Cross Sections of the $^{83}$Rb(p,$\gamma)^{84}$Sr and $^{84}$Kr(p,$\gamma)^{85}$Rb Reactions at Energies Characteristic of the Astrophysical $\gamma$ Process

We have measured the cross section of the $^{83}$Rb(p,$\gamma)^{84}$Sr radiative capture reaction in inverse kinematics using a radioactive beam of $^{83}$Rb at incident energies of 2.4 and $2.7 A$ MeV. Prior to the radioactive beam measurement, the $^{84}$Kr(p,$\gamma)^{85}$Rb radiative capture reaction was measured in inverse kinematics using a stable beam of $^{84}$Kr at an incident energy of $2.7 A$ MeV. The effective relative kinetic energies of these measurements lie within the relevant energy window for the $\gamma$ process in supernovae. The central values of the measured partial cross sections of both reactions were found to be $0.17-0.42$ times the predictions of statistical model calculations. Assuming the predicted cross section at other energies is reduced by the same factor leads to a slightly higher calculated abundance of the $p$ nucleus $^{84}$Sr, caused by the reduced rate of the $^{84}$Sr($\gamma$,p)$^{83}$Rb reaction derived from the present measurement.