The impact of $^{17}$O$+\alpha$ reaction rate uncertainties on the s-process in rotating massive stars

Massive stars are crucial to galactic chemical evolution for elements heavier than iron. Their contribution at early times in the evolution of the Universe, however, is unclear due to poorly constrained nuclear reaction rates. The competing $^{17}$O($\alpha,\gamma$)$^{21}$Ne and $^{17}$O($\alpha,n$)$^{20}$Ne reactions strongly impact weak s-process yields from rotating massive stars at low metallicities. Abundant $^{16}$O absorbs neutrons, removing flux from the s-process, and producing $^{17}$O. The $^{17}$O($\alpha,n$)$^{20}$Ne reaction releases neutrons, allowing continued s-process nucleosynthesis, if the $^{17}$O($\alpha,\gamma$)$^{21}$Ne reaction is sufficiently weak. While published rates are available, they are based on limited indirect experimental data for the relevant temperatures and, more importantly, no uncertainties are provided. The available nuclear physics has been evaluated, and combined with data from a new study of astrophysically relevant $^{21}$Ne states using the $^{20}$Ne($d,p$)$^{21}$Ne reaction. Constraints are placed on the ratio of the ($\alpha,n$)/($\alpha,\gamma$) reaction rates with uncertainties on the rates provided for the first time. The new rates favour the ($\alpha,n$) reaction and suggest that the weak s-process in rotating low-metallicity stars is likely to continue up to barium and, within the computed uncertainties, even to lead.


INTRODUCTION
Massive stars are key contributors to the abundance of chemical elements, producing elements up to the iron group via charged-particle reactions during their evolution and subsequent explosion in core-collapse supernovae, and synthesising elements heavier than iron via neutron-capture reactions. The weak s-process during core-helium (Langer et al. 1989;Prantzos et al. 1990; Baraffe et al. 1992) and to a smaller extent during shell-carbon burning (Raiteri et al. 1991;The et al. 2007) and possibly the weak r-process in the supernova explosion (Thielemann et al. 2011) produce elements up to the strontium peak in standard, non-rotating, models.
Rotation in massive star models significantly boosts the efficiency of the weak s-process, especially at low metallicity (Pignatari et al. 2008), enhancing production of elements above strontium. With rotation, the helium core contribution to the s-process was shown to increase at the expense of the carbon-burning shell. In the models of Frischknecht et al. (2016), the carbon-burning shell contribution is less than 10 % at sub-solar metallicities. During the core helium burning phase, rotation-induced mixing transports 12 C and 16 O from the He-core to the Hshell, leading to substantial overproduction of 13 C and 14 N through the CNO cycle. These isotopes are later engulfed by the growing convective He-burning core, leading to a more efficient activation of neutron sources through the 14 N(α, γ) 18 F(β+) 18 O(α, γ) 22 Ne(α, n) 25 Mg chain and the 13 C(α, n) reaction (Pignatari et al. 2008;Frischknecht et al. 2016;Choplin et al. 2018;Limongi & Chieffi 2018;Banerjee et al. 2019). Specifically, Cescutti et al. (2013) have shown that the Sr/Ba scatter at low metallicity of the observed Milky Way halo stars can be reproduced if the contribution of fast rotating massive stars is included.
The contributions of rotating massive stars to chemical evolution are subject to stellar and nuclear uncertainties. One key nuclear uncertainty is the ratio be-tween the 17 O(α, n) 20 Ne and 17 O(α, γ) 21 Ne reaction rates (Frischknecht et al. 2012;Choplin et al. 2018). At all metallicities, 16 O is abundant in both the helium-burning core and the shell carbon burning. It is a strong neutron absorber, producing copious amounts of 17 O and loss of neutron flux. The neutrons absorbed by 16 O may be recovered via the 17 O(α, n) 20 Ne reaction. Alternatively, the 17 O(α, γ) 21 Ne reaction permanently absorbs the neutron, preventing it from contributing to s-process nucleosynthesis. The 17 O(α, n) 20 Ne to 17 O(α, γ) 21 Ne ratio, therefore, determines the fraction of neutrons released and the strength of the s-process.
