Longitudinal relaxation time for dilute quantum gases

We calculate the longitudinal relaxation timeT1 for a polarized spin-1/2 Fermi gas, in zero magnetic field, for conditions of temperatureT and densityn such that Boltzmann statistics are valid. Our results show generally thatT1 is independent of polarization of the gas. At highT, where the thermal wavelength ? is small compared to the scattering lengtha, T1 is proportionalT1/2, while at lowT, such that ? is greater thana, T1 is proportional toT-1/2.T1 thus has a minimum at some intermediate temperature confirming the numerical results of Shizgal. Physical arguments show that the existence of the minimum does not depend on the presence of an attractive part of the potential. As an example of the expected temperature dependence we calculateT1 numerically, via the distorted-wave Born approximation, for the case of a gas interacting via a hard core. We also computeT1 for a spin-1/2 Bose gas, which also shows a minimum.