Abstract
The purpose of this work is to study the mean free path effect of non-magnetic impurities on superconductors. It is shown by including the impurities in the electron-phonon system that, contrary to the results of the earlier theories, there is no change in the transition temperature which is of the order of 1/w0r, where w0 is the cutoff frequency of the BCS theory and 'C' the relaxation time in the normal state due to the scattering. The same effect on the superconductor with the anisotropic energy gap is studied explicitly. The scattering in this case leads to the reduction of the transition temperature which is initially linear in 1/'t' but becomes logarithmic when 't'Tc<L The gap in the excitation spectrum is shown to become isotropic when the mean free path is smaller than the coherence length. Thus, Anderson's theory of dirty superconductors is formulated and justified.
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