arXiv subjects

M. Lugaro

Publications and source records attributed to M. Lugaro.

At least 19 recordsLinked to original sources

arXiv2026

Detector characterization for a new $^{12}$C+$^{12}$C reaction study at LUNA

The $^{12}$C+$^{12}$C fusion reaction plays a crucial role in stellar evolution, including the occurrence of supernova explosions, and in the synthesis of the chemical elements. However, our understanding of its cross section remains severely deficient, particularly below $E_\textrm{cm}=2.5$\,MeV, the energy range of interest for astrophysics. To address these unresolved issues, the LUNA collaboration will conduct a dedicated study of the $^{12}$C+$^{12}$C reaction at the Bellotti Ion Beam Facility (Bellotti IBF) located deep underground within the Gran Sasso National Laboratory (LNGS) in Italy. Based on the combination of passive and active shields, this campaign aims to achieve unprecedented sensitivity in measuring the cross sections of the two key reaction channels, $^{12}$C($^{12}$C,$\alpha$)$^{20}$Ne and $^{12}$C($^{12}$C,$p$)$^{23}$Na in the low-energy regime via $\gamma$-ray detection. Here, we report on a sensitivity study for the upcoming campaign with a focus on the characterization of two detectors, namely a HPGe detector and a NaI(Tl) array. Furthermore, their intrinsic contamination is thoroughly investigated since this could potentially influence the overall sensitivity. Assuming typical beam intensities of the Bellotti IBF, we will be able to investigate reaction rates significantly below 100 counts per day. In case of the $^{12}$C+$^{12}$C reaction we therefore expect to acquire experimental data well below the current limit of $E_\textrm{cm}=2.1\,$MeV. The results are supported by simulations to highlight the advantageous low-background environment, essential for high-precision nuclear astrophysics studies.

physics.ins-det↗

arXiv2025

Towards a comprehensive study of the 14N(p,g)15O astrophysical key reaction: Description of the experimental technique including novel target preparation

While the 14N(p,g)15O reaction plays a key role in the hydrogen-burning processes in various stellar conditions, its reaction rate is not known with sufficient precision. Therefore, the first scientific project at the recently launched Bellotti Ion Beam Facility of the Laboratori Nazionali del Gran Sasso was the measurement of the 14N(p,g)15O reaction cross section in the proton energy range between 250 and 1500 keV. In this paper, the experimental techniques are summarized with special emphasis on the description of solid state nitrogen target production and characterization. The first results of the reaction yield measured at 55 deg detection angle are also presented.

physics.ins-det↗

arXiv2025

Production of radioactive $^{22}$Na in core-collapse supernovae: the Ne-E(L) component in presolar grains and its possible consequences on supernova observations

Presolar graphite grains carry the isotopic signatures of their parent stars. A significant fraction of presolar graphites shows isotopic abundance anomalies relative to solar for elements such as O, Si, Mg and Ca, which are compatible with nucleosynthesis in core-collapse supernovae (CCSNe). Therefore, they must have condensed from CCSN ejecta before the formation of the Sun. Their most puzzling abundance signature is the $^{22}$Ne-enriched component Ne-E(L), interpreted as the effect of the radioactive decay of $^{22}$Na ($T_{1/2}$ = 2.6 years). Previous works have shown that if H is ingested into the He shell and not fully destroyed before the explosion, the CCSN shock in the He shell material produces large $^{22}$Na amounts. Here we focus on such CCSN models, showing a radioactive $^{26}$Al production compatible with grains measurements, and analyze the conditions of $^{22}$Na nucleosynthesis. In these models, $^{22}$Na is mostly made in the He shell, with a total ejected mass varying between 2.6$\times$10$^{-3}$ M$_{\odot}$ and 1.9$\times$10$^{-6}$ M$_{\odot}$. We show that such $^{22}$Na may already impact the CCSN light curve 500 days after the explosion, and at later stages it can be the main source powering the CCSN light curve for up to a few years before the $^{44}$Ti decay becomes dominant. Based on the CCSN yields above, the 1274.53 keV $\gamma$-ray flux due to $^{22}$Na decay could be observable for years after the first CCSN light is detected, depending on the distance. This makes CCSNe possible sites to detect a $^{22}$Na $\gamma$-ray signature consistently with the Ne-E(L) component found in presolar graphites. Finally, we discuss the potential contribution from the $^{22}$Na decay to the galactic positron annihilation rate.

