Second-order diagrammatic perturbation

The plan of this paper is as follows - In section 2, the basic experimental data required in the re-evaluation of the empirical correlation energies of the N2 CO, BF and NO molecules are collected. The essential theoretical ingredients of our re-determination are given in section 3 including new fully relativistic calculations including the frequency independent Breit interaction and electron correlation effects described by second order diagrammatic perturbation theory for the Be-like ions B", C, O" ... 

Second-order diagrammatic perturbation theory of nuclei and electrons... 

An important technique in diagrammatic perturbation theory is the summation of certain classes of diagrams to infinite order. To illustrate the technique consider our two-state system. The only diagram that contributes in second-order is... 

In order to develop a diagrammatic approach to perturbation theory, it is convenient to work within a second-quantized formalism. The expressions for Ho and V then become... 

These expressions are identical to our previous results for the second- and third-order energies (Eqs. (6.12) and (6.15)) when i = 1. What if we want the perturbation expansion for some state i, which is not necessarily the lowest What do the diagrams look like One can easily verify that we get the same answers as before if we label our hole lines by the index i and the particle lines by the indices m, n, k,..., which can take on the values 1,2,..., i - 1, I + 1,..., N. Thus we now have a complete diagrammatic representation of RS perturbation theory, which is applicable to any perturbation and any zeroth-order state. 

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