A method based on Monte Carlo techniques is presented for evaluating thermonuclear reaction rates. We begin by reviewing commonly applied procedures and point out that reaction rates that have been reported up to now in the literature have no rigorous statistical meaning. Subsequently, we associate each nuclear physics quantity entering in the calculation of reaction rates with a specific probability density function, including Gaussian, lognormal and chi-squared distributions. Based on these probability density functions the total reaction rate is randomly sampled many times until the required statistical precision is achieved. This procedure results in a median (Monte Carlo) rate which agrees under certain conditions with the commonly reported recommended "classical" rate. In addition, we present at each temperature a low rate and a high rate, corresponding to the 0.16 and 0.84 quantiles of the cumulative reaction rate distribution. These quantities are in general different from the statistically meaningless "minimum" (or "lower limit") and "maximum" (or "upper limit") reaction rates which are commonly reported. Furthermore, we approximate the output reaction rate probability density function by a lognormal distribution and present, at each temperature, the lognormal parameters miu and sigma. The values of these quantities will be crucial for future Monte Carlo nucleosynthesis studies. Our new reaction rates, appropriate for bare nuclei in the laboratory, are tabulated in the second paper of this series (Paper II). The nuclear physics input used to derive our reaction rates is presented in the third paper of this series (Paper III). In the fourth paper of this series (Paper IV) we compare our new reaction rates to previous results.
We compare our Monte Carlo reaction rates (see Paper II of this series) to previous results that were obtained by using the classical method of computing thermonuclear reaction rates. For each reaction, the comparison is presented using two types of graphs: the first shows the change in reaction rate uncertainties, while the second displays our new results normalized to the previously recommended reaction rate. We find that the rates have changed significantly for almost all reactions considered here. The changes are caused by (i) our new Monte Carlo method of computing reaction rates (see Pap…
The nuclear physics input used to compute the Monte Carlo reaction rates and probability density functions that are tabulated in the second paper of this series (Paper II) is presented. Specifically, we publish the input files to the Monte Carlo reaction rate code RatesMC, which is based on the formalism presented in the first paper of this series (Paper I). This data base contains overwhelmingly experimental nuclear physics information. The survey of literature for this review was concluded in November 2009.
We analyze enhancement of thermonuclear fusion reactions due to strong plasma screening in dense matter using a simple electron drop model. The model assumes fusion in a potential that is screened by an effective electron cloud around colliding nuclei (extended Salpeter ion-sphere model). We calculate the mean field screened Coulomb potentials for atomic nuclei with equal and nonequal charges, appropriate astrophysical S factors, and enhancement factors of reaction rates. As a byproduct, we study analytic behavior of the screening potential at small separations between the reactants. In this m…
The problem of estimating non-resonant astrophysical S-factors and thermonuclear reaction rates, based on measured nuclear cross sections, is of major interest for nuclear energy generation, neutrino physics, and element synthesis. Many different methods have been applied in the past to this problem, almost all of them based on traditional statistics. Bayesian methods, on the other hand, are now in widespread use in the physical sciences. In astronomy, for example, Bayesian statistics is applied to the observation of extra-solar planets, gravitational waves, and type Ia supernovae. However, nu…
Numerical values of charged-particle thermonuclear reaction rates for nuclei in the A=14 to 40 region are tabulated. The results are obtained using a method, based on Monte Carlo techniques, that has been described in the preceding paper of this series (Paper I). We present a low rate, median rate and high rate which correspond to the 0.16, 0.50 and 0.84 quantiles, respectively, of the cumulative reaction rate distribution. The meaning of these quantities is in general different from the commonly reported, but statistically meaningless expressions, "lower limit", "nominal value" and "upper lim…
Rigorous statistical methods for estimating thermonuclear reaction rates and nucleosynthesis are becoming increasingly established in nuclear astrophysics. The main challenge being faced is that experimental reaction rates are highly complex quantities derived from a multitude of different measured nuclear parameters (e.g., astrophysical S-factors, resonance energies and strengths, particle and gamma-ray partial widths). We discuss the application of the Monte Carlo method to two distinct, but related, questions. First, given a set of measured nuclear parameters, how can one best estimate the …
