Precision mass measurements around {}⁸⁴Mo rule out ZrNb cycle formation in the rapid proton-capture process at type I X-ray bursts

The rapid proton-capture ($rp$-) process is one of the primary, explosive thermonuclear burning processes that drive type I X-ray bursts. A possible termination of the $rp$-process at around ${}^{84}$Mo was previously suggested by the formation of a ZrNb cycle. We report here precision mass measurements at around ${}^{84}$Mo, which have concluded the possibility of the cycle. The experiment was conducted using the multi-reflection time-of-flight spectrograph at RIKEN RI Beam Factory, and the masses of ${}^{79}$Y, ${}^{83}$Nb, ${}^{84}$Mo, ${}^{88}$Ru, and an isomer in ${}^{78}$Y were measured. For ${}^{84}$Mo, and ${}^{88}$Ru, and the isomeric state of ${}^{78}$Y, their masses are experimentally determined for the first time with uncertainties of $\delta m \approx 20~{\rm keV/c^2}$. The mass precision of ${}^{79}$Y and ${}^{83}$Nb is improved to $13~{\rm keV/c^2}$ and $9.6~{\rm keV/c^2}$, respectively. The new $\alpha$-separation energy of ${}^{84}$Mo, 1.434(83) MeV, unambiguously rules out the possibility of forming the ZrNb cycle. The X-ray burst simulation with the new masses shows that our measurements effectively remove the large final abundance uncertainties in the $A=80-90$ mass region. The new mass values improve the prediction power for the composition of the nuclear ashes in X-ray bursts.