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

By incorporating a more precise mass measurement of $^{46}$ Cr and new spectroscopic factors to revise the $^{45}$ V( $p,\gamma$ ) $^{46}$ Cr reaction rate, this study demonstrates that the resulting 69% increase in the rate significantly boosts $^{44}$ Ti yields in proton-rich core-collapse supernova ejecta, thereby reconciling previous conflicting sensitivity analyses.

Original authors: R. S. Sidhu, Y. Luo, C. Sarma, M. Wiescher, X. Xu

Published 2026-08-19

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CC BY 4.0

Original authors: R. S. Sidhu, Y. Luo, C. Sarma, M. Wiescher, X. Xu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

When a massive star runs out of fuel, it does not simply fade away; it collapses under its own weight and then explodes in a cataclysm known as a core-collapse supernova. These violent events are the universe's primary forges, creating and scattering the heavy elements that make up planets and life itself. Among the many radioactive atoms born in the explosion, one is particularly valuable to astronomers: titanium-44. This isotope acts as a cosmic clock. Because it decays over a period of about fifty-nine years, it shines brightly in gamma rays for decades after the explosion, allowing scientists to peer directly into the heart of young supernova remnants like Cassiopeia A. By measuring how much titanium-44 is ejected, researchers can test their theories about how these stars explode and what happens to the matter inside them. However, predicting exactly how much of this element is produced is difficult because it depends on a complex chain of nuclear reactions that occur in the first few seconds of the explosion, where the environment is hot, dense, and filled with free protons and alpha particles.

For years, scientists have known that a specific reaction involving vanadium-45 and a proton is a critical bottleneck in the production of titanium-44. In the searing heat of the explosion, atoms are constantly being built up and torn apart. Titanium-44 can capture a proton to become vanadium-45. If that vanadium-45 captures another proton, it turns into chromium-46 and effectively leaks out of the titanium-44 production line, reducing the final amount of titanium-44 that survives. The speed of this leakage depends on the precise mass of the chromium-46 atom and the properties of the energy states within it. Until recently, the mass of chromium-46 was known with a margin of error that left a significant gap in our understanding. A team of researchers has now closed that gap. By using a more precise measurement of the chromium-46 mass, combined with new calculations of how protons interact with excited states of vanadium-45, they have recalculated the speed of this leakage reaction. Their work reveals that the reaction happens faster than previously thought, but only under very specific conditions found in some supernovae, while having almost no effect in others.

The researchers began by addressing a fundamental uncertainty: the exact weight of the chromium-46 nucleus. Previous studies relied on a mass value that had an uncertainty of about eleven kiloelectron volts. Using a storage ring in Lanzhou, China, a different group had recently measured this mass with four times better precision, pinning it down to a value with an uncertainty of only 2.6 kiloelectron volts. The authors of this new study adopted this superior value. They then combined it with recent experimental data that had identified ten previously unknown energy states in chromium-46. These states act as stepping stones for the reaction. To get a complete picture, the team did not just look at the reaction happening on the ground state of vanadium-45; they also calculated how protons would be captured by the first and second excited states of vanadium-45, which are slightly higher in energy but still present in the hot explosion environment. They used advanced computer models to determine the likelihood of these interactions, known as spectroscopic factors, and found that these new calculations significantly altered the predicted speed of the reaction.

The result of these combined improvements is a revised reaction rate that is up to sixty-nine percent faster than the previous best estimate over the temperature range where titanium-44 is formed. This means that in the right conditions, material leaks out of the titanium-44 production zone much more efficiently than earlier models suggested. However, the story does not end with a simple increase in speed. The researchers then ran detailed simulations of supernova explosions to see how this faster reaction affected the final amount of titanium-44 ejected into space. They tested two different types of stellar explosions: one from a twenty-solar-mass star and another based on the famous supernova 1987A. In the twenty-solar-mass model, which produces an environment rich in free protons, the faster reaction rate caused a significant drop in the final titanium-44 yield, reducing it by about twenty-six percent compared to older predictions. This happens because the abundance of free protons allows the reaction to proceed rapidly, pulling material away from titanium-44.

In stark contrast, when the team applied the same new reaction rate to the model of supernova 1987A, the result was almost unchanged. The amount of titanium-44 produced remained the same regardless of whether they used the old rate or the new, faster one. The reason lies in the composition of the exploding material. The ejecta from supernova 1987A is slightly more neutron-rich, meaning it has fewer free protons available to drive the reaction. Without enough protons, the leakage pathway remains blocked, and the speed of the reaction becomes irrelevant. This finding resolves a long-standing puzzle in the field. Previous studies had reached conflicting conclusions, with some suggesting the reaction was vital and others finding it unimportant. The new work shows that both sides were correct, but only for different types of explosions. The sensitivity of titanium-44 production to this reaction is governed entirely by the electron fraction of the ejecta, a measure of how proton-rich the environment is.

This discovery refines our understanding of how supernovae distribute elements across the universe. It confirms that the nuclear physics governing these explosions is precise enough to be measured and calculated, but it also highlights that the outcome depends heavily on the specific conditions of the dying star. The uncertainty in the reaction rate is no longer driven by the mass of the nucleus, which is now known with high precision, but rather by the theoretical models used to describe how protons interact with the nucleus. Future progress will require even more precise measurements of these interaction probabilities and the decay rates of the excited states. For now, the study provides a clearer map of the nuclear pathways that light up the cosmos, showing that the amount of titanium-44 we see today is a direct fingerprint of the proton-richness of the explosion that created it.

