Superfluid Transition Temperature in a Fermi Gas with Repulsion. Higher Orders Perturbation Theory Corrections

High order perturbation theory corrections to the superfluid transition temperature in a weakly interacting Fermi gas with repulsive interaction are calculated. This involves calculating the contributions of third and fourth order diagrams in the gas parameter and taking into account effects of retardation. The contributions from both second, third and fourth orders result in the effective attraction in p-wave channel. It is shown that the critical temperature is mainly determined by second and third orders terms of perturbation theory. The dependence of the critical temperature on an external magnetic field is found. We discuss possible applications of the results to the diluted 3He-4He mixtures and trapped neutral-atom Fermi gases.