Critical-Point Singularities of the Perturbation Series for the Ground State of a Many-Fermion System
- 1 September 1969
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 10 (9) , 1647-1660
- https://doi.org/10.1063/1.1665012
Abstract
We show that the many‐fermion ground‐state energy with an attractive potential has a critical singularity. This singularity destroys the validity of ``low‐density'' approximations. We also find that the K‐matrix formalism is, in principle, not applicable to attractive potentials because of the presence of ``Emery singularities.'' We introduce an R‐matrix formalism which is numerically very close to the K matrix and free from manifest ``Emery singularities.'' A model calculation is performed on the lattice gas to try to anticipate what quality of results can be expected from summing an R‐matrix expansion with fixed density.Keywords
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