Low-temperature behaviour of magnetic impurities in superconductors

The method used by the authors in a previous paper to calculate the free energy of a superconductor containing spin-1/2 magnetic impurities has been extended to calculate the thermal Green function to order (πv0jsub(z)-2) and to infinite order in Jsub(perpendicular). The finite impurity concentration behaviour is found to be functionally the same as that arising from the non-magnetic Anderson model. The graph of the transition temperature versus the impurity concentration is found to have a finite tail which should lead to the observation of a third transition temperature in re-entrant superconductors. The spatial variation of the order parameter is investigated in the limits of high (T approximately equal to Tsub(c)) and low (T<<Tsub(c)) temperatures for both long and short distances from the impurity. In addition, a numerical analysis of the initial decrease in Tsub(c) for intermediate temperatures shows qualitative agreement with previous high-temperature theories. (author)