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First strength measurements of low-energy resonances in the $^{45}$ Sc( $p,\gamma$ ) $^{46}$ Ti reaction and its astrophysical implications

This paper reports the first direct measurements of resonance strengths for the $^{45}$ Sc( $p,\gamma$ ) $^{46}$ Ti reaction at low energies, which are used to derive an updated thermonuclear reaction rate with significant implications for understanding nucleosynthesis in massive stars, novae, and supernovae.

Original authors: R. S. Sidhu, R. J. deBoer, J. Görres, M. Wiescher, W. N. Catford, C. Dembski, C. R. Jones, Ó. E. López-López, G. Lotay, K. Manukyan, M. Matney, J. O'Neill, J. Rufino, A. T. Sanchez, M. Williams, L. Zi

Published 2026-10-05

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CC BY 4.0

Original authors: R. S. Sidhu, R. J. deBoer, J. Görres, M. Wiescher, W. N. Catford, C. Dembski, C. R. Jones, Ó. E. López-López, G. Lotay, K. Manukyan, M. Matney, J. O'Neill, J. Rufino, A. T. Sanchez, M. Williams, L. Zimmer

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

Stars are not merely distant points of light; they are vast, churning furnaces where the very building blocks of the universe are forged. Inside these stellar cores, atomic nuclei collide and fuse, creating heavier elements from lighter ones in a process known as nucleosynthesis. For decades, scientists have understood that this cosmic alchemy follows specific pathways, but for certain heavy elements, the map has remained blurry. One such puzzle involves the element scandium, specifically a stable version called scandium-45. In the violent environments of dying stars, this nucleus is supposed to capture a proton and transform into titanium-46, acting as a crucial gateway that allows the creation of even heavier elements like iron. However, the speed at which this transformation happens has been a matter of guesswork, relying on theoretical estimates rather than direct observation. Without knowing exactly how fast this reaction occurs, astronomers cannot accurately predict how much scandium or titanium is produced in stellar explosions, leaving gaps in our understanding of how the chemical elements that make up our world came to be.

To solve this mystery, a team of researchers turned to a massive particle accelerator at the University of Notre Dame, a machine capable of firing beams of protons at incredible speeds. Their goal was to watch the scandium-45 nucleus catch a proton in real time and measure exactly how likely that event is to happen. They focused on a specific range of energies, shooting protons at a thin sheet of scandium metal and listening for the unique signal of gamma rays—high-energy flashes of light—that are emitted when the new titanium nucleus forms. By carefully adjusting the energy of the proton beam, the scientists were able to tune in to specific "resonances," which are like musical notes where the reaction happens much more easily. In this study, they directly measured the strength of six of these resonances for the first time, finding them at specific energy levels between 917.4 and 1257.5 kiloelectronvolts. They also identified the combined effect of several weaker, overlapping resonances at lower energies, providing a much clearer picture of the reaction's behavior than ever before.

The results of these measurements allowed the team to calculate a new, more accurate rate for how fast this reaction proceeds under the extreme temperatures found in stars. When they compared their new data with previous computer models, they found that the theoretical predictions were generally in the right ballpark, but the new experimental data provided the necessary precision to confirm them. This confirmation is vital because it tells us that the "bottleneck" in the production of heavy elements is not as unpredictable as once feared. The study also looked at what happens in different types of stellar events, such as the explosive deaths of massive stars and the thermonuclear runaways on the surfaces of white dwarfs known as novae. In these environments, the newly measured reaction rates help explain how elements are distributed in the debris thrown out into space. For instance, the data helps clarify the production of radioactive isotopes that could be detected by future space telescopes, offering a way to directly observe the inner workings of stellar explosions.

While the team successfully measured the most prominent resonances, they also had to look at the lower energy range where the reaction is too weak to see directly. For these lower energies, they relied on data from other types of nuclear experiments to estimate the reaction strength, acknowledging that some uncertainty remains in this specific region. Nevertheless, the combination of their direct measurements and these estimates provides a complete and updated recipe for how scandium turns into titanium in the cosmos. This work does not just fill a gap in a chart; it refines the story of how the universe builds its heaviest elements. By pinning down the speed of this single reaction, scientists can now model the chemical evolution of stars with greater confidence, bringing us one step closer to understanding the precise conditions that led to the formation of the iron in our blood and the titanium in our bones.

