Ground state energy of unitary fermion gas with the Thomson Problem approach

Details Ground state energy of unitary fermion gas with the Thomson Problem approach Ground state energy of unitary fermion gas with the Thomson Problem approach

2006-02-23

arxiv.org/abs/nucl-th/0602065v6

Chinese Phys. Lett. 24 (2007) 1825-1828

Physics

Nuclear Physics

Nuclear Theory

Identical to published version with revisions according to comments

Scientific paper

10.1088/0256-307X/24/7/011

The dimensionless universal coefficient $\xi$ defines the ratio of the unitary fermions energy density to that for the ideal non-interacting ones in the non-relativistic limit with T=0. The classical Thomson Problem is taken as a nonperturbative quantum many-body arm to address the ground state energy including the low energy nonlinear quantum fluctuation/correlation effects. With the relativistic Dirac continuum field theory formalism, the concise expression for the energy density functional of the strongly interacting limit fermions at both finite temperature and density is obtained. Analytically, the universal factor is calculated to be $\xi={4/9}$. The energy gap is $\Delta=\frac{{5}{18}{k_f^2}/(2m)$.

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