Graphical representation of perturbation theory for line spectra

Emanuela Caliceti

Tatsuo Yajima

The multiple quantum process in the off-resonant condition of the three-level gas maser is discussed. The intensity of the emission produced by this process is calculated by a perturbation theory and also by a more general treatment which is the application of Javan's theory to the off-resonant case. Some graphical representations of the signal line under off-resonant pumping are given for the purpose of comparison with experiment. The Doppler effect in three-level maser action is analyzed from both semiclassical and quantum mechanical points of view under the presence of collision relaxation. It was shown that in a saturation process between two levels, Doppler effect behaves as to contribute to both line-width and relaxation time for the transition, and that under strong pumping, Doppler effect in pumping transition has a marked influence on both intensity and shape of the signal line through the effect of multiple quantum transition.

Ingvar Lindgren

In these lectures I shall give a review of the non‐relativistic many‐body perturbation theory (MBPT). In the first section a brief summary will be given of the Rayleigh‐Schrödinger perturbation theory for non‐degenerate and degenerate systems, and in the second section the second quantization and the graphical representation and introduced. In the third section the diagrammatic expansions are developed for closed‐ and open‐shell systems, and in the fourth section, finally, the procedure is generalized to the all‐order and coupled‐cluster approaches.

Niels Henrik David Bohr

Leszek Meissner, K. Jankowski

Abstract Linkage properties of the diagrammatic representation of the energies obtained in the multireference many‐body perturbation calculations with respect to the incompleteness or completeness of the model space are discussed. The case of not completely degenerate model space is considered for which a comparison with the standard single‐reference many‐body perturbation expansion is possible. The Hose–Kaldor type of graphical representation of the perturbation expansion for the effective Hamiltonian is used in this comparison. It is shown that for an incomplete model space the perturbation expansion is not size‐extensive. In this case, for a truncated expansion of the effective Hamiltonian, the energies obtained by diagonalization of the effective Hamiltonian matrix are represented by both linked and unlinked irreducible contributions. The unlinked ones do not appear when the complete model space is used.