Reaction data is essential in nuclear astrophysics to track the changes in composition and the generation of energy inside stellar systems. Reactions are divided into two classes, strong (e.g., captures) and weak (e.g., decays). For strong reactions, interaction probabilities are characterized by cross sections. Nuclear astrophysics studies do not, however, require cross sections of all reaction types at all energies; Figure 1 shows the set of reaction types most predominantly utilized in this field. Noted exceptions to this are the important ¹²C + ¹²C, ¹²C + ¹⁶O, ¹⁶O + ¹⁶O, and similar reactions occurring in carbon and oxygen burning stages of massive stars where the low abundance of light nuclei causes heavy ion reactions to dominate (Nagorcka et al., 1971; Rolfs and Rodney, 1988). Furthermore, cross sections for different reaction types are needed for nuclei in different locations of the nuclear chart (Figure 1). For example, neutron captures are important for stable nuclei and those that have a neutron excess, while proton and alpha captures are needed for stable nuclei and those with a proton excess. Similarly, beta decays are critical for nuclei with excess neutrons, while positron decays are needed for nuclides on the p-rich side of stability. Finally, cross sections are needed at the low relative energies (typically ≤1 MeV/u) characteristic of the interactions of nuclides inside stars. Such low interaction energies are both a help—by placing only modest requirements on accelerators and detection systems—and a hindrance—by causing much lower yields due to the Coulomb barrier—to direct measurements of astrophysical reactions.

Extensive data on the structure of nuclei are also needed for astrophysical studies. The properties of single-particle levels that are within ∼1 MeV of a particle threshold are of particular importance: these levels have the correct energy and configuration to be readily populated by particle capture and other reactions that drive astrophysical processes. In contrast, such reactions do not favor populating levels at higher excitation energy or with collective configurations (e.g., rotational or vibrational excitations). By measuring single-particle level properties—or calculating them with theoretical models—the resonant cross sections (and thermonuclear reaction rates, discussed below) can be determined (Rolfs and Rodney, 1988). This “indirect” approach at estimating thermonuclear rates is especially valuable for nuclei far from stability (Smith and Rehm, 2001) where capture reactions cannot be measured directly, forcing a reliance on other reaction measurement approaches (e.g., transfer reactions, surrogate reactions, decay studies) or on theoretical models. Because resonant contributions to reaction rates depend exponentially on resonance energies, precision energy values are needed. Other important level properties include the partial and total widths, spectroscopic factors, spin-parities, and separation energies (e.g., reaction Q-values or nuclear masses).

Significant experimental and theoretical efforts have been directed at nuclear mass determinations, leading to high precision measurements [e.g., with particle traps (Kankainen et al., 2020)] and sophisticated global models with RMS differences from measurements as low as 600 keV (Goriely, 2023a). Machine learning has been utilized in numerous recent studies of nuclear masses—as well as in other areas of nuclear physics (Boehnlein et al., 2022)—with some studies achieving ∼200 keV RMS deviation from evaluated masses (Shelley and Pastore, 2021). Because there is so much activity in nuclear mass research, a comprehensive review of progress would greatly benefit the field; many advances have been made in the 20 years since the last review (Lunney et al., 2003).

For stable nuclei, many of the relevant properties have been measured, with the exception of a fair number of partial widths and spectroscopic factors for near-threshold single-particle levels. For studies of individual nuclei, shell model codes [e.g., Brown (2004)] and ab initio approaches [e.g., Hergert (2020)] are commonly used. Calculations over the entire nuclear chart are absolutely essential to provide all the necessary data for certain astrophysical simulations. Such “global” calculations are, for example, critical for the neutron-rich, far-from-stability nuclei that are the epicenter of the rapid neutron capture process (r-process) (Cowan et al., 2021), because few of the relevant level properties have been measured and most are experimentally inaccessible. A recent review article (Goriely, 2023a) provides an in-depth discussion of theoretical approaches to model structure information, including level densities, optical model potentials, gamma-ray strength functions, fission product distributions, beta decays, and nuclear masses.

There are other structure data needs in addition to those mentioned above. For example, the properties of bound levels are necessary to calculate the direct reaction cross section component (Brune and Davids, 2015). Also, spontaneous and neutron-induced fission yield distributions are important to treat the synthesis of the heaviest elements in the r-process (Côté et al., 2018); details of this are discussed in Section 2.7. Finally, for weak reactions, beta- and positron-decay lifetimes are needed, as well as delayed single- and multiple-particle emission probabilities after decay; weak reactions are described in more detail in Section 2.3.

