  We present an exact calculation of the mean first-passage time to a target on
the surface of a 2D or 3D spherical domain, for a molecule alternating phases
of surface diffusion on the domain boundary and phases of bulk diffusion. The
presented approach is based on an integral equation which can be solved
analytically. Numerically validated approximation schemes, which provide more
tractable expressions of the mean first-passage time are also proposed. In the
framework of this minimal model of surface-mediated reactions, we show
analytically that the mean reaction time can be minimized as a function of the
desorption rate from the surface.