Technical Summary: Revised 45V(p, γ)46Cr Reaction Rate and Its Impact on 44Ti Production in Core-Collapse Supernovae

Problem Statement
The thermonuclear reaction $^{45}\text{V}(p, \gamma)^{46}\text{Cr}$ serves as the primary leakage pathway from the $^{44}\text{Ti}$ – $^{45}\text{V}$ quasi-statistical equilibrium (QSE) cluster during the $\alpha$ -rich freeze-out phase in core-collapse supernovae (CCSNe). Consequently, this reaction rate is a critical determinant of the final abundance of the $\gamma$ -ray emitting isotope $^{44}\text{Ti}$ , a key diagnostic for explosive nucleosynthesis. Previous sensitivity studies yielded conflicting conclusions regarding the impact of this reaction on $^{44}\text{Ti}$ yields. A recent study by Cousins et al. (2026) provided the first experimentally constrained rate by identifying ten new proton-unbound states in $^{46}\text{Cr}$ . However, that calculation relied on the AME2020 mass excess of $^{46}\text{Cr}$ ($ME = -29472(11)$ keV), which introduced a significant uncertainty in the proton separation energy ( $S_p$ ) and, by extension, the resonance energies. Furthermore, the Cousins et al. rate did not account for proton capture on the thermally populated excited states of the $^{45}\text{V}$ target.

Methodology
This work recalculates the $^{45}\text{V}(p, \gamma)^{46}\text{Cr}$ reaction rate by integrating three primary improvements:

Improved Mass Measurement: The authors adopt the more precise mass excess of $^{46}\text{Cr}$ ($ME = -29477.2(2.6)$ keV) measured via B $\rho$ -defined isochronous mass spectrometry (B $\rho$ -IMS) at the CSRe storage ring. This reduces the uncertainty in the proton separation energy by a factor of 3.9 compared to the AME2020 value used previously.
Inclusion of Excited States: The calculation explicitly includes proton capture on the first ( $E_x = 56.7$ keV) and second ( $E_x = 56.8$ keV) excited states of $^{45}\text{V}$ , which are in thermal equilibrium during $\alpha$ -rich freeze-out.
New Shell-Model Calculations: New shell-model calculations were performed using the KShell code with GXPF1A and SDPF-MU effective interactions to determine the proton spectroscopic factors ( $C^2S$ ) for transitions from the ground and excited states of $^{45}\text{V}$ to the resonant states in $^{46}\text{Cr}$ .

The total reaction rate was computed as the incoherent sum of resonant contributions (from ten identified proton-unbound states) and non-resonant direct capture. The resonance strengths were calculated using the Breit-Wigner formalism, incorporating the updated mass values, new spectroscopic factors, and $\gamma$ -decay widths adopted from Cousins et al.

Key Results

Revised Reaction Rate: The updated reaction rate is up to 69% higher than the Cousins et al. rate over the temperature range relevant to $\alpha$ -rich freeze-out ( $T_9 \approx 1.5–2$ GK). This increase is driven primarily by the newly calculated shell-model spectroscopic factors, followed by the inclusion of excited-state captures and the improved mass value.
Uncertainty Analysis: The use of the precise $^{46}\text{Cr}$ mass reduces the mass-related contribution to the reaction-rate uncertainty to a subdominant level. The remaining uncertainty is now dominated by the proton spectroscopic factors (uncertainty factor $\sim 1.7$ ) and the $\gamma$ -decay widths (uncertainty factor $\sim 1.5$ ).
Nucleosynthesis Impact (20 M $_\odot$ Model): In post-processing calculations for a 20 M $_\odot$ CCSN model, the revised rate increases the ejected $^{44}\text{Ti}$ yield by approximately 26% relative to the rate of The et al. (1998). However, compared to the Cousins et al. rate, the revised rate results in a lower $^{44}\text{Ti}$ yield ( $1.13^{+0.21}_{-0.23} \times 10^{-4}$ M $_\odot$ vs. $1.25^{+0.19}_{-0.29} \times 10^{-4}$ M $_\odot$ ) due to the enhanced leakage from the $^{44}\text{Ti}$ – $^{45}\text{V}$ cluster caused by the higher reaction rate.
Nucleosynthesis Impact (SN 1987A Model): For the SN 1987A progenitor model, the revised rate produces a negligible change in the $^{44}\text{Ti}$ yield ( $\sim 1.31 \times 10^{-4}$ M $_\odot$ ), with variations of less than 0.004% compared to other rates.
Electron Fraction Dependence: The study identifies that the sensitivity of $^{44}\text{Ti}$ production to the $^{45}\text{V}(p, \gamma)^{46}\text{Cr}$ reaction is governed by the electron fraction ( $Y_e$ ) of the ejecta. Significant sensitivity occurs only in proton-rich ejecta ( $Y_e \approx 0.50$ ) where free-proton abundance is sufficient to sustain the reaction flow. In more neutron-rich ejecta ( $Y_e \approx 0.496$ ), the low free-proton abundance suppresses the reaction, rendering the final $^{44}\text{Ti}$ yield insensitive to the reaction rate.

Significance
The paper claims to reconcile previously conflicting conclusions regarding the sensitivity of $^{44}\text{Ti}$ production to the $^{45}\text{V}(p, \gamma)^{46}\text{Cr}$ reaction. The authors demonstrate that the apparent discrepancy between studies (e.g., The et al. vs. Subedi et al.) arises from differences in the electron fraction distributions of the specific supernova models used. By establishing that the reaction's impact is conditional on the proton richness of the ejecta, this work clarifies the astrophysical role of the reaction. Additionally, the reduction of mass-related uncertainties establishes that future improvements in the reaction rate must focus on experimental constraints of the nuclear structure inputs (spectroscopic factors and $\gamma$ -widths) rather than mass measurements.

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