We calculate Bardeen–Cooper–Schrieffer (BCS) state of a unitary Fermi gas of atoms interacting with the finite-ranged Jost-Kohn potential which has been recently shown to account for the resonant interactions (2019 J. Phys. B: At. Mol. Opt. Phys. 52 165004). Using exact scattering solution of the potential, we derive two-body T-matrix element which is employed to construct the BCS Hamiltonian in momentum space. We present results on the energy- and range-dependence of the pairing gap and superfluid density and the range-dependence of the chemical potential for a wide variation of the scattering length including the unitary regime. In the zero range limit our calculated gap at the Fermi energy is found to be nearly equal to that calculated in mean-field theory with contact potential. The mean gap averaged over the full width at half maximum of the gap function in the zero range and unitary limits is found to be 0.42E _F which is quite close to the recent result of the quantum Monte-Carlo simulation (2018 Phys. Rev. A 97 013601). The chemical potential in the zero range limit also agrees well with that for the contact potential.

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与有限范围势相互作用的单一费米原子气体的超流模型研究

我们计算了原子的单一费米气体与有限范围的 Jost-Kohn 势相互作用的 Bardeen-Cooper-Schrieffer (BCS) 态，该态最近被证明可以解释共振相互作用 (2019J.物理学。乙：在。摩尔。选择。物理。52165004）。使用势能的精确散射解，我们推导出二体吨-用于在动量空间中构建 BCS 哈密顿量的矩阵元素。我们提出了配对间隙和超流体密度的能量和范围依赖性以及散射长度的广泛变化（包括单一状态）的化学势的范围依赖性的结果。在零范围限制中，我们发现费米能量处的计算间隙几乎等于平均场理论中具有接触电势的计算间隙。发现在零范围和单一限制中间隙函数的半峰全宽上平均的平均间隙为 0.42乙 _F与最近的量子蒙特卡洛模拟结果非常接近（2018物理。牧师A97013601）。零范围极限内的化学势也与接触势一致。