astro-ph.SR↗

arXiv2025

Status and future directions for direct cross-section measurements of the 13C(a,n)16O reaction for astrophysics

The 13C(a,n)16O reaction is the main neutron source of the s-process taking place in thermally pulsing AGB stars and it is one of the main candidate sources of neutrons for the i-process in the astrophysical sites proposed so far. Therefore, its rate is crucial to understand the production of the nuclei heavier than iron in the Universe. For the first time, the LUNA collaboration was able to measure the 13C(a,n)16O cross section at Ec.m.=0.23-0.3 MeV drastically reducing the uncertainty of the S(E)-factor in the astrophysically relevant energy range. In this paper, we provide details and critical thoughts about the LUNA measurement and compare them with the current understanding of the 13C(a,n)16O reaction in view of future prospect for higher energy measurements. The two very recent results (from the University of Notre Dame and the JUNA collaboration) published after the LUNA data represent an important step forward. There is, however, still room for a lot of improvement in the experimental study of the 13C(a,n)16O reaction, as emphasized in the present manuscript. We conclude that to provide significantly better constraints on the low-energy extrapolation, experimental data need to be provided over a wide energy range, which overlaps with the energy range of current measurements. Furthermore, future experiments need to focus on the proper target characterisation, the determination of neutron detection efficiency having more nuclear physics input, such as angular distribution of the 13C(a,n)16O reaction below Ea<0.8 MeV and study of nuclear properties of monoenergetic neutron sources and/or via the study of sharp resonances of 13C(a,n)16O. Moreover, comprehensive, multichannel R-matrix analysis with a proper estimate of uncertainty budget of experimental data are still required.

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arXiv2025

Exploring giant barium stars: $^{12}\rm{C}/^{13}\rm{C}$ ratio and elemental abundances of carbon, nitrogen, and oxygen

Barium (Ba) stars belong to binary systems that underwent mass transfer events. As a consequence, their envelopes were enriched with material synthesized in the interiors of their evolved companions via \textit{slow} neutron-capture nucleosynthesis, the $s$-process. As post-interacting binaries, Ba stars figure as powerful tracers of the $s$-process. In this study, we conduct a classical local thermodynamic equilibrium analysis for a sample of 180 Ba giant stars to find complementary insights for the $s$-process, in form of elemental abundances of carbon, nitrogen, and oxygen, as well as the $^{12}\rm{C}/^{13}\rm{C}$ ratio. We found carbon abundances systematically larger than those observed in normal giants, with [C/Fe] ratios ranging within from $-0.30$ to $+0.60$~dex. As expected, the [C/Fe] ratios increase for lower metallicity regimes and are strongly correlated with the average $s$-process abundances. Nitrogen abundances have a flat behavior around $\rm{[N/Fe]}\sim+0.50$~dex and are moderately correlated with sodium abundances. Except for HD~107541, the entire sample shows $\rm{C/O}<1$. We found $^{12}\rm{C}/^{13}\rm{C}<20$ for $\sim80\%$ of the sampled stars and $^{12}\rm{C}/^{13}\rm{C}>60$ for three objects.

astro-ph.SR↗

arXiv2025

An AGB star as the source of the abundance pattern of hyper-metal-poor star HE 1327-2326

Abridged. HE 1327-2326 (HE 1327), with [Fe/H]=-5.2, is one of the most metal-poor stars detected and a candidate to be the offspring of the first stars. Numerous efforts have been made to match its abundance pattern. However, no model satisfactorily explains its entire surface chemical composition. The high CNO pattern with [N/Fe]>[C/Fe]>[O/Fe], the light element 'slide' (between Na and Si), and the presence of Sr and Ba in HE 1327 is reminiscent of those asymptotic giant branch (AGB) stars that undergo third dredge-up, hot bottom burning, and s-processing, suggesting that AGBs may have been progenitors of the star. We assume that, where HE 1327 formed, the interstellar medium was well-mixed, and adopt an initial stellar composition based on the observed chemical evolution of the early universe. We calculated models of hyper-metal-poor AGB stars and compared their yields to the observed abundances of HE 1327. Our 3 Msun models match 13 of the 14 measured elements in HE1327. They are also consistent with the seven elements with upper limits. The only discrepancy is O, underproduced by 0.5-1.0 dex. Unlike the SN models, the AGB models also match Sr and Ba. Our model predicts high abundances of P and Pb, which would be useful in testing the AGB scenario. We propose that HE 1327 is the oldest known object that shows nucleosynthetic evidence of the first AGB stars. With lifetimes as short as 200 Myr, these stars may have formed and polluted the universe very early. Recent Pop III star formation simulations support their formation, and their strong N production is qualitatively consistent with recent JWST observations showing high N/O ratios just 440 Myr after the Big Bang. Importantly, our results also suggest that the interstellar medium may have shown some degree of homogeneity and mixing even at these early epochs.

