  We report the superconducting transition temperature $T_c$ vs. thickness
$d_F$ of Ferromagnet/Superconductor (F/S) bilayers, where F is a strong $3d$
ferromagnet (Ni, Ni$_{0.81}$Fe$_{0.19}$ (Permalloy), Co$_{0.5}$Fe$_{0.5}$) and
S = Nb, taken from superfluid density measurements rather than resistivity. By
regrouping the many physical parameters that appear in theory, we show that the
effective exchange energy is determined from the F film thickness $d_F$ where
$T_c$ vs. $d_F$ begins to flatten out. Using this rearranged theory we
conclude: 1) the effective exchange energy, $E_{ex}$, is about 15 times smaller
than measured by ARPES and 5 times smaller than deduced in previous studies
similar to ours; 2) the dirty-limit coherence length, $\xi_{F}$, for Cooper
pairs in F is larger than the electron mean free path, $\ell_F$; and 3) the
$3d$-F/Nb interface is enough of a barrier that Cooper pairs typically must hit
it several times before getting through. The Py/Nb and CoFe/Nb interfaces are
more transparent than the Ni/Nb interface.
