SEMINAR ANNOUNCEMENT: “Correlations in the low-density Fermi gas: Fermi-Liquid state, Dimerization, and BCS Pairing"

Eckhard Krotscheck

Department of Physics, University at Buffalo, SUNY

“Correlations in the low-density Fermi gas: Fermi-Liquid state,
Dimerization, and BCS Pairing"

Abstract:

We present FHNC-EL ground state calculations for low-density Fermi
gases described by two model interactions, of varying strength. We
first examine the low-density expansion of the energy and compare with
the exact answer by Huang and Yang (H. Huang and C. N. Yang, {\em
Phys. Rev.\/} {\bf 105}, 767 (1957)). It is shown that a locally
correlated wave function of the Jastrow-Feenberg type does not recover
the quadratic term in the expansion of the energy in powers of
$\a0\KF$, where $\a0$ is the vacuum $s$-wave scattering length and
$\KF$ the Fermi wave number. The problem is cured by adding
second-order perturbation corrections in a correlated basis.  Going to
higher densities and/or more strongly coupled systems, we encounter an
instability of the normal state of the system which is characterized
by a divergence of the {\em in-medium\/} scattering length. We
interpret this divergence as a phonon-exchange driven dimerization of
the system, similar to what one has at zero density when the vacuum
scattering length $\a0$ diverges. We then study, in the stable regime,
the superfluid gap and its dependence on the density and the
interaction strength. We identify two different corrections to
low-density expansions: One is medium corrections to the pairing
interaction, and the other one finite-range corrections. We show that
the most important finite-range corrections are a direct manifestation
of the many-body nature of the system.