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Critical currents $I_c$ were measured in Superconducting - normal -superconducting SNS c-axis junctions, where S was optimally doped$YBa_2Cu_3O_{7-\delta}$ below $T_c$ (90 K) and N was $La_{2-x}Sr_xCuO_4$ aboveits $T_c$ ($<$25 K) but in the pseudogap regime. $I_c$ was measured versustemperature T in junctions with various N-barrier thicknesses $d$ and dopinglevels $x$. From the proximity effect relation $I_c(T)\proptoexp[-d/\xi_N(T)]$, the normal coherence length $\xi_N(T)$ of N was extractedand plotted versus T. Besides finding a long range proximity effect as reportedalso by others, we found a crossing at about 55 K above which$\xi_N(x=0.1)>\xi_N(x=0.18)]$. This unexpected result where junctions withlower carrier density in the barrier have higher conductance, is attributed tothe presence of pre-formed pairs in the pseudogap regime of the cupratebarrier. Our data yields a new phase diagram of $\xi_N(T,x)$ whose contours ofconstant $\xi_N$ follow the trend of the superconducting dome of$La_{2-x}Sr_xCuO_4$ above its $T_c$, with $\xi_N$ enhancement in the underdopedregime above 55 K.

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Pairing and the phase diagram of the normal coherence length  $\xi_N(T,x)$ above $T_c$ of $La_{2-x}Sr_xCuO_4$ thin films probed by the  Josephson effect