Density expansion of the magnetic susceptibility

The pressure of a system may be expanded as a power series in the density, whose coefficients are the virial coefficients. In this paper, the magnetic susceptibility of a $\text{spin}\text{-}\text{1}\text{2}$ fermion system is also expanded in powers of density. This process explicitly separates the temperature and density dependence of the magnetic susceptibility. The coefficients of this series are shown to be related to certain virial coefficients. The first (previously established) and second corrections to Curie's law are explicitly expressed in terms of second and third virial coefficients. These corrections to Curie's law are small for temperatures above 4K, but become important below that temperature. The first correction has been previously measured. Given a set of second and third virial coefficients, the importance of the second correction can be calculated immediately at any density of interest.