astro-ph.SR↗

arXiv2025

Improved direct measurement of low-energy resonances in the $^{21}$Ne(p,$\gamma$)$^{22}$Na reaction

In the nova temperature range, 0.1 GK $< T <$ 0.4 GK, several low-energy resonances dominate the $^{21}$Ne(p,$\gamma$)$^{22}$Na reaction rate, which is currently affected by large uncertainties. We present a high-precision study of the resonances at $E^{\rm{lab}}_{\rm{r}}$ = 127.3, 271.4, 272.3, 291.5, and 352.6 keV, measured directly at the Laboratory for Underground Nuclear Astrophysics in Italy. The strengths of the 127.3, 271.4, and 291.5 keV resonances are consistent with previous measurements within 1$\sigma$. However, for the 272.3 keV and 352.6 keV resonances, we report strength values of (129.9 $\pm$ 5.8) meV and (14.9 $\pm$ 0.8) meV, respectively, more than a factor of 1.5 higher than literature values. In addition, we report on new branching ratios for the 127.3, 272.3, and 352.6 keV resonances, leading to updated decay schemes. Finally, we present a revised thermonuclear reaction rate and investigate its impact on the NeNa nucleosynthesis.

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arXiv2025

The Occurrence and Impact of Carbon-Oxygen Shell Mergers in Massive Stars

In their final stages before undergoing a core-collapse supernova, massive stars may experience mergers between internal shells where carbon (C) and oxygen (O) are consumed as fuels for nuclear burning. This interaction, known as a C-O shell merger, can dramatically alter the internal structure of the star, leading to peculiar nucleosynthesis and potentially influencing the supernova explosion and the propagation of the subsequent supernova shock. Our understanding of the frequency and consequences of C-O shell mergers remains limited. This study aims to identify for the first time early diagnostics in the stellar structure which will lead to C-O shell mergers in more advanced stages. We also assess their role in shaping the chemical abundances in the most metal poor stars of the Galaxy. We analyze a set of 209 of stellar evolution models available in the literature, with different initial progenitor masses and metallicities. We then compare the nucleosynthetic yields from a subset of these models with the abundances of odd-Z elements in metal-poor stars. We find that the occurrence of C-O shell mergers in stellar models can be predicted with good approximation based on the outcomes of the central He burning phase, specifically, from the CO core mass ($\rm M_{CO}$) and the $\rm ^{12}C$ central mass fraction ($\rm X_{C12}$): 90$\%$ of models with a C-O merger have $\rm X_{C12}< 0.277$ and $\rm M_{CO}< 4.90 M_{\odot}$, with average values $\rm M_{CO} = 4.02 M_{\odot}$ and $\rm X_{C12}= 0.176$. Additionally, we confirm that the Sc-rich and K-rich yields from models with C-O mergers would solve the long-standing underproduction of these elements in massive stars. Our results emphasize the crucial role of C-O shell mergers in enriching the interstellar medium, particularly in the production of odd-Z elements.

astro-ph.SR↗

arXiv2025

The aluminium-26 distribution in a cosmological simulation of a Milky Way-type Galaxy

Context. The 1.8 MeV gamma-rays corresponding to the decay of the radioactive isotope Al-26 (with a half-life of 0.72 Myr) have been observed by the SPI detector on the INTEGRAL spacecraft and extensively used as a tracer of star formation and current nucleosynthetic activity in the Milky Way Galaxy. Further information is encoded in the observation related to the higher Al-26 content found in regions of the Galaxy with the highest line-of-sight (LoS) velocity relative to an observer located in the Solar System. However, this feature remains unexplained. Aims. We ran a cosmological "zoom-in" chemodynamical simulation of a Milky Way-type galaxy, including the production and decays of radioactive nuclei in a fully self-consistent way. We then analyzed the results to follow the evolution of Al-26 throughout the lifetime of the simulated galaxy to provide a new method for interpreting the Al-26 observations. Methods. We included the massive star sources of Al-26 in the Galaxy and its radioactive decay into a state-of-the-art galactic chemical evolution model, coupled with cosmological growth and hydrodynamics. This approach allowed us to follow the spatial and temporal evolution of the Al-26 content in the simulated galaxy. Results. Our results are in agreement with the observations with respect to the fact that gas particles in the simulation with relatively higher Al-26 content also have the highest LoS velocities. On the other hand, gas particles with relatively lower Al-26 content (i.e., not bright enough to be observed) generally display the lowest LoS velocities. However, this result is not conclusive because the overall rotational velocity of our simulated galaxy is higher than that observed for cold CO gas in the Milky Way Galaxy. Furthermore, we found no significant correlation between gas temperature, rotational velocity, and Al-26 content at any given radius. We also [...]

