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

TL;DR

This study addresses the rp-process sensitivity near the branching nucleus $^{42}$Ti by replacing Hauser-Feshbach rates with a resonance-summed forward rate for $^{42}$Ti($p$,$\gamma$)$^{43}$V, augmented by a revised direct capture component and the latest AME2020 masses. Using updated near-threshold levels for $^{43}$V, a proton separation energy of $S_p = 105(40)$ keV, and a Monte Carlo treatment of uncertainties, the authors find large deviations from HF predictions across the rp-process temperature range, with reverse rates especially sensitive to $Q$-value uncertainties. Post-processing nucleosynthesis with the NuGrid ppn code on a $T_{{\rm max}}$ trajectory shows notable changes in specific isotopes (e.g., $^{43}$V and $^{44}$Cr) and a substantial Ca decrease alongside a Sc increase, yet the overall abundance pattern remains largely unaffected and the rp-process path still traverses $^{43}$V. The results demonstrate that HF approaches are inappropriate for this reaction, and emphasize the critical role of precise resonance data and nuclear masses for modeling X-ray burst nucleosynthesis.

Abstract

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.

Figures (5)

• Figure 1: (Color online) The fractional contributions to the total $^{42}$Ti($p$,$\gamma$)$^{43}$V reaction rate. Resonances are labeled by their center-of-mass resonance energies and the label DC refers to the direct capture process. The contribution ranges are shown as colored bands, with the band thickness representing the uncertainty of the contribution.
• Figure 2: (Color online) Ratio of previous rates $^{42}$Ti($p$,$\gamma$)$^{43}$V normalized to present recommended rates (the median rates in \ref{['tab2']}). The different patterns of lines correspond to the rates from Cyburt et al. Cyburt10; Herndl Herndl95; Rauscher & Thielemann Rauscher00; He et al. He14; Wormer et al. Wormer94
• Figure 3: (Color online) Same as Fig. \ref{['fig_2']}, but for the reverse rates.
• Figure 4: (Color online) The decayed elemental abundance distribution in rp-process for cases with different forward and reverse reaction rates for $^{42}$Ti($p$,$\gamma$)$^{43}$V. The red triangle, black square, and yellow cross correspond to cases using new rate, ths8, and rath, respectively.
• Figure 5: (Color online) The main reaction flows in rp-process for the adoption of different forward and reverse reaction rates for $^{42}$Ti($p$,$\gamma$)$^{43}$V. Panels (a), (b), (c) are for the cases using new rate, ths8 rate, and rath rate, respectively. The reaction flow is integrated over the entire X-ray burst duration. The thickness of the arrow depicts the magnitude of the reaction flux.