Oðn; αÞ 13 C, is important for a wide range of applications in nuclear physics. In nuclear astrophysics, the low-energy cross section determines the neutron production in a variety of stellar environments and is critical for modeling the chemical evolution of our Universe. In asymptotic giant branch (AGB) stars, the mixing of hydrogen into the helium burning shell triggers the 12 Cðp; γÞ 13 Nðβ þ νÞ 13 C sequence producing 13 C to feed the 13 Cðα; nÞ 16 O reaction. The strength of this neutron source depends on hydrodynamic intershell mixing conditions, the so-called carbon pocket, and the strength of the reaction. Thus, it determines the neutron flux for the slow-neutron-capture or s process, which is responsible for the synthesis of approximately half the heavy, naturally occurring, elements [1]. It is also necessary for modeling neutron production in AGB stars by comparing the abundance distribution of s-process elements [2]. At higher energies, it plays an important role in determining the neutron flux for intermediate neutron capture (i process) in carbon enhanced metal poor stars [3], where the neutron production occurs in a deep, convective, hot, environment in which 13 N is mixed into the hotter regions of the hydrogen burning shell before its decay, and the subsequent 13 Cðα; nÞ 16 O reaction occurs at much higher temperatures [4,5].

In some large scale neutrino detector measurements, such as period 1 of the Kamioka Liquid Scintillator Antineutrino Detector (KamLAND), the 13 Cðα; nÞ 16 O reaction is a main background source, competing with signals from geoneutrinos, in the determination of neutrino mixing ν 1 -ν 2 [6][7][8]. The reaction is induced by α particles released through the natural decay chains in impurities in the liquid scintillator material. Thus, the background depends on both actinide impurities and the neutron branching in the deexcitation channel. There are two ways the 13 Cðα; nÞ 16 O reaction can mimic these interactions. First, through the production of high energy neutrons from the 13 Cðα; n 0 Þ 16 O reaction that inelastically scatters on 12 C producing a prompt γ ray followed by a neutron capture. Second, the 13 Cðα; n 1 Þ 16 O reaction [9,10] produces an E0 decay, e þ =e-followed by neutron capture, which is indistinguishable from inverse β decay. Therefore, experimentally determining the partial cross section to each of the individual final states is essential.

Additionally, neutron transport simulations play an important role in the nuclear energy sector. They are based on cross section evaluations like ENDF=B, where the 16 Oðn; αÞ 13 C reaction is given high priority [11][12][13]. These simulations are necessary to estimate the flux of neutrons traversing from reactor or other neutron environments, to determine the energy distribution, calculate shielding and moderator requirements, and assess the lifetime of reactor fuel. Monte Carlo simulations of neutron transport are critical for studying the response of neutron detectors employed in low-, intermediate-, and high-energy physics as well as for estimating the activity induced in different detectors by intense neutron fields. The latter is an important aspect for neutron dosimetry.

Past experimental studies have focused on reaction cross section measurements via detection of thermalized neutrons using "4π" moderator counters [14][15][16][17][18]. This measurement technique has the advantage of high detection efficiency, and, in principle, insensitivity to the angular distributions of the outgoing neutrons. However, it also has its drawbacks. With no sensitivity to outgoing neutron energy, backgrounds are more difficult to discriminate. Simulations have shown that when the moderator size is too small and the detector configuration is not optimized, the efficiency can be highly dependant on neutron energy and the neutron angular distribution [19]. The branching ratios to different final states and angular distributions are often unknown, and thus, the yields cannot be accurately converted to cross sections [20,21]. For these reasons, Harissopulos et al. [17] significantly underestimated their uncertainties, causing large inconsistencies to develop between the ENDF/B-VII.1 and ENDF/B-VIII.0 evaluations [12,22].

In order to resolve these discrepancies, new measurements were performed at the University of Notre Dame Nuclear Science Laboratory using the 5 MV Stable ion Accelerator for Nuclear Astrophysics [23]. Helium beams were produced over a laboratory energy range from E α ¼ 0.8 to 6.5 MeV, with typical beam intensities of ≈10 eμA on target. The energy of the accelerator was calibrated using resonances in the 13 Cðα; nÞ 16 O reaction that correspond to those observed in n þ 16 O time-of-flight measurements [24]. Targets were fabricated at the Institute for Nuclear Research (ATOMKI) in Debrecen, Hungary. Enriched (99%) 13 C powder was evaporated onto a 0.5 mm Ta backing, which also served as a beam stop, creating a thin layered reference target of 10.3ð6Þ μg=cm 2 . The target thickness was determined by measuring the energy loss over the narrow resonance in the 13 Cðα; nÞ 16 O reaction at E α ¼ 1.05 MeV. To mitigate deterioration from beam heating, the target backing was water-cooled throughout the experiment and the beam was rastered over the target area. A liquid-nitrogen cooled and electrically isolated copper pipe, biased to -300 V, was mounted in the target chamber to serve as both as a cold trap and electron suppressor.

