  The Stimulated Raman Adiabatic Passage on a three-state system interacting
with a spin bath is considered focusing on the efficiency of the population
transfer. Our analysis is based on the perturbation treatment of the
interaction term evaluated beyond the Rotating Wave Approximation, thus
focusing on the limit of weak system-bath coupling. The analytical expression
of the correction to the efficiency and consequent numerical analysis show that
in most of the cases the effects of the environment are negligible, confirming
the robustness of the population transfer.
