  We give an analytical calculation of solar neutrino masses and mixing at
one-loop order within bilinear R-parity breaking supersymmetry, and compare our
results to the exact numerical calculation. Our method is based on a systematic
perturbative expansion of R-parity violating vertices to leading order. We find
in general quite good agreement between approximate and full numerical
calculation, but the approximate expressions are much simpler to implement. Our
formalism works especially well for the case of the large mixing angle MSW
solution (LMA-MSW), now strongly favoured by the recent KamLAND reactor
neutrino data.
