Ground-State Energy of the Anderson Hamiltonian

The ground-state energy of the Anderson Hamiltonian for infinite $d-d$ correlation energy is calculated using a perturbation scheme developed by Kondo for the $s-d$ Hamiltonian. The ground-state energy is found, as in the $s-d$ model, to differ from the perturbation ground state by $-\mathrm{C}\exp (-\frac{E}{2{V^2}_{\rho }})$, where $E$ is the energy of the $d$ electron (measured from the Fermi surface), $V$ is the $s-d$ mixing strength, and $\rho$ is the density of states. $C$ is an energy cutoff $\sim E$.