At He-core burning temperatures (0.2-0.3 GK), the 17 O+α reactions are dominated by resonant contributions from states between Ex = 7600 and 8100 keV (Er ≈ 250 − 750 keV) in 21 Ne. However key properties of the most important states have not been measured. These unknown properties lead to large uncertainties in the reaction rates though no previous rate estimates have provided uncertainties (Best et al. 2013;Caughlan & Fowler 1988). Here, a new calculation of the 17 O+α reaction rates is presented, providing realistic uncertainties for the first time. The rates are derived from a rigorous evaluation of excited states in 21 Ne based on a new measurement of the 20 Ne(d, p) 21 Ne reaction, together with an evaluation of existing literature.

EXISTING LITERATURE ON 21 NE LEVELS
Some experimental data on levels in 21 Ne are available from studies using a variety of populating reactions. As these works are used in the present paper to constrain the properties of observed levels, they are briefly summarised.
Direct measurements of 17 O(α, γ) 21 Ne (Best et al. 2011;Taggart et al. 2019;Williams et al. 2022) and 17 O(α, n) 20 Ne (Best et al. 2013) have been performed but were not able to observe all states within the Gamow window due to the prohibitively low cross-sections. The 17 O(α, γ) 21 Ne and 17 O(α, n) 20 Ne measurements in forward kinematics of Best et al. (2011Best et al. ( , 2013 used anodised tantalum-oxide targets with enriched 17 O and a germanium detector. Measurements of the 17 O(α, γ) 21 Ne radiative-capture reaction were performed in inverse kinematics with the DRAGON recoil separator by Taggart et al. (2019) and Williams et al. (2022).
The 17 O(α, γ) 21 Ne measurement of Best et al. (2011) observed three resonances at Er = 811, 1122, and 1311 keV. The subsequent study of the same reaction by Taggart et al. (2019) observed resonances at Er = 633, 721, 810 and 1122 keV. Some of the resonance strengths were revised by Williams et al. (2022) based on new DRAGON measurements with higher beam intensities, including an upper limit for the strength of the Er = 612-keV resonance in 17 O(α, γ) 21 Ne. Best et al. (2013) also measured the 17 O(α, ntot) 20 Ne reaction using tantalum-oxide targets. The neutrons were detected in 20 3 He counters within a polyethylene moderator. The 17 O(α, n1γ) 20 Ne reaction was measured by observation of γ rays depopulating the first-excited state of 20 Ne. The excitation function was measured between Ecm = 650 and 1860 keV. A number of resonance structures were observed and an R-matrix analysis was performed. Rates of the 17 O(α, γ) 21 Ne and 17 O(α, n) 20 Ne reactions were reported. These rates included estimated contributions from unmeasured resonances below the region scanned in the excitation function, making assumptions about unknown spins and parities in combination with known information about levels in 21 Ne (Firestone 2015).
A subsequent uncertainty analysis of the measured 17 O(α,n) 20 Ne excitation functions presented in the literature was performed by Mohr (2017), which raised some doubts about the consistency of the data presented in Best et al. (2013) in comparison to historical literature. However, the study found the largest discrepancy was in the high-energy cross section affecting the reaction rate at temperatures above 1 GK. At those energies, Mohr (2017) suggested that the cross section presented in Best et al. (2013) should be lowered by a factor of 2-3. At lower energies, though, their data appears to be in better agreement with the literature (see Fig. 5 of Mohr (2017)). Furthermore, at the temperatures of interest in the present work (0.2-0.3 GK), the reaction rate is dominated by un-observed resonances that we treat in a rigorous manner and were not considered in Mohr (2017), which focused on applying the statistical model to compute reaction rates.
Additional key information about the excited states has been extracted from earlier measurements, including scattering and transfer studies. Cohn & Fowler (1959) performed a neutron resonance-scattering experiment. Neutrons were produced by bombarding a zirconium tritide and 7 Li targets with protons. The incident neutron energies were varied by changing the bombarding energy of the proton beam. Information on excitation energies, widths, and spins and parities for 21 Ne levels above the neutron threshold was determined. The uncertainty in the neutron energy scale was less than 5 keV and the neutron energy resolution was around 13 keV. Resonances with widths as small as Γ = 6(2) keV were observed in this experiment.
Various γ-ray studies using reactions such as 18 O(α, nγ) 21 Ne (Rolfs et al. 1972;Hoffman et al. 1989), 12 C( 13 C,α) 21 Ne (Andritsopoulos et al. 1981;Hallock et al. 1975) and 16 O( 7 Li, np) 21 Ne (Thummerer et al. 2003;Wheldon, C. et al. 2005) provided additional information. Spins and parities of excited levels were assigned on the basis of observed decay branching and angular distributions. The observation of γ-ray decays from neutron-unbound levels in 21 Ne can be used in combination with other observables to rule out certain spins and parities since the neutron partial width of a state cannot exceed the γ-ray partial width by a significant factor if a γ-ray transition is observed depopulating the state.