Cross sections can be converted to thermonuclear reaction rates through a convolution with the Maxwell-Boltzmann temperature-dependent energy distribution of interacting particles in a star (Rolfs and Rodney, 1988). This holds for cross sections obtained from laboratory measurements, as well as for those calculated from a reaction model or from the properties of relevant levels. The rates of charged particle reactions depend exponentially on temperature, with some rates varying by 30 orders of magnitude or more over the 10⁷ K–10¹⁰K temperature range relevant for astrophysical environments. Figure 2 shows a typical example, the rate for the ¹⁷F(p,γ)¹⁸Ne reaction that plays a critical role in the synthesis of ¹⁷O in nova explosions (Bardayan et al., 1999). Collections of hundreds to thousands of individual reaction rates—rate “libraries”—are the core nuclear physics input for simulations of astrophysical environments.

The Evaluated Nuclear Data File ENDF (Brown et al., 2018; National Nuclear Data Center, 2023a) is a reaction cross section database that is managed and hosted at the National Nuclear Data Center (NNDC) (Brookhaven National Laboratory, 2023b) in the US. ENDF has an overwhelming focus on neutron-induced reactions because of their importance in nuclear energy and nuclear science applications. ENDF only has entries for reactions that have been measured in laboratories—that is, it contains no cross sections calculated entirely from theoretical models. ENDF entries are evaluated, meaning that nuclear reaction models (discussed below) are used by experts to combine multiple measurements to quantitatively determine the “best” value, to extrapolate to higher (∼20 MeV/u) or lower energies, to calculate all reaction channels at all angles, and to determine robust uncertainty information in the form of covariances (Smith DL., 2011; NNDC, 2023a).

Data from individual experiments are not stored in ENDF; these are stored in the EXFOR database (Zerkin and Pritychenko, 2018; IAEA Nuclear Data Services, 2023a). Members of the nuclear data community work with researchers to compile and import experimental results into EXFOR for subsequent dissemination to the community. ENDF evaluations, which are coordinated by the Cross Section Evaluation Working Group (CSEWG) (NNDC, 2023b), are significantly expedited by importing data into the standardized EXFOR format.

ENDF is not the only evaluated library of its kind: other similar libraries include the Joint European Fusion File (JEFF) (Nuclear Energy Agency, 2023), the Japanese Evaluated Nuclear Data Library (JENDL) (Japan Atomic Energy Agency, 2023), the Russian Nuclear Data Library (ROSFOND) (Inst Phys Power Engr, 2023), and the Chinese Evaluated Nuclear Data Library (CENDL) (Chinese Institute of Atomic Energy, 2023). The ENDF database format, unchanged since the 1960s, will soon be replaced by the Generalised Nuclear Data Structure (GNDS) format (NEA OECD, 2023). This follows more than a decade of work by international data experts to bring this critical database into the modern era.

Because ENDF contains neutron capture reaction cross sections on stable isotopes, it can be used in simulations of the slow neutron capture process (s-process) (Käppeler et al., 2011) in AGB stars (Busso et al., 1999). In Section 2.3 below, the generation of reaction rates from ENDF cross sections will be discussed. It should be noted that, for s-process studies, there is a need to supplement ENDF cross sections with cross sections of neutron captures on long-lived radioactive “branch-point” isotopes (Bisterzo et al., 2015) that are a few mass units from stability.

During the evaluation process, the cross sections in ENDF are adjusted to agree with benchmarks from nuclear criticality safety and nuclear reactors. While this is ideal for nuclear science applications, it does mean that the cross sections are optimized at energies above those typically found in astrophysical environments. Additionally, since the ENDF evaluation methodology (Brown et al., 2018; National Nuclear Data Center, 2023a) includes all reaction channels and angles over a broad energy range, it is rarely followed by researchers in nuclear astrophysics. Rather, more streamlined reaction evaluations focused on the total cross section (and uncertainty) at astrophysical (i.e., lower) energies are often favored in the nuclear astrophysics community. Such reaction “assessments” (using this term to distinguish from full ENDF evaluations) that are streamlined and optimized for nuclear astrophysics can, in some cases, generate significantly different cross sections than those in ENDF—and which can subsequently produce different element synthesis and energy generation in astrophysical simulations [e.g., Zhang et al. (2022)].

