  In the framework of the quark delocalization color screening model, we
investigate the meson-meson interaction in the fully light four-quark system .
The calculation of the effective potentials of all the $S-$wave states shows
that for most states the interaction between two vector mesons is attractive;
the one between a pseudoscalar meson and a vector meson is repulsive or weakly
attractive; and the one between two pseudoscalar mesons is always repulsive.
However, there is still some exception. The interaction of the $IJ=00$ $\pi\pi$
channel is attractive, while the one of the $IJ=02$ $\phi\phi$ channel is
repulsive. So it is difficult to use the $S-$wave $\phi\phi$ state to explain
the $X(2239)$ at present calculation. The $S-$wave $\rho\rho$ states are more
likely to be resonance states, which are worthy of investigating in future
work. The study of the contribution of each interaction term shows that both
the one-gluon exchange and the kinetic energy interaction are important in the
interaction between two mesons. The study of the variation of the
delocalization parameter indicates that the contribution of the kinetic energy
relates to the intermediate-range attraction mechanism in QDCSM, which is
achieved by the quark delocalization.
