$\beta$ decay of N=Z isotopes $^{96}$Cd, $^{98}$In and $^{100}$Sn

The $\beta$-decay properties of the N=Z isotopes $^{96}$Cd, $^{98}$In and $^{100}$Sn have been studied. The isotopes were produced at the National Superconducting Cyclotron Laboratory (NSCL) by fragmenting a 120 MeV/u $^{112}$Sn primary beam in a Be target. The resulting radioactive beam was filtered in the A1900 and the newly commissioned Radio Frequency Fragment Separator to achieve a purity level suitable for decay studies. The observed production cross sections of these isotopes are lower than expected by factors of 10 to 30. The $^{100}$Sn cross section is 0.25(15) pb, in sharp contrast with the 120 pb lower limit established at 63 MeV/u incident energy of the same primary beam. The half-life of $^{96}$Cd, which was the last experimentally unknown waiting point half-life of the astrophysical rp-process, is 1.03$^{+0.24}_{-0.21}$ s. The implications of the experimental T$_{1/2}$ value of $^{96}$Cd on the abundances predicted by the rp-process and the origin of A=96 isotopes such as $^{96}$Ru are explored. The measured half-lives of $^{98}$In are 47(13) ms and 0.66(40) s, and 0.55$^{+0.70}_{-0.31}$ s for $^{100}$Sn. They are in agreement with previous determinations and lead to an improved precision.