  We consider a mechanism to create the $\eta - \eta'$ mass difference by the
gluon anomaly in a squeezed vacuum. We find that the mass shift of the $\eta_0$
governing this mass difference is determined by the magnetic part of the gluon
condensate. For the squeezed vacuum this magnetic part coincides with the total
gluon condensate, so that we get a relation between the gluon condensate and
the mass shift of the $\eta_0$ as a function of the strong coupling constant
$\alpha_s$. The values of the gluon condensate obtained through this relation
are compared with the value by Shifman, Vainshtein and Zakharov and the recent
update values by Narison.
