Improved thermonuclear rate of $^{42}$Ti($p$,$γ$)$^{43}$V and its astrophysical implication in rp-process

Accurate $^{42}$Ti($p$,$γ$)$^{43}$V reaction rates are crucial for understanding the nucleosynthesis path of the rapid capture process (rp-process) that occurs in X-ray bursts. We aim to improve the thermonuclear rates of $^{42}$Ti($p$,$γ$)$^{43}$V based on more complete resonance information and accurate direct component, together with the recently released nuclear masses data. We reevaluated the $^{42}$Ti($p$,$γ$)$^{43}$V rate by the sum of the isolated resonance contribution instead of the Hauser-Feshbach statistical model. A Monte Carlo method is used to derive the uncertainties of new rates. The nucleosynthesis simulations are performed via the NuGrid post-processing code ppn. The new rates differ from previous estimations because of using a series of updated resonance parameters and direct S-factor. Compared with the previous results from Hauser-Feshbach statistical model, which assumes compound nucleus $^{43}$V with a sufficiently high-level density in the energy region of astrophysical interest, differences exist over the entire temperature region of rp-process interest, even up to 4 orders of magnitude. Using a trajectory with a peak temperature of 1.95$\times$10$^9$ K, we perform the rp-process nucleosynthesis simulations to investigate the impact of the new rates. Our calculations show that the adoption of the new forward and reverse rates result in abundance variations for Sc and Ca by 128\% and 49\% respectively compared to the case using statistical model rates. On the other hand, the overall abundance pattern is not significantly affected. The results of using new rates also confirm that the rp-process path does not bypass the isotope $^{43}$V. It is found that the Hauser-Feshbach statistical model is inappropriate to the reaction rate evaluation for $^{42}$Ti($p$,$γ$)$^{43}$V.