Free energy of superfluidHe3

We present a systematic scheme for calculating the free energy of superfluid Fermi liquids by an asymptotic expansion in the small parameter $\frac{T_c}{T_F}$. We use this scheme to evaluate the strong-coupling corrections to the free energy of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. We show that the leading corrections can be expressed in terms of the normal-state quasiparticle scattering amplitude, and discuss the strong-coupling results using the $s-p$ approximation for the scattering amplitude.