Solution of the exchange-scattering problem without inadmissible complex poles

As previously demonstrated, the $S$-matrix formulation of the problem of exchange scattering of electrons in metals can lead to the appearance of inadmissible complex poles in the spin-flip scattering amplitude as the temperature falls below a certain value $T_c$. This amplitude then fails to satisfy the original scattering equations. In this paper, it is shown that such difficulties can be removed by making the proper analytic continuation in the temperature (or analytic continuation in the coupling strength for a fixed temperature). The scattering amplitudes, and with them such transport coefficients as conductivity, thermoelectric power, and Lorentz number are, in fact, smooth functions of temperature across $T_c$. Curves of these transport quantities versus temperature are plotted for a wide variety of values of the ordinary and exchange potentials.