Double Singlet Pair in the Kondo Ground-State

In the Kondo ground-state the magnetic impurity d₀ forms a singlet state with the conduction electrons, i.e., with one localized electron state a₀ composed of the conduction band. This state a₀ has the opposite spin as d₀ and has maximum amplitude at the impurity. In the sub-band with the same spin as d₀ the electrons try to minimize the amplitude at the impurity. This is achieved by avoiding a second localized state b₀ with maximum amplitude at d₀, i.e. leaving b₀ empty. Although one might expect that the singlet state (d₀,a₀) between d₀ and a₀ represents the full Kondo ground-state, this is not the case. The system forms a combination of two singlet pairs: (d₀,a₀) and (d₀,b₀). This is counter intuitive because (d₀,b₀) has a relative large Ising energy. But its spin-flip matrix element is not reduced by orthogonality. The dominant energy reduction in the ground-state is due to the mixed terms between the individual pairs. Despite the long history of the Kondo effect the importance of this composition of the Kondo ground-state has been overlooked so far.