Cooper pairs in atomic nuclei

Abstract

We consider the development of Cooper pairs in a self-consistent Hartree Fock mean field for the even Sm isotopes. Results are presented at the level of a BCS treatment, a number-projected BCS treatment and an exact treatment using the Richardson ansatz. While projected BCS captures much of the pairing correlation energy that is absent from BCS, it still misses a sizable correlation energy, typically of order $1MeV$. Furthermore, because it does not average over the properties of the fermion pairs, the exact Richardson solution permits a more meaningful definition of the Cooper wave function and of the fraction of pairs that are collective.

5 pages, 3 figures

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• A Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains
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