An update of the NACRE compilation [Angulo et al., Nucl. Phys. A 656 (1999) 3] is presented. This new compilation, referred to as NACRE II, reports thermonuclear reaction rates for 34 charged-particle induced, two-body exoergic reactions on nuclides with mass number $A<16$, of which fifteen are particle-transfer reactions and the rest radiative capture reactions. When compared with NACRE, NACRE II features in particular (1) the addition to the experimental data collected in NACRE of those reported later, preferentially in the major journals of the field by early 2013, and (2) the adoption of p…
The thermonuclear rate of the 50Fe(p,gamma)51Co reaction in the Type I X-ray bursts (XRBs) temperature range has been reevaluated based on a recent precise mass measurement at CSRe lanzhou, where the proton separation energy Sp=142+/-77 keV has been determined firstly for the 51Co nucleus. Comparing to the previous theoretical predictions, the experimental Sp value has much smaller uncertainty. Based on the nuclear shell model and mirror nuclear structure information, we have calculated two sets of thermonuclear rates for the 50Fe(p,gamma)51Co reaction by utilizing the experimental Sp value. I…
The $^{16}$O(p,$γ$)$^{17}$F reaction is the slowest hydrogen-burning process in the CNO mass region. Its thermonuclear rate sensitively impacts predictions of oxygen isotopic ratios in a number of astrophysical sites, including AGB stars. The reaction has been measured several times at low bombarding energies using a variety of techniques. The most recent evaluated experimental rates have a reported uncertainty of about 7.5\% below $1$~GK. However, the previous rate estimate represents a best guess only and was not based on rigorous statistical methods. We apply a Bayesian model to fit all rel…
A new thermonuclear $^{17}$O($n$,$γ$)$^{18}$O rate is derived based on a complete calculation of the direct-capture (DC) and resonant-capture contributions, for a temperature region up to 2 GK of astrophysical interest. We have firstly calculated the DC and subthreshold contributions in the energy region up to 1 MeV, and estimated the associated uncertainties by a Monte-Carlo approach. It shows that the present rate is remarkably larger than that adopted in the JINA REACLIB in the temperature region of 0.01 $\sim$ 2 GK, by up to a factor of $\sim$80. The astrophysical impacts of our rate have …
We explore the sensitivity of the nucleosynthesis due to type Ia supernovae with respect to uncertainties in nuclear reaction rates. We have adopted a standard one-dimensional delayed detonation model of the explosion of a Chandrasekhar-mass white dwarf, and have post-processed the thermodynamic trajectories of every mass-shell with a nucleosynthetic code, with increases (decreases) by a factor of ten on the rates of 1196 nuclear reactions. We have computed as well hydrodynamic models for different rates of the fusion reactions of 12C and of 16O. For selected reactions, we have recomputed the …
The 2025 Evaluation of Experimental Thermonuclear Reaction Rates (ETR25)
Triangle Universities Nuclear Laboratory (TUNL), Duke University（三角大学核实验室，杜克大学）；Department of Physics & Astronomy, University of North Carolina at Chapel Hill（北卡罗来纳大学教堂山分校物理与天文学系）；Department of Physics, North Carolina State University（北卡罗来纳州立大学物理系）；HUN-REN Institute for Nuclear Research (Atomki)（匈牙利研究与创新网络核研究所）
The thermonuclear $^{19}$F($p$,$α_0$)$^{16}$O reaction rate in a temperature region of 0.007--10 GK has been derived by re-evaluating the available experimental data, together with the low-energy theoretical $R$-matrix extrapolations. Our new rate deviates up to about 30\% compared to the previous ones, although all rates are consistent within the uncertainties. At very low temperature (e.g. 0.01 GK) our reaction rate is about 20\% smaller than the most recently published rate, because of a difference in the low energy extrapolated $S$-factor and a more accurate estimate of the reduced mass en…
We investigate the effects of thermonuclear reaction rate variations on 26Al production in massive stars. The dominant production sites in such events were recently investigated by using stellar model calculations: explosive neon-carbon burning, convective shell carbon burning, and convective core hydrogen burning. Post-processing nucleosynthesis calculations are performed for each of these sites by adopting temperature-density-time profiles from recent stellar evolution models. For each profile, we individually multiplied the rates of all relevant reactions by factors of 10, 2, 0.5 and 0.1, a…