Because ENDF does not contain cross sections for the thousands of neutron capture reactions on short-lived, neutron-rich unstable nuclei that are critical for the rapid neutron capture process (r-process) in neutron star mergers (Wanajo et al., 2021) and core collapse supernovae (Yamazaki et al., 2022), this database is not suitable for r-process studies.

Nuclear reaction codes play an invaluable role in data analysis and in data evaluations. Examples widely used for charged-particle induced reactions include FRESCO (Thompson and Nunes, 2009) for analyzing angular distributions using coupled channels, DWUCK (Kunz, 1996) and TWOFNR (Igarashi, 1977) which use a Distorted Wave Born Approximation (DWBA) approach, and AZURE (Azuma et al., 2010) for multi-level R-matrix fits. For neutron-induced reactions, the SAMMY (Larson, 2008) code is widely used for multilevel R-matrix fits to neutron data with a Bayesian approach. SAMMY has long been an integral part of the ENDF evaluation methodology.

Nuclear reaction codes are also critical for estimating cross sections that have not yet been (or cannot practically be) measured. For capture reactions in astrophysical environments, the total cross section is the sum of three different components: direct capture into bound states (Brune and Davids, 2015), resonant capture into low-lying (non-overlapping) single-particle levels, and capture into overlapping levels. Given the bound level properties, the direct capture component can be treated with a code like RADCAP (Bertulani, 2003); given properties of the individual resonances, a standard Breit-Wigner formulation can be used for the resonant capture component. These level properties are usually obtained from experimental results (e.g., ENSDF or XUNDL) or from theoretical models as discussed in Section 2.2. The third component, capture into overlapping levels, often dominates the direct and resonant capture contributions to cross sections. The third component is usually treated with a statistical (or Hauser-Feshbach) reaction mechanism model (Hauser and Feshbach, 1952).

Statistical model codes, in fact, provide the overwhelming majority of reaction cross sections that (after being processed into reaction rates) are used in astrophysical simulations. Popular modern statistical model codes from the nuclear data community include CoH (Kawano et al., 2010; Kawano et al., 2016), EMPIRE (Herman et al., 2007), and TALYS (Goriely et al., 2008; Koning, 2023a); older codes include GNASH (Young et al., 1992) and ALICE (Dityuk et al., 1998). Of these, TALYS has obtained wide acceptance for many studies in basic and applied nuclear science—including nuclear astrophysics. This code performs advanced global nuclear reaction modeling with robust uncertainties, and contains multiple reaction components including pre-equilibrium reaction effects, multi-particle emissions, width fluctuations, coupled channels, nuclear deformation, fission products, and many choices for nuclear level densities.

TALYS is used to generate TENDL, the TALYS Evaluated Nuclear Data Library (Koning et al., 2019; Koning, 2023b), which combines reaction evaluations with TALYS calculations to obtain reaction cross sections with nearly complete coverage of the nuclide chart for certain reaction types. This coverage makes TENDL very useful for certain astrophysics studies—specifically, of s-process and r-process nucleosynthesis driven by neutron-induced reactions. It should be noted that TENDL cross sections are optimized at energies above those needed for astrophysics and are provided, for many reactions, on a ∼1 MeV energy grid—which does not have sufficient fidelity for the low energies needed for studies of most astrophysical systems.

The nuclear astrophysics community has also developed their own statistical model codes. Early efforts, such as those by Woosley et al. (1978), set the approach followed by later efforts: calculate all binary reactions where an intermediate-mass nucleus (in that case, oxygen to krypton) reacts with a proton, neutron, alpha particle, or gamma ray over a broad energy (temperature) range characteristic of astrophysical environments. The codes also generally use theoretical expressions for nuclear partition functions and the nuclear level density, unless experimentally determined excited states are available. F. Thielemann developed the SMOKER code (Thielemann et al., 1987) that was later advanced by T. Rauscher into NON-SMOKER (Rauscher and Thielemann, 2000; Rauscher, 2023a). This Hauser-Feshbach reaction model code is fine-tuned for astrophysical applications and has been used to calculate rates for (n, γ), (n, p), (n, α), (p, γ), (p, α), (α, γ), and their inverse reactions on nuclides from Ne to Bi and for isotopes ranging from the neutron to proton driplines. Reaction rates generated from NON-SMOKER are the foundation of the JINA REACLIB (Joint Institute for Nuclear Astrophysics, 2023a) reaction rate database described below. Nucleosynthesis simulations were used to benchmark NON-SMOKER rates (Hoffman et al., 1999) and demonstrate their advantages over some earlier statistical model rate collections [including Woosley et al. (1978)].

