Resonant Fermi Gases with a Large Effective Range

We calculate the equation of state of a Fermi gas with resonant interactions when the effective range is appreciable. Using an effective field theory for a large scattering length and large effective range, we show how calculations in this regime become tractable. Our results are model independent, and as an application, we study the neutron matter equation of state at low densities of astrophysical interest $0.002{\mathrm{fm}}^{-3}<\rho <0.02{\mathrm{fm}}^{-3}$, for which the interparticle separation is comparable to the effective range. We compare our simple results with those of conventional many-body calculations.

Figure 1

Hartree-Fock results for the energy per particle of neutron matter calculated from $V_{\mathrm{low}k}$ for different cutoffs.

Figure 2

Result for ${\xi }_{\mathrm{HF}}(k_{\mathrm{F}}{r}_{\mathrm{e}})$ (solid line) which describes the equation of state of resonant Fermi gases with large effective range $k_{\mathrm{F}}{r}_{\mathrm{e}}\gtrsim 1$. The dashed lines provide an error estimate for ${\xi }_{\mathrm{HF}}$ as discussed in the text.

Figure 3

Comparison of the energy per particle for neutron matter calculated from Eq. (10) for $a_{\mathrm{s}}=-18.5\mathrm{fm}$ and $r_{\mathrm{e}}=2.7\mathrm{fm}$ (solid line) to Fermi hypernetted-chain (triangles) [18] and Brueckner results (circles) [19]. We also show the $V_{\mathrm{low}k}$ Hartree-Fock results of Fig. 1. The dashed lines provide an error estimate for ${\xi }_{\mathrm{HF}}$.