Collective excitations of a general spin-3/2 Fermi gas

Collective excitation modes in a general 3D homogenous spin-3/2 Fermi gas with spin-dependent contact interactions are investigated by two-particle Green's functions and diagram techniques. Energy spectra for two branches of charge-density waves and three branches of transverse spin-density waves are obtained within the random-phase approximation. All spectra are gapless and linear in the small wave vector q, with their slopes dependent on the interaction parameters. It is also found that the spin-mixing interaction has effects on the transverse spin-density waves, but not on the charge-density modes. When the system satisfies SU(4) symmetry, the two charge-density modes become degenerate and two of the three transverse spin-density modes are degenerate, too. Furthermore, static spin susceptibilities are discussed in detail. It is found that susceptibilities increase with the enhancement of all interaction parameters, and become divergent at certain points. This phenomenon is analogous to the Stoner transition in spin-1/2 fermion gas.