. The nuclear excitation by electron transition (NEET) effect is studied. The NEET process probability and cross section are determined within the S-matrix Gell-Mann and Low formalism (energy approach) combined with the relativistic many-body perturbation theory (PT). Summary of the experimental and theoretical works on the NEET effect is presented. The calculation results of the NEET probabilities for the y Os, yy Ir, and yg Au atoms are presented and compared with available experimental and alternative theoretical data. The theoretical and experimental study of the cooperative electron-gamma-nuclear process such as the NEET effect is expected to allow the determination of nuclear transition energies and the study of atomic vacancy effects on nuclear lifetime and population mechanisms of excited nuclear levels. 

The relativistic many-body perturbation theory of atomic and molecular electronic structure can be formulated within the algebraic approximation in a manner analogous to the non-relativistic formulation. A detailed discussion of the method, which is still under development, lies outside the scope of this chapter but the technique s potential will be illustrated by displaying some results for the relativistic version of the model problem considered in Section V.B, a hydrogenic atom with nuclear charge Z perturbed by the potential — Z lrP The exact energy of the perturbed problem in its ground state is... 

Quiney, H.M., 1988, Relativistic many-body perturbation theory, in Relativistic Effects in Atoms and Molecules, Methods in Computational Chemistry, Vol. 2, ed. S. Wilson (Plenum, New York). 

Y. Ishikawa, H. M. Quiney. Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave equations. Phys. Rev. A, 47 (1993) 1732-1739. 

H. M. Quiney, I. P. Grant, S. Wilson. On the Relativistic Many-Body Perturbation Theory of Atomic and Molecular Electronic Structure, p. 307-344,1989. 

Relativistic many-body perturbation theory has been applied to study the polarizabilities of the ions of the francium isoelectronic sequence.This approach, which adopts SOS expressions, decomposes the polarizability into an ionic core contribution, a counterterm compensating for excitations from the core to the valence shell, and a valence electron contribution. These calculations have presented benchmark results for comparison with experiment. A similar relativistic many-body perturbation theory study of the energies and oscillator strengths of the nsij2, npj, ndj, and nfj (n < 6) states of Li has been carried out and has enabled to evaluate the polarizabilities of its ground state. 

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