The Evaluated Nuclear Structure Data File (ENSDF) (National Nuclear Data Center, 2023b) hosted at the NNDC (Brookhaven National Laboratory, 2023b) is the international standard database for evaluated structure properties of nuclei. Some of the information contained in ENSDF includes level energies, spin-parities, total and partial widths, spectroscopic factors, reaction Q values, 1- and 2-particle separation energies, BE (2) values, beta decay lifetimes, binding energies, pairing gaps, decay schemes and branching ratios, bibliographic tags for measurements of these properties (that link to Nuclear Science References (NSR) (Pritychenko et al., 2011)), and much more. ENSDF contains evaluated data on many low-lying, single-particle resonances that are critical for thermonuclear reactions, as well as on bound levels needed for direct capture cross section calculations.

Evaluators from around the world (International Atomic Energy Agency, 2023) contribute to ENSDF evaluations. A companion database, the eXperimental Unevaluated Nuclear Data Library (XUNDL) (Brookhaven National Laboratory, 2023a), holds data from individual experiments that are used by evaluators for their ENSDF evaluations. The formats for ENSDF and XUNDL are being modernized along with the database structure, and the visualization by NuDat (National Nuclear Data Center, 2023c) is being upgraded with new capabilities.

There are other sources of level information on nuclei. One is NUBASE2020 (Kondev et al., 2021), which is a companion to the 2020 Atomic Mass Evaluation (AME) (Huang et al., 2021; Wang et al., 2021) (discussed below). NUBASE contains properties of the ground state, and any metastable states, in over 3,100 nuclides; in contrast, ENSDF contains the properties of all levels in over 3,400 nuclides. The NUBASE evaluations are consistent with the masses in the AME, but are evaluated independently from ENSDF. NUBASE is online at the Atomic Mass Data Center (AMDC) (Atomic Mass Data Center, 2023), hosted at the IAEA Nuclear Data Service (International Atomic Energy Agency, 2023a).

For neutron resonances, the Atlas of Neutron Resonances (Mughabghab, 2023) is a valuable source of experimental information. This work contains an extensive list of the individual resonance parameters for each nucleus as determined from analyzing available captures, fissions, and total neutron cross sections. Thermal cross sections are also contained in this work, along with average resonance parameters. For charged particle reactions, there are numerous targeted studies in the nuclear astrophysics community that contain resonance properties to calculate capture reactions. Some of these just contain information on one or a few nuclei [see, e.g., Smith et al. (1993); Bardayan and Smith (1997); Nesaraja et al. (2007)] while others are more expansive in scope [e.g., Iliadis et al. (2001)].

There are numerous resources for theoretical structure information. Predominant among these is the Reference Input Parameter Library (RIPL) (Capote et al., 2009; Capote, 2023). The product of an international effort, RIPL is a valuable collection of model calculations of nuclear information needed for reaction calculations and nuclear data evaluations. RIPL includes eight sub-libraries: masses, nuclear levels, resonance spacing, optical model, level densities, giant dipole resonances, fission barriers, and computer codes. RIPL has seen wide utilization through the nuclear data community and contains valuable information for nuclear astrophysics research.

A series of global theoretical model predictions have been published by Möller et al. (1995), Möller et al. (1997), Möller et al. (2016), Möller et al. (2019) and are available online at Möller (1997). These collections contain ground-state masses, deformations, alpha-decay Q values, half-lives, beta-decay Q-values for beta-minus and electron capture decays, beta-delayed neutron-emission probabilities, potential-energy surfaces, fission-potential-energy surfaces, and (for ground states) odd-proton and odd-neutron spins, proton and neutron pairing gaps, and proton and neutron separation energies. These quantities are calculated for nearly 9,000 nuclides starting at ¹⁶O and ranging from the proton-to neutron-drip line up to Z = 136. The 2012 version of the Finite Range Drop Model (FRDM) (Möller, 1997) is a central component of these models. The site also has single-particle level diagrams and other graphical information.

A separate, smaller collection of global structure model predictions were produced together with cross section predictions from the NON-SMOKER code (Rauscher, 2023a); these are posted online at Rauscher (2023b). The available structure quantities include nuclear partition functions, nuclear levels, and ground state contributions to nuclear rates. In similar fashion, the BRUSLIB (Goriely, 2023b) library, discussed below in Section 2.3, supplements its collection of thermonuclear reaction rates with theoretical structure data, including ground state and single-particle level properties, densities and potentials, nuclear level densities, partition functions, E1 strength functions, and fission properties. The importance of the properties of bound levels for direct capture on neutron-rich unstable nuclei was pointed out in Goriely (1998a) and remains a challenge to this day.