The reference target was used to perform the majority of the measurements, accumulating ≈0.8 C of charge, and no deterioration was observed above the ≈5% level. A target of half this thickness was used to scan over narrow resonances in order to reduce the distortion from energy averaging effects. After ≈0.46 C of accumulated charge, the thin target was found to degrade by ≈15%. The targets were similar to those used by Ciani et al. [25].

The measurement of differential cross sections was accomplished using the Oak Ridge National Laboratory Deuterated Spectroscopic Array (ODeSA) [26], used previously in Refs. [9,27,28]. The array consisted of nine deuterated scintillators mounted on a swing arm, which was rotated to two different positions, with an offset of 7.5°, in order to map 18 point angular distributions between 0°and 157.5°. The response matrix for the ODeSA detectors [26] was measured at the Edwards Accelerator Laboratory at Ohio University using time-of-flight and the well-known 9 Beðd; nÞ 10 B thick-target neutron yield [29], which was determined relative to measurements with a 235 U fission chamber [30]. In this way, direct current beams could be used, optimizing run times by way of higher beam intensities and simplified beam preparation. Neutron spectroscopy was accomplished by unfolding the light response spectra using the calibrated detector response matrix and an unfolding algorithm [31,32]. The data are provided in the Supplemental Material [33] and are shown in Fig. 1.

Because of the positive Q value of the 13 Cðα; n 0 Þ 16 O (þ2.2 MeV) reaction, the above method was ideal, able to achieve better spectral resolution than time-of-flight for the target-to-detector distance of ≈63 cm [32]. The Ta backing produced very little background with peaks from the 19 Fðα; nÞ 22 Ne reaction observed only at beam energies in excess of E α ≈ 3 MeV. The large difference in Q value (Q ¼ -1.95 MeV) ensured that the background was well separated, clearly distinguishable with the ≈6% energy resolution of the spectrum unfolding. However, this background source, and the unfolding resolution, prevented the extraction of excited state cross sections from the data.

The most significant corrections to the present data came from neutron scattering on the target backing, holder, and other beam components very close to the target. These corrections were simulated using MCNP6 [34], where a detailed model of the setup was created. These corrections were most significant at 0°and 90°, up to 30%, but were less than 10%, otherwise. The corrections were verified through comparison to previously measured neutron PHYSICAL REVIEW LETTERS 132, 062702 (2024) angular distributions on the thick target plateau of the E α ¼ 1.05 MeV resonance [35] and angular distributions of

Liðp; nÞ 7 Be reaction [36,37]. These corrections proved to be the most significant source of systematic uncertainty as summarized in Table I.

The main framework used for interpreting 13 C þ α and

O þ n data over the resolved resonance region has been the R matrix [39,40]. A comprehensive analysis has been developed by the Los Alamos National Laboratory group for the ENDF=B evaluations [11,12] using the energy dependant analysis (EDA) code [41] and several other R-matrix studies have also been published [16,[42][43][44]. The R-matrix parameters from the EDA fit were transformed into the Brune parametrization [45] and used as initial fit parameters for the AZURE2 [46,47] analysis described here. These parameter conversions have been tested previously in Thompson et al. [48].

Up to ≈2.6 MeV, the EDA parameters give a good reproduction of the present measurements owing to the previous measurements of Walton et al. [35], but at higher energies, the agreement worsens considerably because of the much more limited amount of data [49][50][51]. The recent measurements of Prusachenko et al. [52] provide 36 additional angular distributions, which have not yet been incorporated into the ENDF=B evaluation. The level of agreement between the present data and the EDA calculation is demonstrated by a comparison of the 0°cross section and two representative angular distributions in Fig. 2. The discrepancies highlight the improvement the present data can have on future evaluations.

