Revised ${}^{45}$V($p,\gamma$)${}^{46}$Cr reaction rate and its impact on the production of ${}^{44}$Ti in core-collapse supernovae

Abstract

The thermonuclear ${}^{45}$V($p,\gamma$)${}^{46}$Cr reaction is the primary leakage pathway from the ${}^{44}$Ti--${}^{45}$V quasi-equilibrium cluster during $\alpha$-rich freeze-out in core-collapse supernovae (CCSN), governing the final abundance of the $\gamma$-ray-emitting isotope ${}^{44}$Ti. A recent high-resolution $\gamma$-ray study [C. Cousins \textit{et al.}, Phys. Rev. Lett. 136, 252701 (2026)] identified ten previously unknown low-spin proton-unbound states in ${}^{46}$Cr, enabling the first experimentally constrained ${}^{45}$V($p,\gamma$)${}^{46}$Cr reaction rate using the AME2020 mass excess, $\text{ME}{(}^{46}\text{Cr})=-29472(11)$~keV. Here, we adopt the four-fold more precise CSRe mass excess $\text{ME}{(}^{46}\text{Cr})=-29477.2(2.6)$~keV [M.~Wang \textit{et al.}, Phys. Rev. C \textbf{106}, L051301 (2022)] to recalculate the reaction rate. Including proton capture on the ground and first two excited states of ${}^{45}$V alongside new shell-model proton spectroscopic factors, we reduce mass-related rate uncertainties to a subdominant level. The revised rate is up to 69% higher than that of Cousins \textit{et al.} at $\alpha$-rich freeze-out temperatures ($T\simeq 1.5$--$2$~GK). CCSN nucleosynthesis calculations show this revised rate increases the ejected ${}^{44}$Ti yield by $\sim$26% in a $20M_{\odot }$ model compared to The \textit{et al.} [ApJ \textbf{504}, 500 (1998)], while causing negligible changes for the SN~1987A trajectory. We demonstrate that ${}^{44}$Ti production sensitivity is dictated by the ejecta electron fraction ($Y_e$): the reaction significantly affects proton-rich ejecta ($Y_e\approx 0.50$) but has little impact on neutron-rich ejecta ($Y_e\approx 0.496$), where lower free-proton abundances suppress reaction flow. This reconciles conflicting results from past sensitivity studies.