The 20 Ne(d, p) 21 Ne single-neutron transfer reaction has previously been studied by Stanford & Quin (1980). In this experiment, the differential cross sections and analysing powers of eight states in 21 Ne were measured using a vector polarised deuteron beam on an enriched 20 Ne gas cell target. The resolution was around 100 keV, largely due to the significant energy loss through the target for the deuteron beam. Large deviations between the calculated differential cross sections from the DWBA and the experimental data were observed at higher angles. This is likely due to the strong deformation of the 20 Ne core. Inelastic excitation of deformed nuclei means that treatment with the DWBA may no longer accurately reflect the observed differential cross section (e.g. the 20 Ne(d, 3 He) 19 F study of Dudek & Edens (1971). For this reason, analysis of the strength of the 20 Ne(d, p) 21 Ne singleneutron transfer reaction should be limited to centre-of-mass angles below around 30 degrees.

EXPERIMENTAL DETAILS
The experiment was performed at the Triangle Universities Nuclear Laboratory (TUNL). Deuterons were accelerated to 14 MeV through the tandem accelerator with an energy precision of better than 1 keV. Typical currents recorded with an electron-suppressed beamstop downstream from the target were 300-575 nA, except at the most forward angle where currents were limited to around 90 nA.
The target consisted of 20 Ne implanted into a 44 µg/cm 2 carbon foil with a Ne/C abundance ratio of 4.3±0.3% determined by Rutherford Backscattering Spectrometry. The neon content was monitored with deuteron elastic scattering at θ lab = 25°after collecting 20 Ne(d, p) 21 Ne data at each angle to account for any target degradation. Uncertainties in neon target areal density were of the order of 7%. Reaction products entered the TUNL Enge split-pole spectrograph through a 0.54±0.01 msr aperture and were momentum analyzed at the focal plane. The focal-plane detector comprised of two position-sensitive gas avalanche counters, a ∆E proportional counter, and a scintillation counter (Marshall et al. 2018). Protons were identified using a ∆E-position cut. Data were collected at five laboratory angles: 10°, 15°, 20°, 25°and 38°. Additional data for background characterisation were collected using a natural carbon target at each angle.
A quadratic internal calibration using the 21 Ne states at Ex = 6609(1), 7420(1), 8069(2) and 8189(2) keV (Firestone 2015) was used to convert focal-plane position to excitation energy. The Bayesian method outlined by Marshall et al. (2018) gave realistic Ex uncertainties, explicitly including the statistical uncertainties in the fitted peak centroids and the systematic uncertainties from the focal-plane calibration. For peaks observed at multiple angles, our recommended energy was obtained from a weighted average of individual measurements. The reported energy uncertainty was conservatively constrained to be no smaller than the uncertainty at a single angle.
An example focal-plane spectrum for the astrophysically important region is shown in Fig. 1. To extract peak intensities and positions, the focal plane was divided into regions based on the behaviour of the background reactions determined from the carbon target. For more details on the peak  (Cohn & Fowler 1959;Firestone 2015) while the 7602-and 7820-keV states have unknown J π . Note that, while the 38°data are included in the plot, they are not used in the DWBA analysis.
fitting see Frost-Schenk (2020). Angular distributions were extracted from the yields for each state observed at each angle accounting for beam on target, aperture solid angle, target content and dead time, which was typically below 9%.

CALCULATION OF NEUTRON WIDTHS
The code fresco (Thompson 1988) was used to calculate differential cross-sections under the assumption of a single-step reaction, in order to assign the transferred angular momentum, n, and extract the neutron width, Γn. Calculations were performed using the first-order distorted-wave Born approximation since at these low energies the breakup effects on the deuteron in the entrance channel are minimal (Johnson & Soper 1970). Past 20 Ne(d, p) 21 Ne transfer reactions reported in Stanford & Quin (1980) have observed significant deviation between the expected differential cross section and the observed data at angles higher than θ lab = 25°degrees. For this reason, θ lab = 38°data was not used to assign n. The θ lab = 38°data were used to determine Ex and constrain the total width for observed states.
