Binding from repulsive interaction in a degenerate Fermi gas

The binding of two fermions in a degenerate Fermi gas is examined in terms of the T-matrix. We deal with effective T-matrix: of two fermions in the degenerate Fermi gas in terms of the scattering amplitude. This makes approach valid for the retarded as well as non-retarded interactions. We show that for the interaction of a pair of fermions in a quiescent Fermi sea there are two different series of the ladder diagrams-Exchange and Hartree diagrams, describing a bound state and producing two different T-scattering matrices. The exchange series of the ladder diagrams corresponds to the T-matrix in the triplet-state. This T-matrix contains the pole solution corresponding to the bound state for the attractive interaction only. In contrast, the Hartree diagrams lead to the T-matrix of a pair of fermions in the singlet-state, which have a pole solution corresponding to the bound state of a pair of fermions for the repulsive interaction. Thus, we are led to assert that the bound state of a pair of fermions in the singlet-state in the quiescent Fermi sea can form for the repulsive interaction only and there is no bound state in the singlet-state from the attractive interaction.