We study the plasma correlation effects on nonresonant thermonuclear reactions of carbon and oxygen in the interiors of white dwarfs and liquid envelopes of neutron stars. We examine the effects of electron screening on thermodynamic enhancement of thermonuclear reactions in dense plasmas beyond the linear mixing rule. Using these improved enhancement factors, we calculate carbon and oxygen ignition curves in white dwarfs and neutron stars. The energy balance and ignition conditions in neutron star envelopes are evaluated, taking their detailed thermal structure into account. The result is com…
We study the impact of plasma correlation effects on nonresonant thermonuclear reactions for various stellar objects, namely in the liquid envelopes of neutron stars, and the interiors of white dwarfs, low-mass stars, and substellar objects. We examine in particular the effect of electron screening on the enhancement of thermonuclear reactions in dense plasmas within and beyond the linear mixing rule approximation as well as the corrections due to quantum effects at high density. In addition, we examine some recent unconventional (Yukawa-potential and "quantum-tail") theoretical results on ste…
For stars between 0.8-8.0 solar masses, nucleosynthesis enters its final phase during the asymptotic giant branch (AGB) stage. During this evolutionary period, grain condensation occurs in the stellar atmosphere, and the star experiences significant mass loss. The production of presolar grains can often be attributed to this unique stellar environment. A subset of presolar oxide grains features dramatic 18O depletion that cannot be explained by the standard AGB star burning stages and dredge-up models. An extra mixing process, referred to as "cool bottom processing" (CBP), was proposed for low…
Abundance anomalies in globular clusters provide strong evidence for multiple stellar populations within each cluster. These populations are usually interpreted as distinct generations, with the currently observed second-generation stars having formed in part from the ejecta of massive, first-generation "polluter" stars, giving rise to the anomalous abundance patterns. The precise nature of the polluters and their enrichment mechanism are still unclear. Even so, the chemical abundances measured in second-generation stars within the globular cluster NGC 2419 provide insight into this puzzling p…
Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiesc…
Uncertainties in the thermonuclear rates of the $^{15}$O($α,γ$)$^{19}$Ne and $^{18}$F($p,α$)$^{15}$O reactions affect model predictions of light curves from type I X-ray bursts and the amount of the observable radioisotope $^{18}$F produced in classical novae, respectively. To address these uncertainties, we have studied the nuclear structure of $^{19}$Ne over $E_{x} = 4.0 - 5.1$ MeV and $6.1 - 7.3$ MeV using the $^{19}$F($^{3}$He,t)$^{19}$Ne reaction. We find the $J^π$ values of the 4.14 and 4.20 MeV levels to be consistent with $9/2^{-}$ and $7/2^{-}$ respectively, in contrast to previous as…
The method for the evaluation of the non-resonant thermonuclear function in the Maxwell-Boltzmann case with depleted tail is discussed. Closed forms of the analytical results are obtained in computational format, and written in terms of the H-function in two variables. The standard non-resonant cases are extended to Tsallis reaction rates through the pathway model. Behavior of the depleted non-resonant thermonuclear function is studied. A comparison of the Maxwell-Boltzmann energy distribution with a more general energy distribution called pathway energy distribution is also done.
Thermonuclear supernovae originating from the explosion of a white dwarf accreting mass from a companion star have been suggested as a site for the production of $p$ nuclides. Such nuclei are produced during the explosion, in layers enriched with seed nuclei coming from prior strong $s$ processing. These seeds are transformed to proton-richer isotopes mainly by photodisintegration reactions. Several thousand trajectories from a 2D explosion model were used in a Monte Carlo approach. Temperature-dependent uncertainties were assigned individually to thousands of rates varied simultaneously in po…
The impact of nuclear physics uncertainties on nucleosynthesis in thermonuclear supernovae has not been fully explored using comprehensive and systematic studies with multiple models. To better constrain predictions of yields from these phenomena, we have performed a sensitivity study by post-processing thermodynamic histories from two different hydrodynamic, Chandrasekhar-mass explosion models. We have individually varied all input reaction and, for the first time, weak interaction rates by a factor of ten and compared the yields in each case to yields using standard rates. Of the 2305 nuclea…
Investigation of $^{31}$P levels near the proton threshold by Nuclear Resonance Fluorescence and the impact on the $^{30}$Si(p,$γ$)$^{31}$P thermonuclear rate
Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar luminosity and neutrino emission rates. The composite parameter {C} that determines the standard nuclear reaction rate through the Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended reaction rates through a more general distribution than the Maxwell-Boltzmann distribution. The new distribution is obtained by the pathway model introduce…
It has been suggested that hydrogen ingestion into the helium shell of massive stars could lead to high $^{13}$C and $^{15}$N excesses when the shock of a core-collapse supernova passes through its helium shell. This prediction questions the origin of extremely high $^{13}$C and $^{15}$N abundances observed in rare presolar SiC grains which is usually attributed to classical novae. In this context $^{13}$N($α$,p)$^{16}$O the reaction plays an important role since it is in competition with $^{13}$N $β^+$-decay to $^{13}$C. The $^{13}$N($α$,p)$^{16}$O reaction rate used in stellar evolution calc…
Recently, the triple-α(3α) process, by which three 4He nuclei are fused into a 12C nucleus in stars, was studied by different methods in solving the quantum mechanical three-body problem. Their results of the thermonuclear reaction rate for the process differ by several orders at low stellar temperatures of 10^7 - 10^8 K. In this paper, we will present calculations of the 3αprocess by a modified Faddeev three-body formalism in which the long-range effects of Coulomb interactions are accommodated. The reaction rate of the process is calculated via an inverse process, three-alpha (3-α) photodisi…
The $^{18}$Ne($α$,$p$)$^{21}$Na reaction is thought to be one of the key breakout reactions from the hot CNO cycles to the rp-process in type I x-ray bursts. In this work, the resonant properties of the compound nucleus $^{22}$Mg have been investigated by measuring the resonant elastic scattering of $^{21}$Na+$p$. An 89 MeV $^{21}$Na radioactive beam delivered from the CNS Radioactive Ion Beam Separator bombarded an 8.8 mg/cm$^2$ thick polyethylene (CH$_{2}$)$_{n}$ target. The $^{21}$Na beam intensity was about 2$\times$10$^{5}$ pps, with a purity of about 70% on target. The recoiled protons w…
We explore properties of core-collapse supernova progenitors with respect to the composite uncertainties in the thermonuclear reaction rates by coupling the reaction rate probability density functions provided by the STARLIB reaction rate library with $\texttt{MESA}$ stellar models. We evolve 1000 15 $M_{\odot}$ models from the pre main-sequence to core O-depletion at solar and subsolar metallicities for a total of 2000 Monte Carlo stellar models. For each stellar model, we independently and simultaneously sample 665 thermonuclear reaction rates and use them in a $\texttt{MESA}$ in situ reacti…
Photodisintegration reaction rates involving charged particles are of relevance to the p-process nucleosynthesis that aims at explaining the production of the stable neutron-deficient nuclides heavier than iron. In this study, the cross sections and astrophysical rates of (g,p) and (g,a) reactions for about 3000 target nuclei with 10<Z<100 ranging from stable to proton dripline nuclei are computed. To study the sensitivity of the calculations to the optical model potentials (OMPs), both the phenomenological Woods-Saxon and the microscopic folding OMPs are taken into account. The systematic com…
We propose a $(p,xn)$ mechanism with dynamic production as a new set of nuclear reactions that could produce high density neutrons and explain the r- and rp-elements. We calculate the rate of thorium and uranium produced by our proposed mechanism and show that it is compatible with different stellar conditions found in explosive events at an initial temperature of $T \geq 3\times 10^{9} K$ with a "freeze-out" by a neutrino-driven wind. We show that charged particle reactions could explain the discrepancies in the abundances of ${}^{232}Th$ and ${}^{235,238}U$ nucleochronometers. We extend the …
(Abridged) The explosion mechanism of electron-capture supernovae (ECSNe) remains equivocal. We attempt to constrain the explosion mechanism (neutron-star-forming implosion or thermonuclear explosion) and the frequency of occurrence of ECSNe using nucleosynthesis simulations of the latter scenario, population synthesis, the solar abundance distribution, pre-solar meteoritic oxide grain isotopic ratio measurements and the white dwarf mass-radius relation. Tracer particles from 3d hydrodynamic simulations were post-processed with a large nuclear reaction network in order to determine the complet…
The $^{14}$O($α$,$p$)$^{17}$F reaction is one of the key reactions involved in the breakout from the hot-CNO cycle to the rp-process in type I x-ray bursts (XRBs). The resonant properties in the compound nucleus $^{18}$Ne have been investigated through resonant elastic scattering of $^{17}$F+$p$. The radioactive $^{17}$F beam was separated by the CNS Radioactive Ion Beam separator (CRIB) and bombarded a thick H$_2$ gas target at 3.6 MeV/nucleon. The recoiling light particles were measured by three $Δ$E-E silicon telescopes at laboratory angles of $θ$$_{lab}$$\approx$3$^\circ$, 10$^\circ$ and 1…
