Recent advances in description of few two-component fermions

Abstract

Overview of the recent advances in description of the few two-component fermions is presented. Themodel of zero-range interaction is generally considered to discuss the principal aspects of the few-body dynamics. Particular attention is paid to detailed description of two identical fermions of mass m and a distinct particle of mass m1: it turns out that two LP = 1− three-body bound states emerge if mass ratio m/m1 increases up to the critical value µc ≈ 13.607, abovewhich the Efimov effect takes place. The topics considered include rigorous treatment of the few-fermion problem in the zero-range interaction limit, lowdimensional results, the four-body energy spectrum, crossover of the energy spectra for m/m1 near µc, and properties of potential-dependent states. At last, enlisted are the problems, whose solution is in due course.