astro-ph.GA↗

arXiv2025

Impact of $\textit{T}$- and $\rho$-dependent decay rates and new (n,$\gamma$) cross sections on the $\textit{s}$ process in low-mass AGB stars

We study the impact of nuclear input related to weak-decay rates and neutron-capture reactions on predictions for the $s$ process in AGB stars. We provide the first database of surface abundances and stellar yields of the isotopes heavier than iron from the $Monash$ models. We run nucleosynthesis calculations with the $Monash$ post-processing code for 7 stellar structure evolution models of low-mass AGB stars with 3 different sets of nuclear input. The reference set has constant decay rates and represents the set used in the previous $Monash$ publications. The second set contains the temperature and density dependence of $\beta$ decays and electron captures based on the default rates of NETGEN. In the third set, we update 92 neutron-capture rates based on reevaluated experimental cross sections from the ASTRAL. We compare and discuss the predictions of each set relative to each other in terms of isotopic surface abundances and total stellar yields. We also compare results to isotopic ratios measured in presolar stardust SiC grains from AGB stars. The new sets of models resulted in a $\sim$66% solar $s$-process contribution to the $p$-nucleus $\mathrm{^{152}Gd}$, confirming that this isotope is predominantly made by the $s$ process. The nuclear input updates resulted in predictions for the $\mathrm{^{80}Kr/^{82}Kr}$ ratio in the He intershell and surface $\mathrm{^{64}Ni/^{58}Ni}, \mathrm{^{94}Mo/^{96}Mo}$ and $\mathrm{^{137}Ba/^{136}Ba}$ ratios more consistent with the corresponding ratios measured in stardust, however, the new predicted $\mathrm{^{138}Ba/^{136}Ba}$ ratios are higher than the typical values of the stardust SiC grain data. The W isotopic anomalies are in agreement with data from analysis of other meteoritic inclusions. We confirm that the production of $\mathrm{^{176}Lu}$ and $\mathrm{^{205}Pb}$ is affected by too large uncertainties in their decay rates from NETGEN.

astro-ph.SR↗

arXiv2025

A Comparative Analysis of R-Matrix Fitting: ${}^{12}$C$(p,\gamma)$${}^{13}$N as Test Case

In nuclear astrophysics, the accurate determination of nuclear reaction cross sections at astrophysical energies is critical for understanding stellar evolution and nucleosynthesis. This study focuses on the $^{12}$C($p, \gamma$)$^{13}$N reaction, which takes part in the CNO cycle and is significant for determining the $^{12}$C/$^{13}$C ratio in stellar interiors. Data from various studies, including recent LUNA measurements, reveal high discrepancies in cross section values, underscoring the need for robust fitting approaches. Utilizing the R-matrix theory, we compare different frequentist and Bayesian methodologies for estimating reaction cross sections and their uncertainties. The analysis evaluates the strengths and weaknesses of different statistical techniques, highlighting the importance of systematic uncertainty treatment and the estimate of covariance matrix estimation to enhance the reliability and reproducibility of uncertainty estimates in nuclear astrophysics.

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arXiv2024

High-temperature $^{205}$Tl decay clarifies $^{205}$Pb dating in early Solar System

