Exact analysis of a δ-function spin-1/2 attractive fermi gas with an external magnetic field

We study the excitation spectrum of a one-dimensional delta-function attractive spin-1/2 fermions by the thermal Bethe ansatz method at zero temperature. The integral equation for the dressed energies of the system with an external magmatic field is solved in the form of power series. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. We also study the magnetization as a function of the coupling constant and the external field.