London penetration depth of superconductors having lifetime broadened density of states

London penetration depth λ/sub L/ was calculated for superconductors having lifetime broadened density of states. With the increase of gap states, λ/sub L/ increases and the temperature dependence deviates from the ordinary form. The model gives a T2 dependence of λ/sub L/ in the case of weak-coupling limit of the Bardeen--Cooper--Schrieffer theory. The results are discussed referring to some experimental results of magnetic field penetration depth of oxide superconductors