  Radiative decays X --> psi(1S) + gamma and X --> psi(2S) + gamma might be
expected to have a ratio of branching fractions following the phase space
volumes ratio. However data suggest the opposite, indicating a value for R=B(X
--> psi^prime + gamma) / B(X --> psi +gamma) consistently larger than one. In
this paper we present a calculation of R for both a compact Born-Oppenheimer
cc-bar q-qbar state and a DD^* molecule. In the former case R~1 or larger is
found, a value to be confronted with forthcoming high statistics data analyses.
In the molecular picture, with D and D^* mesons described by the universal wave
function used by Voloshin, Braaten and Kusunoki, we find that R would be of
order 10^-2. A more precise experimental measure would be extremely helpful in
clarifying the true nature of the X(3872).
