  We introduce a new approach to the Josephson effect in SIS tunnel junctions.
The Josephson coupling energy is calculated from the overlap of real space
Cooper pair wavefunctions in two superconductors through an insulating barrier.
It is shown that the Josephson tunneling is limited by the size of the Cooper
pair and its shrinking during the tunneling. Therefore, the Josephson coupling
energy and the critical current become extremely small in high $T_{c}$
superconductors, including $MgB_{2}$. This shrinking also causes the observed
DC supercurrent in low $T_{c}$ superconductors, such as Pb and Sn, to fall off
much faster than $1/R_{n}$ for tunneling resistance $R_{n}$ above several ohms.
Consequently there is a material-dependent threshold resistance, above which
the supercurrent decreases much faster with increasing resistance. The
impurity-induced shrinking is also shown to limit the critical current.
Furthermore, the (weak) temperature dependence of the Cooper pair size is found
to contribute to the temperature dependence of the DC supercurrent.
