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.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.

AIP conference proceedingsJan 1, 19893 citations

Many-Body Perturbation Theory

Yoshio Kuramoto

Lecture notes in physicsJan 1, 20202 citations

Calculation of fine-structure splittings in high-lying F2 states of rubidium

Steven A. Blundell

We present relativistic many-body calculations of the fine-structure splittings of the $n\phantom{\rule{0.16em}{0ex}}{}^{2}F$ Rydberg states of Rb $(n=4$ --16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the $^{2}\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.We present relativistic many-body calculations of the fine-structure splittings of the $n\phantom{\rule{0.16em}{0ex}}{}^{2}F$ Rydberg states of Rb $(n=4$--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the $^{2}\mathrm{F}$ states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.

Physical Review AOct 31, 20147 citations

Many-Body Perturbation Theory

Reiner M. Dreizler, Eberhard K. U. Gross

Springer eBooksJan 1, 19904 citations

We present relativistic many-body calculations of the fine-structure splittings of the

n\phantom{\rule{0.16em}{0ex}}{}^{2}F

Rydberg states of Rb

(n=4

--16) using both order-by-order relativistic many-body perturbation theory (RMBPT), up to a subset of fourth-order corrections, and relativistic equation-of-motion coupled-cluster methods, including singles, doubles, and an approximate treatment of valence triples. Good overall agreement is found with the measurements of Brandenberger et al. [Phys. Rev. A 65, 042510 (2002); Phys. Rev. A 81, 032515 (2010)] to better than the 1% level, which is our expected level of theoretical uncertainty due to omitted higher-order correlation effects. It is shown that the RMBPT of the fine-structure splittings is complex and slowly convergent, and that relativistic effects are enhanced compared with the RMBPT of the ionization energy of the

^{2}\mathrm{F}

states. We also analyze smaller field-theoretic contributions to the fine-structure splittings from retardation and the radiative self-energy and vacuum polarization, finding them to enter at the 0.1% level.