  Radiative energy transfer between closely spaced bodies is known to be
significantly larger than that predicted by classical radiative transfer
because of tunneling due to evanescent waves. Theoretical analysis of
near--field radiative transfer is mainly restricted to radiative transfer
between two half--spaces or spheres treated in the dipole approximation (very
small sphere) or proximity force approximation (radius of sphere much greater
than the gap). Sphere--sphere or sphere--plane configurations beyond the dipole
approximation or proximity force approximation have not been attempted. In this
work, the radiative energy transfer between two adjacent non--overlapping
spheres of arbitrary diameters and gaps is analyzed numerically. For spheres of
small diameter (compared to the wavelength), the results coincide with the
dipole approximation. We see that the proximity force approximation is not
valid for spheres with diameters much larger than the gap, even though this
approximation is well established for calculating forces. From the numerical
results, a regime map is constructed based on two non--dimensional length
scales for the validity of different approximations.