Radioactive nuclei with lifetimes on the order of millions of years can reveal the formation history of the Sun and active nucleosynthesis occurring at the time and place of its birth. Among such nuclei whose decay signatures are found in the oldest meteorites, $^{205}$Pb is a powerful example, as it is produced exclusively by slow neutron captures (the s process), with most being synthesized in asymptotic giant branch (AGB) stars. However, making accurate abundance predictions for $^{205}$Pb has so far been impossible because the weak decay rates of $^{205}$Pb and $^{205}$Tl are very uncertain at stellar temperatures. To constrain these decay rates, we measured for the first time the bound-state $\beta^-$ decay of fully ionized $^{205}$Tl$^{81+}$, an exotic decay mode that only occurs in highly charged ions. The measured half-life is 4.7 times longer than the previous theoretical estimate and our 10% experimental uncertainty has eliminated the main nuclear-physics limitation. With new, experimentally backed decay rates, we used AGB stellar models to calculate $^{205}$Pb yields. Propagating those yields with basic galactic chemical evolution (GCE) and comparing with the $^{205}$Pb/$^{204}$Pb ratio from meteorites, we determined the isolation time of solar material inside its parent molecular cloud. We find positive isolation times that are consistent with the other s-process short-lived radioactive nuclei found in the early Solar System. Our results reaffirm the site of the Sun's birth as a long-lived, giant molecular cloud and support the use of the $^{205}$Pb--$^{205}$Tl decay system as a chronometer in the early Solar System.

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arXiv2024

Characterization of the LUNA neutron detector array for the measurement of the 13C(a,n)16O reaction

We introduce the LUNA neutron detector array developed for the investigation of the 13C(a,n)16O reaction towards its astrophysical s-process Gamow peak in the low-background environment of the Laboratori Nazionali del Gran Sasso (LNGS). Eighteen 3He counters are arranged in two different configurations (in a vertical and a horizontal orientation) to optimize neutron detection effciency, target handling and target cooling over the investigated energy range Ea;lab = 300 - 400 keV (En = 2.2 - 2.6 MeV in emitted neutron energy). As a result of the deep underground location, the passive shielding of the setup and active background suppression using pulse shape discrimination, we reached a total background rate of 1.23 +- 0.12 counts/hour. This resulted in an improvement of two orders of magnitude over the state of the art allowing a direct measurement of the 13C(a,n)16O cross-section down to Ea;lab = 300 keV. The absolute neutron detection efficiency of the setup was determined using the 51V(p,n)51Cr reaction and an AmBe radioactive source, and completed with a Geant4 simulation. We determined a (34+-3) % and (38+-3) % detection efficiency for the vertical and horizontal configurations, respectively, for En = 2.4 MeV neutrons.

physics.ins-det↗

arXiv2024

First direct measurement of the 64.5 keV resonance strength in $^{17}$O(p,$\gamma$)$^{18}$F reaction

The CNO cycle is one of the most important nuclear energy sources in stars. At temperatures of hydrostatic H-burning (20 MK $<$ T $<$ 80 MK) the $^{17}$O(p,$\gamma$)$^{18}$F reaction rate is dominated by the poorly constrained 64.5~keV resonance. Here we report on the first direct measurements of its resonance strength and of the direct capture contribution at 142 keV, performed with a new high sensitivity setup at LUNA. The present resonance strength of $\omega\gamma_{(p, \gamma)}$\textsuperscript{bare} = (30 $\pm$ 6\textsubscript{stat} $\pm$ 2\textsubscript{syst})~peV is about a factor of 2 higher than the values in literature, leading to a $\Gamma$\textsubscript{p}\textsuperscript{bare} = (34 $\pm$ 7\textsubscript{stat} $\pm$ 3\textsubscript{syst})~neV, in agreement with LUNA result from the (p,$\alpha$) channel. Such agreement strengthen our understanding of the oxygen isotopic ratios measured in red giant stars and in O-rich presolar grains.

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arXiv2024

Barium stars as tracers of s-process nucleosynthesis in AGB stars III. Systematic deviations from the AGB models

Barium (Ba) stars help to verify asymptotic giant branch (AGB) star nucleosynthesis models since they experienced pollution from an AGB binary companion and thus their spectra carry the signatures of the slow neutron capture process (s process). For 180 Ba stars, we searched for AGB stellar models that match the observed abundance patterns. We employed three machine learning algorithms as classifiers: a Random Forest method, developed for this work, and the two classifiers used in our previous study. We studied the statistical behaviour of the s-process elements in the observational sample to investigate if the AGB models systematically under- or overpredict the abundances observed in the Ba stars and show the results in the form of violin plots of the residuals between spectroscopic abundances and model predictions. We find a significant trend in the residuals that implies an underproduction of the elements Nb, Mo, and Ru in the models relative to the observations. This may originate from a process (e.g. the intermediate neutron-capture process, i process) at the metallicity of the Ba stars not yet included in the AGB models. Correlations are found between the residuals of these elements, suggesting a common origin for the deviations. In addition, there is a weak metallicity dependence of their residuals. The s-process temperatures derived with the [Zr/Fe] - [Nb/Fe] thermometer have an unrealistic value for the majority of our stars. The most likely explanation is that at least a fraction of these elements are not produced in a steady-state s process, and instead may be due to processes not included in the AGB models. The mass distribution of the identified models confirms that our sample of Ba stars was polluted by low-mass AGB stars. Most of the matching AGB models require low accreted mass, but a few systems with high accreted mass are needed to explain the observations. (abridged)

