We introduce a new φ-derivable approach for the Anderson impurity model in a BCS superconductor. The regime of validity of this conserving theory extends well beyond that of the Hartree - Fock approximation. This is the first generalization of the U-perturbation theory to encompass a superconductor.
Alastalo, A. T., Joynt, R. J., & Salomaa, M. M. (1998). Anderson model in a superconductor: Φ-derivable theory. Journal of Physics: Condensed Matter, 10(3), L63-L68. https://doi.org/10.1088/0953-8984/10/3/003