The optical model potentials for 20 Ne+d, 21 Ne+p, 20 Ne+n, n + p and 20 Ne+p were taken from An & Cai (2006), Varner et al. (1991), Madland (1997), Yahiro et al. (1986) and Menet et al. (1971), respectively. Spectroscopic factors (C 2 S) relating the DWBA and experimental cross sections: were found by normalising the calculations to the experimental data. Example differential cross sections for four states are shown in Fig. 2. Two states with known J π (the J π = 3 /2 − , Ex = 7981-keV state and J π = 3 /2 + , 8068-keV state) have been included to demonstrate that the DWBA calculations reproduce the data well. Two states with inconclusive J π assignments are also shown.
The wave-functions from fresco, φ(r), were used to compute the neutron widths, Γn as in Iliadis (1997): where P (En, a) is the penetrability of a neutron of energy En and orbital angular momentum evaluated at the radius a; µ is the reduced mass. The radius, a, was chosen to be where the 20 Ne+n wave-function is at 99% of the asymptotic value (Meyer et al. 2020) and varied for different binding energies and n. We used the weak-binding approximation, calculating at various positive binding energies and extrapolating with a quadratic function to the negative, physical neutron binding energy (Meyer et al. 2020). The uncertainties resulting from the calculations are much smaller than the uncertainty in the absolute normalisation from other sources. Table 1 summarises the spectroscopic information on relevant states in 21 Ne above the α-particle threshold. We discuss below the spin-parity assignments of astrophysically important states from which we produce physically-motivated reaction rates, with uncertainties for the first time. A comprehensive discussion on all of the states observed in this work will be presented in a forthcoming paper. The Ex = 7559-, 7820-, 8146-and 8189-keV states all have differential cross sections which are consistent with n = 1 or 2 assignments. For n = 1 the Γn are, for J π = 1 /2 − , 25(1), 20(3), 19(5) and 130(13), respectively (for J π = 3 /2 − , Γn = 14(1), 11(2), 11(3), and 74(7) keV, respectively). Resonances with Γn of this size would both have been observed in the neutron-scattering study reported in Cohn & Fowler (1959) and would additionally result in visible broadening of the states in the focal-plane spectrum. Since neither of these are observed, n = 1 is ruled out for all of these states.

EVALUATION OF 17 O+α REACTION RATES
The differential cross section of the Ex = 7602-keV state is consistent with n = 2 − 4. This state has been observed in γray data of Rolfs et al. (1972). An n = 2 assignment results in a neutron width of more than 100 eV. Based on lifetimes reported in that work, this neutron width greatly exceeds realistic γ-ray partial widths. It is, therefore, unlikely that γ-ray decay from this state would be observed if the n = 2 assignment were made. We therefore assign this level n = 3 or n = 4.
Close to Ex = 7982 keV are two states, one narrow at Ex = 7982.1(6) keV (Firestone 2015;Taggart et al. 2019), likely not observed in this experiment, and a broader one at Ex = 7981(2) keV, likely the state populated in the present work. The neutron width (Γn = 6(2) keV), spin and parity (J π = 3 /2 − ) of the Ex = 7981(2)-keV state are known from 20 Ne+n resonance scattering (Cohn & Fowler 1959). From the current data, we determine Γn = 14(5) keV. Table 1. Spectroscopic information for relevant states above the α-particle threshold in 21 Ne. Previous excitation energies from other sources are given in the second column. The neutron partial widths (Γn) are those determined in the present experiment. Widths given in bold are measured or experimentally constrained values. The Γγ = 0.20(14) eV are taken from the average of measured lifetimes in Rolfs et al. (1972) except where noted in the final column to preserve the Γn/Γγ ratio of Best et al. (2013) for resonances for which no updated information is available. Resonance information on higher resonances is taken from Best et al. (2013).   Best et al. (2013) there are no listed uncertainties. These were arbitrarily assumed to be 10% for all widths. For any resonances for which all partial widths could be estimated, the reaction rate was numerically integrated.

Ex
For resonances with no measured Γα, the reduced αparticle width was sampled from a Porter-Thomas distribution (see Sallaska et al. 2013;Longland et al. 2012, for details). The neutron widths were, where available, taken from the present work. Γγ = 0.20(14) eV was used, from the average of the lifetimes in Rolfs et al. (1972). For resonances where the Γn and Γγ are unknown, the ratio of these widths is adopted from Best et al. (2013). Importantly, we adopt the tentative J π = 7 /2 + assignment for the Er = 308-keV resonance from Firestone (2015) which reduces the contribution of this state to the 17 O(α, γ) 21 Ne reaction rate compared to Best et al. (2013) in which a J π = 5 /2 + assignment was used. We furthermore note that a 5 /2 + assignment is inconsistent with systematic trends in 21 Ne in which no other J π = 5 /2 + states at a similar excitation energy decay by γ-ray emission.
