On the Ground-state Energy of a Mixture of Two Different Oppositely Polarized Fermionic Gases

We report the results of computation order $(k_{\rm F}a_0)^2$ correction, where $k_{\rm F}=3\pi^2\rho$ is Fermi wave vector and $a_0$ $s$-wave scattering length repulsive interaction, to ground-state energy a mixture oppositely polarized $N_a$ spin $1/2$ fermions $a$ masses $m_a$ $N_b$ $b$ $m_b$ ($\rho=N/V$, $N=N_a+N_b$). It shown that paper \cite{FraPil} in which same correction has been computed entirely numerically, using more traditional approach, can be easily semianalytically reproduced effective field theory technique.