  A single-level quantum dot with Coulomb repulsion attached to two
superconducting leads is studied via the perturbation expansion in the
interaction strength. We use the Nambu formalism and the standard many-body
diagrammatic representation of the impurity Green functions to formulate the
Matsubara self-consistent perturbation expansion. We show that at zero
temperature second order of the expansion in its $\it{spin-symmetric}$ version
yields a nearly perfect agreement with the numerically exact calculations for
the position of the $0-\pi$ phase boundary at which the Andreev bound states
reach the Fermi energy as well as for the values of single-particle quantities
in the 0-phase. We present results for phase diagrams, level occupation,
induced local superconducting gap, Josephson current, and energy of the Andreev
bound states with the precision surpassing any (semi)analytical approaches
employed thus far.
