# What happens to the scattering cross section of two fermions with different spins at low temperature?

The scattering cross section for two identical fermions at low temperature is given by: $$\sim 8\pi a_1^2(ka_1)^4$$. I was wondering what happens if the two fermions have different spins - does it change the form of the cross section?

I was wondering if BCS or BEC attraction would mean the particles form a meta stable state and hence the scattering length would increase but even if this was true would this change the cross section?