Effect of Ordinary Scattering on Exchange Scattering from Magnetic Impurity in Metals

We investigate the ordinary and exchange scattering of conduction electrons by magnetic impurities. We find that for thermodynamic properties the effect of ordinary scattering is entirely absorbed into an effective exchange interaction $J$ ${cos}^2\eta$, where $\eta$ is the phase shift due to the ordinary scattering alone. The resistivity is calculated by using the Nagaoka-Hamann scheme. The $n\mathrm{th}$-order leading logarithmic term ($\sim J^{n+2\mathrm{}}{log}^{n}T$ in the absence of ordinary scattering) is multiplied by ${\left(cos\eta \right)}^{2n+4}$ $cos2\eta$, in agreement with Fischer, who obtained this result for $n=1\mathrm{}$. We discuss the alloy Rh-Fe, where the resistivity was interpreted in terms of a positive exchange interaction, whereas the susceptibility data indicated a negative one. We point out that these results are not inconsistent with each other in the light of the present theory.