Effects of Hoyle state de-excitation on $\nu p$-process nucleosynthesis and Galactic chemical evolution

The partcle-induced hadronic de-excitation of the Hoyle state in $^{12}$C induced by inelastic scattering in a hot and dense plasma can enhance the triple-alpha reaction rate. This prevents the production of heavy nuclei within the neutrino-driven winds of core-collapse supernovae and raises a question as to the contribution of proton-rich neutrino-driven winds as the origin of $p$-nuclei in the solar system abundances. Here we study $\nu p$-process nucleosynthesis in proton-rich neutrino-driven winds relevant to the production of $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ by considering such particle-induced de-excitation. We show that the enhancement of the triple-alpha reaction rate induced by neutron inelastic scattering hardly affects the $\nu p$-process, while the proton scattering contributes to the nucleosynthesis in proton-rich neutrino-driven winds at low temperature. The associated enhanced triple-alpha reaction rate decreases the production of $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ in a wind model of ordinary core-collapse supernovae. On the other hand, the abundances of these $p$-nuclei increase in an energetic hypernova wind model. Hence, we calculate the galactic chemical evolution of $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ by taking account of both contributions from core-collapse supernovae and hypernovae. We show that the hypernova $\nu p$-process can enhance the calculated solar isotopic fractions of $^{92,94}\mathrm{Mo}$ and $^{96,98}\mathrm{Ru}$ and make a significant impact on the GCE of $p$-nuclei regardless of the particle-induced Hoyle state de-excitation.