Technical Summary: First Strength Measurements of Low-Energy Resonances in the 45Sc(p, γ)46Ti Reaction

Problem Statement
The thermonuclear reaction rate for $^{45}\text{Sc}(p, \gamma)^{46}\text{Ti}$ is a critical input for nucleosynthesis models in massive stars (hydrostatic oxygen/silicon burning and convective C-O shell mergers), core-collapse supernovae (CCSNe), and oxygen-neon (ONe) novae. In these environments, the reaction acts as a bottleneck regulating the flow of material from the Sc-Ti mass region toward the Fe-Ni region and influences the production of radioactive isotopes such as $^{47}\text{Sc}$ and $^{44}\text{Ti}$ . Historically, reaction rates for this process have relied on statistical model calculations (e.g., TALYS, NON-SMOKER) due to a lack of experimental data. These models assume high level densities that may not be valid near the closed $Z=20$ shell, and previous experimental studies have failed to report absolute resonance strengths for the low-energy resonances relevant to astrophysical temperatures. Consequently, significant uncertainties remain regarding the reaction flow and the synthesis of elements beyond $^{40}\text{Ca}$ .

Methodology
The authors performed direct measurements of the $^{45}\text{Sc}(p, \gamma)^{46}\text{Ti}$ reaction using the 5 MV St. ANA Pelletron accelerator at the Nuclear Science Laboratory, University of Notre Dame.

Experimental Setup: Proton beams with intensities $<5\,\mu\text{A}$ were directed onto a fresh, vacuum-evaporated $^{45}\text{Sc}$ target ( $\approx 50\,\mu\text{g/cm}^2$ ) mounted on a tantalum backing. The target was water-cooled and positioned at $45^\circ$ relative to the beam.
Detection: Gamma rays were detected using a high-purity germanium (HPGe) detector. Measurements were conducted in both "close geometry" ( $d=1.7$ cm) for resonance scans and "far geometry" ( $d=25.4$ cm) for yield measurements to minimize summing effects.
Energy Range: The study covered a laboratory proton energy range of 526–1275 keV.
Analysis:
- Resonance Scans: Resonance strengths were determined by scanning beam energies and observing the yield of the secondary 889 keV $\gamma$ -ray transition (from the first excited state of $^{46}\text{Ti}$ to the ground state).
- Strength Extraction: For resonances above 900 keV, individual strengths were extracted by fitting the yield curves with an empirical function derived from the Breit-Wigner formalism. For energies below 900 keV, where broad structures of unresolved resonances were observed, integrated resonance strengths were reported.
- Low-Energy Estimation: For energies below the direct measurement threshold (526 keV), resonance strengths were estimated using transfer-reaction data ( $^{45}\text{Sc}(^3\text{He}, d)^{46}\text{Ti}$ ) and nuclear structure predictions (single-particle formalism with shell-model spectroscopic factors).
- Rate Calculation: An updated thermonuclear reaction rate was calculated by summing contributions from 11 directly measured resonances and 7 estimated low-energy resonances.

Key Contributions and Results

First Direct Strength Measurements: The paper reports the first direct measurements of resonance strengths for six resonances at $E_{\text{lab}} = 917.4, 1026.0, 1031.1, 1049.7, 1059.4,$ and $1257.5$ keV.
Integrated Strengths: Integrated resonance strengths were determined for five broad structures at $E_{\text{lab}} = 555, 630, 700, 761,$ and $871$ keV.
Low-Energy Constraints: Using transfer-reaction data, the authors estimated strengths for seven additional resonances below 526 keV, providing a more complete dataset for astrophysical rate calculations.
Updated Reaction Rate: A new thermonuclear reaction rate was derived. The authors found that:
- At low temperatures ( $T < 0.5$ GK, relevant to ONe novae), the rate is dominated by the low-energy resonances inferred from transfer data.
- At higher temperatures ( $T > 0.5$ GK, relevant to CCSNe and C-O shell mergers), the rate is governed by the higher-energy resonances measured directly in this work.
- The experimentally derived rate agrees with statistical model predictions (TALYS, NON-SMOKER) within a factor of 3 up to $T \approx 1.2$ GK. At higher temperatures ( $T \gtrsim 1.2$ GK), the experimental rate falls below statistical predictions, likely because the statistical models include unresolved states not individually identified in the experiment.

Significance and Claims
The authors claim that this work provides the first experimental constraints on the resonance strengths of the $^{45}\text{Sc}(p, \gamma)^{46}\text{Ti}$ reaction in the astrophysically relevant energy range. The results suggest that the level density in the $^{46}\text{Ti}$ compound nucleus is sufficiently high that a single-resonance-based reaction rate aligns well with statistical model predictions within the stated uncertainties. This supports the validity of statistical models for this mass region while highlighting the necessity of experimental data to constrain the rate in specific temperature regimes, particularly for ONe novae where low-energy resonances dominate. The authors note that further precise measurements of excitation energies and spin-parity assignments for the low-energy states are required to reduce uncertainties in the ONe nova reaction rate.

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