The Ex = 7749-keV state was only observed at one angle due to 16 O contamination. The peak observed in the present experiment does not appear in the background spectrum and was therefore assumed to be a 21 Ne state, but confirmation of this state with additional measurements is required. An angular distribution could not be extracted and the spin remains unconstrained. For the calculation of the rate we adopted the assumptions of Best et al. (2013).
For the 17 O(α, γ) 21 Ne reaction, the Monte-Carlo calculations show that the dominant contributions are from the resonances at Er = 308, 634 and 811keV (Ex = 7656, 7961, 7982 and 8159 keV). The 634-and 811-keV resonances have measured strengths (Williams et al. 2022;Taggart et al. 2019;Best et al. 2011). For the 17 O(α, n) 20 Ne reaction, the dominant contributions are from the Er = 401-, 472-and 721-keV resonances (Ex = 7749, 7820 and 8069 keV) with a small contribution from the Er = 633-keV resonance. The dominant contributions to the uncertainty in the reaction-rate ratio are the unknown Γα partial widths.
The 17 O(α, n) 20 Ne to 17 O(α, γ) 21 Ne reaction-rate ratio for our median rates is presented in Fig. 3. Also shown are 1σ 'high' and 'low' ratios from our work, and those from Caughlan & Fowler (1988) and Best et al. (2013). The present ratio is significantly higher than that of Best et al. between 0.25 and 0.7 GK for a number of reasons. There are some inconsistencies in the data in Table II of Best et al. (2013) (e.g. the Er = 308-keV resonance state), for which the listed resonance strengths are in disagreement with the Γn and Γγ ratio (Best 2021). We have, additionally, changed spin-parity assignments where appropriate resulting in some changes in contributions of states to the reaction rates. Lastly, we have utilised the direct 17 O(α, γ) 21 Ne measurements from DRAGON (Williams et al. 2022).
Contribution plots for the two reactions are shown in Fig.  4 (see caption for details). For the 17 O(α, γ) 21 Ne reaction, the main contribution within the astrophysically relevant region is the Er = 308-keV resonance, for which no estimate of the α-particle width is yet available. More resonances can potentially contribute to the 17 O(α, n) 20 Ne reaction, since for many of these resonances the neutron partial width is known to be much larger than the γ-ray partial width. For most resonances, therefore, the γ-ray decay is vanishingly small and these states cannot meaningfully contribute to the flux of abundances through the 17 O(α, γ) 21 Ne reaction.

ASTROPHYSICAL IMPLICATIONS
We tested the impact of the new 17 O(α, n) 20 Ne and 17 O(α, γ) 21 Ne rates on s-process nucleosynthesis using a simplified one-zone nucleosynthesis code mimicking core helium burning. Details on this code can be found in Choplin et al. (2016). The code was also used in Placco et al. (2020) to make comparisons with an observed star enriched in transiron elements. We follow the central temperature and density profiles obtained from a complete rotating 25 M stellar model at a metallicity of 10 −3 in mass fraction, computed with the Geneva stellar evolution code (Eggenberger et al. 2008). The initial composition of the one-zone code is extracted from the core of this stellar model, at core heliumburning ignition. To mimic rotation, 13 C and 14 N are injected (cf. Sect. 1) at a constant rate (expressed in M yr −1 ) during the nucleosynthesis calculation (Choplin et al. 2016). During injection, 100 times more 14 N as 13 C is injected as a typical value in full stellar models (e.g. Fig. 9 in Choplin et al. 2018). This factor of ∼ 100 corresponds to the CNO 14 N/ 13 C equilibrium ratio at T ∼ 80 MK, which is found at the bottom of the H-burning shell in massive stars. The injection rate  s-process pattern from non-rotating massive stars (black pattern).
