  The Sun and $\alpha$ Cen A and B are the nearest stars to us. Despite the
general agreement between their models and seismic and non-seismic constraints,
there are serious problems pertaining to their interior. The good agreement
between the sound speed and base radius of the convective zone of the Sun and
the solar models is broken apart by a recent revision in solar chemical
composition. For $\alpha$ Cen A and B, however, it is not possible to fit
models with the same age and chemical composition to all seismic and
non-seismic observational constraints. At the age deduced from seismic
constraints, the luminosity ratio ($L_{\rm A}/L_{\rm B}$) of the models is
significantly lower than the ratio taken from the observed luminosities.
Enhancement of opacity as a function of temperature is one way to restore the
agreement between solar models and the Sun, but such an enhancement does not
alter the situation for $\alpha$ Cen A and B. The reason is that models of both
components are influenced in a similar manner and consequently the luminosity
ratio doesn't change much. In the present study, problems pertaining to the
interior of these three stars with a single expression for opacity enhancement
are modelled. The opacity enhancement is expressed as a function of density,
ionization degree of heavy elements (oxygen), and temperature. According to
this expression, for improvement of the models the required opacity enhancement
for $\alpha$ Cen A and B at $\log(T)$= 6.5, for example, is about 7 and 22 per
cent, respectively. The enhancement tak es place in the region in which
pressure ionization is effective, and is higher for low-mass stars than for
high-mass stars. This result seems to be a possible explanation for the serious
differences between models and observational results of cool stars.
