Extended Parquet Theory fors-dSystem

•1 ) explained the phenomenon on the resistance minimum in dilute magnetic alloys, a new electron state appearing below some characteristic tem perature, say T x, has attracted a great interest. This new electron state seems to be associated with the occurrence of the resonance scattering of conduction electrons by magnetic impurities and this resonance nature makes the treatment of the problem very difficult. Kondo 1 ) has assumed the exchange interaction between conduction electrons and an impurity spin, the so-called s-d exchange interaction. As pointed out by him, the non-commutativity of the spin operator and the sharpness of the Fermi surface have brought about a characteristic feature to s-d problem, namely the logarithmic divergence at the Fermi surface. In more detail, the perturbation expansion turns to contain a term such as Jn (ln D / E)m, in which J is the exchange coupling constant. Abrikosov 2 ) succeeded for the first time in summing up the most divergent sub-series of the perturbation expansion, using the so-called parquet theory. As is the case with an electron gas, if the coupling is ferromagnetic, the sum thus obtained is finite over the whole range of energy. Moreover, the sum of the next divergent sub-series turns out to be also finite and of order J as compared with the former and so on. Here we notice that the sums of the next and the lower divergent terms can· be calculated from some skeleton diagrams in a simple manner; replacing the basic vertex J by the parquet diagram r and inserting the self-energy correction which itself is the sum of the most divergent corrections. In this way, one may finally obtain the rearranged series of the perturbation ex