astro-ph.SR↗

arXiv2024

Tungsten in barium stars

Classical barium stars are red giants that received from their evolved binary companions material exposed to the \textit{slow} neutron-capture nucleosynthesis, i.e., the $s$-process. Such a mechanism is expected to have taken place in the interiors of Thermally-Pulsing Asymptotic Giant Branch (TP-AGB) stars. As post-interacting binaries, barium stars figure as powerful tracers of the $s$-process nucleosynthesis, evolution of binary systems, and mechanisms of mass transfer. The present study is the fourth in a series of high-resolution spectroscopic analyses on a sample of 180 barium stars, for which we report tungsten (W, $Z=74$) abundances. The abundances were derived from synthetic spectrum computations of the W\,{\sc i} absorption features at 4\,843.8~\AA\ and 5\,224.7~\AA. We were able to extract abundances for 94 stars; the measured [W/Fe] ratios range from $\sim0.0$ to $2.0$ dex, increasing with decreasing of metallicity. We noticed that in the plane [W/Fe] versus [$s$/Fe] barium stars follow the same trend observed in post-AGB stars. The observational data were also compared with predictions of the {\sc fruity} and Monash AGB nucleosynthesis models. These expect values between $-0.20$ and $+0.10$ dex for the [W/hs] ratios, whereas a larger spread is observed in the program stars, with [W/hs] ranging from $-0.40$ to $+0.60$ dex. The stars with high [W/hs] ratios may represent evidence for the operation of the intermediate neuron-capture process at metallicities close to solar.

astro-ph.SR↗

arXiv2023

First measurement of the low-energy direct capture in 20Ne(p, {\gamma})21Na and improved energy and strength of the Ecm = 368 keV resonance

The $\mathrm{^{20}Ne(p, \gamma)^{21}Na}$ reaction is the slowest in the NeNa cycle and directly affects the abundances of the Ne and Na isotopes in a variety of astrophysical sites. Here we report the measurement of its direct capture contribution, for the first time below $E\rm_{cm} = 352$~keV, and of the contribution from the $E^{\rm }_{cm} = 368$~keV resonance, which dominates the reaction rate at $T=0.03-1.00$~GK. The experiment was performed deep underground at the Laboratory for Underground Nuclear Astrophysics, using a high-intensity proton beam and a windowless neon gas target. Prompt $\gamma$ rays from the reaction were detected with two high-purity germanium detectors. We obtain a resonance strength $\omega \gamma~=~(0.112 \pm 0.002_{\rm stat}~\pm~0.005_{\rm sys})$~meV, with an uncertainty a factor of $3$ smaller than previous values. Our revised reaction rate is 20\% lower than previously adopted at $T < 0.1$~GK and agrees with previous estimates at temperatures $T \geq 0.1$~GK. Initial astrophysical implications are presented.

nucl-ex↗

arXiv2023

New proton-capture rates on carbon isotopes and their impact on the astrophysical $^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio

The ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio is a significant indicator of nucleosynthesis and mixing processes during hydrogen burning in stars. Its value mainly depends on the relative rates of the ${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ and ${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$ reactions. Both reactions have been studied at the Laboratory for Underground Nuclear Astrophysics (LUNA) in Italy down to the lowest energies to date ($E_\mathrm{c.m.} = 60\,\mathrm{keV}$) reaching for the first time the high energy tail of hydrogen burning in the shell of giant stars. Our cross sections, obtained with both prompt $\gamma$-ray detection and activation measurements, are the most precise to date with overall systematic uncertainties of $7-8\%$. Compared with most of the literature, our results are systematically lower, by $25\%$ for the ${}^{12}\mathrm{C}(p,\gamma){}^{13}\mathrm{N}$ reaction and by $30\%$ for ${}^{13}\mathrm{C}(p,\gamma){}^{14}\mathrm{N}$. We provide the most precise value up to now of $(3.6 \pm 0.4)$ in the $20-140\,\mathrm{MK}$ range for the lowest possible ${}^{12}\mathrm{C}/{}^{13}\mathrm{C}$ ratio that can be produced during H burning in giant stars.

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