In Febbraro et al. [9], it was confirmed that above ≈5 MeV the transitions to the excited states in 16 O quickly become significant contributors to the total reaction cross section. The present data give an improved mapping of the high energy 13 Cðα; n 0 Þ 16 O cross section up to 6.5 MeV. A Legendre fit was used to integrate the differential data to compare with the reaction cross section data of Brandenburg et al. [53] as shown in Fig. 3. The Brandenburg et al. [53] measurements should be more accurate than previous measurements as the efficiency of the detector was designed to minimize its sensitivity to neutron energy and angular distribution. Over the region where only the ground state transition is energetically accessible, the present data are ≈15% higher than those of Brandenburg et al. [53], 10% higher than those of Febbraro et al. [9], and ≈15% lower than those of Prusachenko et al. [52], in good agreement when these systematic uncertainties are considered. The data of Prusachenko et al. [52] do show some differences in their energy dependence, but this is likely due to energy resolution effects resulting from their thicker target.

Recently, measurements have been extended to lower energies [54,55], now directly overlapping a portion of the Gamow window for helium burning temperatures. Even so, an extrapolation of the cross section is still required to cover the full range of astrophysical interest. Using the R matrix, the uncertainty can be more fully characterized as the framework provides the means for combining direct measurements with asymptotic normalization coefficients Cross Section (barns) (ANC) from α-transfer measurements. This has become particularly important given the advances in ANC determinations [56][57][58][59] and the Trojan horse method [60].

To demonstrate the effect that this data has on the extrapolation of the S factor, the uncertainty range estimated in deBoer et al. [61] is indicated in Fig. 4. This uncertainty comes from the systematic differences in the absolute cross sections of Refs. [17,18] compared to those of Refs. [14][15][16] and differences in extrapolation techniques. The data of the present work and that of Gao et al. [55] both strongly favor an absolute cross section consistent with the measurements of Refs. [14][15][16]. Thus, the assertion is made that this source of systematic uncertainty has been greatly reduced.

An R-matrix fit was performed that utilized the consistent data of Refs. [15,16,54,55] up to E c:m: ¼ 2.6 MeV as well as the 16 Oðn; totalÞ data of Refs. [24,62]. A Bayesian uncertainty analysis was then performed using the code BRICK [63]. In addition to providing more detailed information about the parameter and cross section uncertainties through the posterior probability distributions, this methodology provided a natural way for the sub-Coulomb ANC and its uncertainty for the near threshold state [59] to be included directly as a prior. It should be noted that, as found in Gao et al. [55], a consistent value for the ANC is found even if a uniform prior is assumed. The systematic uncertainties of each data set are also considered assuming Gaussian priors and that no correlations exist. The resulting best fit gives an ≈10% uncertainty over the Gamow energy range. This analysis is similar to that performed in Ciani et al. [54].

To demonstrate their affect, the new data were then introduced into the fit. It should be noted that while the angle integrated cross section, obtained through a Legendre fit of the angular distributions has been shown for comparison in Fig. 4, the actual fit used the differential data directly. This resulted in a further reduction in the S-factor uncertainty to ≈5% over the Gamow energy range. The two fits are largely consistent with one another over the Gamow energy range, indicating the consistency of the present data set with previous ones, but the reduced uncertainty demonstrates the significant additional constraint that the differential cross section data have on the R-matrix model. The differential data are especially significant given the presence of broad, overlapping, resonances that produce additional angle dependent interference. This highlights the very complementary nature of extremely low-energy angleintegrated measurements, that require high detection efficiency, with high resolution differential measurements, that can only be made where the cross section is larger. It must be emphasized, however, that this fit only represents the potential effect of the present data and that a full evaluation of all of the data must still be made to fully characterize the uncertainties. Further details on the fit can be found in the Supplemental Material [33].

The 13 Cðα; nÞ 16 O reaction is one of the main sources of neutrons for s-process nucleosynthesis, it is a significant background in many kiloton-scale, low-event-rate, neutrino and dark matter detectors, and its inverse 16 Oðn; αÞ 13 C is needed to model neutron induced α-particle production for a variety of applications. The realization of additional sources of uncertainty in past measurements has prompted new experimental techniques. In this work, we report new high-resolution measurements, in both energy and angle, for the 13 Cðα; n 0 Þ 16 O cross section, using the state-of-theart ODeSA array, resulting in 714 distinct angular distributions that encompass the energy ranges applicable for many applications. To demonstrate the effect of these new data on the extrapolation of the low-energy S factor, fits were combined with Bayesian uncertainty estimation, which indicate the potential for a substantial reduction in the uncertainty over the entire Gamow energy range.