In the left panel of Fig. 6, all one-zone models were computed with the standard injection rate of 2.5 × 10 −7 M yr −1 obtained from the calibration discussed previously. The only differences between the models shown in Fig. 6 (left panel) and the model shown by the solid red line in Fig. 5 are the rates of 17 O(α, n) 20 Ne and 17 O(α, γ) 21 Ne. The recommended reaction rates were used (fs21), as well as the limiting cases of the minimum (fs21_min) and maximum (fs21_max) (α, n)/(α, γ) ratio. These results show that the s-process in rotating massive stars is likely to continue at least to barium, and potentially up to lead for the largest (α, n)/(α, γ) reaction-rate ratio. The scatter for elements with atomic number Z > 40 goes up to about 2 dex. The bg13 and fs21_min sets have the lowest 17 O(α, n) 20 Ne/ 17 O(α, γ) 21 Ne ratios (Fig. 3) hence giving the lowest yields (green and red dotted pattern). The cf88 and fs21 sets with higher (α, n)/(α, γ) ratios substantially produce elements with Z > 55 and the fs21_max set shows the highest yields, as expected from the high (α, n)/(α, γ) ratio.
As an estimate of the impact of the new rate at very low metallicity, we include in the right panel of Fig. 6 a onezone calculation similar to the fs21 model (black pattern) but computed with an initial composition corresponding to a metallicity of 10 −5 in mass fraction (red pattern). This shows that a lower initial metallicity combined with a similar neutron production leads to a stronger overproduction of elements heavier than atomic number Z ∼ 50 at the expense of lighter elements. This is even more visible if considering a higher injection rate (green pattern) which would correspond to a more efficient rotational mixing in full stellar models. A higher injection rate at lower metallicity is not unrealistic since rotational mixing is expected to be more efficient with decreasing metallicity (e.g. Maeder & Meynet 2001). We note that contrary to the fs21 rates, the bg13 rates at lower metallicity do not lead to significant changes in the overproduction factors (compare the green patterns in the two panels of Fig. 6) Full stellar models would be required to get a more accurate estimate of the overproduction factors.

CONCLUSIONS
For the first time, available data on the energies, spins, parities and partial widths of excited states in 21 Ne have been thoroughly evaluated including a careful consideration of their ambiguities and uncertainties. In addition, states in 21 Ne have been populated via the 20 Ne(d, p) 21 Ne reaction, using an implanted 20 Ne target. Angular distributions and neutron widths for states within the Gamow window for massivestar He-core burning were extracted. By combining these data with the evaluated data, reaction rates for 17 O(α, n) 20 Ne and 17 O(α, γ) 21 Ne have been calculated using updated excitation energies, J π assignments and experimentally derived neutron widths. Using the RatesMC Monte Carlo code, uncertainties have been estimated consistently for the first time. Our recommended rates indicate enhanced s-process abundances between Sr and Pb. Production of these elements via the enhanced weak s-process in massive stars significantly shortens the timescale for the production of Pb (otherwise only produced via the main s-process in low-mass stars with much longer lifetimes) and provides an alternative to the r-process for producing elements between Fe and Ba in the early Universe. Experimental constraints on the α-widths of the key states in 21 Ne are thus crucial to allow the production of elements above barium in such massive stars, and so for the evolution of elements heavier than iron in the early Universe to be understood. Overprod. factors fs21 fs21 (lower metallicity) fs21 (lower metallicity, inj.×4) bg13 (lower metallicity) Figure 6. Overproduction factors of a one zone nucleosynthesis model mimicking the core helium burning phase of a rotating massive star at low metallicity. Left panel: the five sets of rates shown in Fig. 3 are tested: cf88 (Caughlan & Fowler 1988), bg13 (Best et al. 2013), the recommended rates derived in this work (fs21) plus the two limiting cases shown in Fig. 3. The 4 vertical lines highlight the elements Fe, Sr, Ba and Pb. Right panel: the fs21 model at a metallicity of 10 −3 in mass fraction is shown again (black pattern) together with the same model but with initial abundances corresponding to a metallicity of 10 −5 (red pattern). The blue model is computed like the red one but with an injection rate 4 times higher. The bg13 model at a metallicity of 10 −5 is also shown.
Initiative (WPI Initiative), MEXT, Japan. RH also acknowledges funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 101008324 (ChETEC-INFRA).

DATA AVAILABILITY
The nuclear physics data used in the evaluation are available from NNDC (https://www.nndc.bnl.gov) via ENS-DEF and EXFOR. The reaction rates in tabular form will be available as part of the Starlib reaction rate library (https://github.com/Starlib/Rate-Library). Other data arising from the present work are available on reasonable request to the corresponding author.