Addendum to "Quasiparticle branch mixing rates in superconducting aluminum"

The quasiparticle charge distribution generated in a superconductor by tunnel injection from a normal metal is computed as a function of temperature and injection voltage. The low-voltage limiting form is compared with the distributions obtained from the Tinkham-Clarke and Pethick-Smith chemical potential models. The quasiparticle charge relaxation rate τ_Q*^-1 due to inelastic scattering is computed for temperatures between 0.3Tc and 0.9999Tc, and for injection voltages between 0.01Δ(T)e and 20Δ(T)e. The limit T→Tc yields the voltage-independent Schmid-Sch\"on and Pethick-Smith result τ_Q*^-1=πτE=0^-1(Tc)Δ(T)4kBT, where τE=0^-1(Tc) is the inelastic scattering rate at the Fermi energy and at Tc. At temperatures below Tc, both the steady-state distribution function and τ_Q*^-1 depend on the injection voltage.