Anomalies and Bound State Due to the Anisotropics-dExchange Interaction

The Kondo problem for the anisotropic s-d exchange interaction is investigated in de­ taiL The scattering amplitude of a conduction electron is calculated in the most divergent approximation (Abrikosov's approximation). The importance of some types of terms over­ looked in the previous work by Miwa and Nagaoka is pointed out. By changing the degree of anisotropy of the exchange integral the behaviors of the obtained scattering amplitude­ especially the divergence difficulties-are examined. To see physical meaning of the diver­ gence difficulties the problem of the existence of the bound state realized as the ground state of this coupled many-body system is discussed by extending the Yosida-Okiji-Yoshimori theory to the anisotropic case. It is shown that the exact solution of the bound state can be obtained also for the anisotropic s-d interaction, and that the divergence difficulties stated above are closely connected with the existence of the bound state.