Finally, a number of structure datasets are posted the Nuclear Computational Low Energy Initiative (NUCLEI) site (NUCLEI Collaboration, 2023). This collaboration is using high performance computing and advanced theoretical techniques to model the properties of nuclei. The data posted at their site includes mass tables, global mass model predictions, tables of 2⁺ level energies, fission barriers, giant dipole resonance parameters, and more. They also have a repository of nuclear codes available for download.

The latest evaluated nuclear mass datasets from the AME effort, as well as their NUBASE structure properties dataset, are available online at the Atomic Mass Data Center (AMDC) (Atomic Mass Data Center, 2023), hosted at the IAEA Nuclear Data Service (International Atomic Energy Agency, 2023a); the masses are also published online in Huang et al. (2021) and Wang et al. (2021). The evaluated masses in the AME are critical for determining the energy release of thermonuclear reactions and for calculating cross sections of unmeasured reactions. There is also a longstanding (2008–2022) independent effort by B. Singh to compile nuclear mass measurements. Those compilations are posted online at the nuclearmasses.org service (Smith MS. et al., 2023), which enables customized visualization and rapid comparisons (e.g., RMS differences) between theoretical, experimental, and evaluated nuclear masses (Smith MS., 2011).

Early efforts to generate charged particle reaction rates for studies of stellar burning were carried out by W. Fowler and his collaborators, resulting in five published collections from 1967 to 1988 (Fowler et al., 1967; Fowler et al., 1975; Harris et al., 1983; Caughlan et al., 1985; Caughlan and Fowler, 1988). The last of these libraries (Caughlan and Fowler, 1988; Smith M. et al., 2023) contains 159 rates and served as a standard for well over a decade. That collection provides a different analytical function of temperature for each rate, as well as pointwise rate values. Other smaller charged-particle reaction rate collections were subsequently created, specialized for solar burning [e.g., Adelberger et al. (1998); Adelberger et al. (2011)], for nuclei in the mass range 20–40 (Iliadis et al., 2001), for nova nucleosynthesis [e.g., Politano et al. (1995); Starrfield et al. (1998); Iliadis et al. (2001); Starrfield et al. (2001)], for X-ray bursts [e.g., van Wormer et al. (1994); Schatz et al. (1998)], and for Big Bang nucleosynthesis [e.g., Wagoner et al. (1967); Wagoner (1969); Smith et al. (1993); Descouvemont et al. (2004)].

The NACRE (Angulo et al., 1999) rate collection was assembled by the first large, international, multi-institution effort to assess charged-particle induced rates for stellar burning. This library, published in 1999, contained 86 rates on mostly stable nuclei, many of them updated from rates in the CF88 collection (Caughlan and Fowler, 1988). The effort utilized a methodology of streamlined assessments directed at determining the total cross section [or astrophysical S-factor (Rolfs and Rodney, 1988)] at low energies, with a focus on the resonant contributions from single-particle levels near a particle threshold. NACRE contains analytical expressions for S-factors, while the rates are given pointwise on a temperature grid. NACRE-II (Xu et al., 2013a; Goriely, 2013), a 2013 update, featured new rates for 34 reactions and the use of potential models for extrapolating measured cross sections to lower energies.

Rates from the NACRE collections form the core of the Brussels nuclear reaction rate library (BRUSLIB) (Goriely, 2004; Aikawa et al., 2005; Xu et al., 2013b; Goriely, 2023b). The early versions of BRUSLIB also included theoretical rates calculated from the MOST statistical reaction code (Goriely, 1998b), while later BRUSLIB versions (Goriely, 2023b) use statistical model rates calculated from TALYS (Koning, 2023a) cross sections. As mentioned above, BRUSLIB includes a large collection of theoretical structure properties, and (as discussed below) it also includes rate of neutron-induced reactions. The Nuclear Network Generator NETGEN (Aikawa et al., 2005; Jorissen, 2023) is a companion software tool that generates pointwise reaction rates from BRUSLIB for subsequent use in nucleosynthesis calculations.

