Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Correlations in the low-density Fermi gas: Fermi-Liquid state,
  Dimerization, and BCS Pairing   We present ground state calculations for low-density Fermi gases described by
two model interactions, an attractive square-well potential and a Lennard-Jones
potential, of varying strength. We use the optimized Fermi-Hypernetted Chain
integral equation method which has been proved to provide, in the density
regimes of interest here, an accuracy better than one percent. 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.

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The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
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The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat