  Radiative decays of X(3872) with $J^{PC}=1^{++}$ are studied in the
coupled-channel approach, where the $c\bar c$ states are described by
relativistic string Hamiltonian, while for the decay channels $DD^*$ a string
breaking mechanism is used. Within this method a sharp peak and correct mass
shift of the $2 {}^3P_1$ charmonium state just to the $D^0D^{*0}$ threshold was
already obtained for a prescribed channel coupling to the $DD^*$ decay
channels. For the same value of coupling the normalized wave function (w.f.) of
X(3872) acquires admixture of the $1 {}^3P_1$ component with the w.f. fraction
$c_1=0.153 (\theta=8.8^\circ$), which increases the transition rate
$\Gamma(X(3872)\rightarrow J/\psi\gamma)$ up to 50-70 keV, making the ratio
$R=\frac{\mathcal{B}(X(3872)\rightarrow
\psi^{\prime}\gamma)}{\mathcal{B}(X(3872)\rightarrow J/\psi \gamma)}=0.8\pm
0.20 (th)$ significantly smaller, as compared to $R\simeq 5$ for X(3872) as a
purely $2 {}^3P_1$ state.
