Another important property of Fermi liquids is related to the scattering cross section for electrons. Suppose we have an electron with energy ϵ ϵ 1 above the Fermi surface, and suppose it scatters with a particle in the Fermi sea with energy ϵ ϵ 2 . By Pauli's exclusion principle, both the particles after scattering have to lie above the Fermi surface, with energies ϵ ϵ 3 , ϵ ϵ 4 > ϵ ϵ F . Now, suppose the initial electron has energy very close to the Fermi surface ϵ ϵ ≈ ≈ ϵ ϵ F Then, we have that ϵ ϵ 2 , ϵ ϵ 3 , ϵ ϵ 4 also have to be very close to the Fermi surface. This reduces the phase space volume of the possible states after scattering, and hence, by Fermi's golden rule, the scattering cross section goes to zero. Thus we can say that the lifetime of particles at the Fermi surface goes to infinity.