Study of the Perturbation Series for the Ground-State Energy of a Many-Fermion System
- 1 November 1963
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 132 (3), 1373-1387
- https://doi.org/10.1103/physrev.132.1373
Abstract
In order to investigate the validity of the Brueckner and the simple sum of the ladder diagrams approximations to the energy of an infinite system of fermions, we have calculated as a function of density all the terms in the perturbation expansion through the fourth order in the strength of the potential. We have done this for a repulsive, square-well, two-body potential spin-½ fermions. We are able to construct rigorous upper and lower bounds from the coefficients for the value of the ladder approximation and find that the standard solution procedures give reasonably accurate results (within a few percent). We find that the error in the solution as obtained in practice to the equations of the Brueckner approximation is large compared to the size of its departure from the ladder approximation. We further find for low-to-moderate densities and for low-to-moderate potential strengths that the Brueckner approximation both as a sum of a certain class of diagrams and as computed in practice lies above the ladder approximation while the complete perturbation theory lies below it. This result arises from the neglect of the ring diagrams by the Brueckner approximation.Keywords
This publication has 14 references indexed in Scilit:
- Divergence and Summability of the Many-Fermion Perturbation SeriesPhysical Review B, 1963
- Further Applications of the Padé Approximant Method to the Ising and Heisenberg ModelsPhysical Review B, 1963
- Nuclear Matter Calculations and Phenomenological PotentialsPhysical Review B, 1962
- The Calculation of Thermodynamic Functions in Lattice DynamicsProceedings of the Physical Society, 1962
- Application of the Padé Approximant Method to the Investigation of Some Magnetic Properties of the Ising ModelPhysical Review B, 1961
- Properties of Nuclear MatterPhysical Review B, 1958
- Derivation of the Brueckner many-body theoryProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
- Effect of a repulsive core in the theory of complex nucleiProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1957
- Perturbation theory of large quantum systemsPhysica, 1957
- Nuclear Many-Body ProblemPhysical Review B, 1956