THIRD-ORDER CORRECTIONS TO THE GROUND-STATE ENERGY OF THE POLARIZED DILUTED GAS OF SPIN 1/2 FERMIONS

We present the results of the computation of the third-order corrections to the ground-state energy of the diluted gas of nonrelativistic spin 1/2 fermions interacting through a spin-independent repulsive two-body potential. The corrections are computed within the effective field theory approach which does not require specifying the interaction potential explicitly but to characterize it by only a few parameters- the scattering lengths a(0), a(1),... and effective radii r(0),... - measurable in low-energy fermion-fermion elastic scattering. The corrections are computed semi-analytically, that is, are expressed in terms of two functions of the system's polarization. The functions are given by the integrals which can be easily evaluated using the Mathematica built-in routine for numerical integration.