The JINA REACLIB library (Cyburt et al., 2010; Joint Institute for Nuclear Astrophysics, 2023a) is one of the most widely utilized rate libraries in astrophysical simulations. It is the default library for many of the nucleosynthesis codes discussed in Section 2.4. REACLIB had its origin in 1987 (Thielemann et al., 1987) as a set of statistical model calculations using the SMOKER Hauser-Feshbach reaction model code, the precursor code to NON-SMOKER (Rauscher and Thielemann, 2000). REACLIB features one functional form [described in Cyburt et al. (2010)] to fit (parameterize) all reaction rates, and the library itself is a table of the parameter values for each rate. REACLIB has since had many upgrades and expansions, including the addition of approximately 200 rates based on assessments performed by the nuclear astrophysics community [e.g., Schatz et al. (1998); Angulo et al. (1999); Iliadis et al. (2001); Xu et al. (2013a) and many more]. Approximately 48,000 of the total 55,000 rates in JINA REACLIB are based on statistical model calculations, specifically the 2008 version of NON-SMOKER code (Rauscher and Thielemann, 2000; Rauscher, 2023a). It should be noted that JINA REACLIB also contains rates for neutron-induced reactions, as discussed below.

An important advance in the methodology of reaction rate determinations was made with the STARLIB reaction rate library (Iliadis et al., 2010a; Iliadis et al., 2010b; Iliadis et al., 2010c; Longland et al., 2010; Sallaska et al., 2013; Iliadis, 2023). STARLIB features rate determinations, upper and lower limits, and probability distribution functions based on Monte Carlo propagations of nuclear level uncertainties through the reaction rate calculation. STARLIB contains 62 charged particle-induced reactions on nuclei in the mass range of 14–40 that are treated with this method. This library provides pointwise rates (no analytical formulae), and adds a large number (over 47,000) of rates determined from TALYS (Koning, 2023a) cross section calculations and additional rates from other sources (e.g., NACRE, decays from ENSDF, and more) (Sallaska et al., 2013) to produce a rate library useful for astrophysical simulations of proton-rich environments.

For neutron-induced reactions, many collections do not provide thermonuclear reaction rates; rather, they feature Maxwellian-averaged Cross Sections (MACS) [see, for example, Käppeler (2012)] calculated at an average temperature characteristic of s-process nucleosynthesis. A MACS is obtained by folding the energy-dependent differential cross section with the thermal velocity distribution of neutrons in the stellar plasma, and is proportional to the thermonuclear rate divided by the mean thermal velocity. Many collections of MACS provided values only at kT = 25 keV [e.g., Kaeppeler et al. (1982); Käppeler (2012)], in part because many neutron-induced reaction measurements are made using the ⁷Li (p,n) reaction as a source of neutrons; this reaction produces a Maxwellian-like distribution of neutrons peaked at that energy (Beer et al., 1980). It should be noted that some authors prefer to provide MACS at kT = 30 keV [e.g., Bao et al. (2000)]. The approach of providing MACS at one average temperature is, however, problematic for simulations that feature thermonuclear burning at other temperatures. Examples of other important temperatures for stellar neutron-induced reactions include 8 keV for the ¹³C pocket formation after the third dredge up in AGB stars (Bisterzo et al., 2015), 90 keV for shell carbon burning in AGB stars (Käppeler, 2012), and up to 1 MeV for r-process nucleosynthesis (Horowitz et al., 2019).

Early efforts to generate collections of MACS for neutron-induced reactions—primarily for neutron captures—were made in the 1960s and 1970s by Macklin and Gibbons (1965) and Allen et al. (1971). These libraries formed the basis for early quantitative studies of s-process nucleosynthesis by W. Fowler and others. It should be noted that these collections included MACS on a grid of kT values from 5 to 90 keV, making them suitable for a wider range of studies than some later collections.

As experimental measurements improved, rate collections were revised and expanded. The collections of Kaeppeler et al. (1982), Bao and Kaeppeler (1987), and Bao et al. (2000) significantly advanced the quality of neutron capture data processed for s-process studies. A 2005 update of Bao et al. (2000) forms the core of the Karlsruhe Astrophysical Database of Nucleosynthesis in Stars (KADONIS) (Dillmann et al., 2006; Dillman, 2023), which is supplemented from rates from other sources as well. This is a web-based collection of experimental (n, γ) MACS relevant for studies of s-process nucleosynthesis. KADONIS was subsequently extended in 2013 to contain neutron capture rates on 32 p-rich unstable nuclei for studies of the p-process (Szucs et al., 2014).

In the nuclear data community, MACS have been calculated (Pritychenko et al., 2010; Pritychenko and Mughaghab, 2012; Pritychenko, 2020; National Nuclear Data Center, 2023d) for neutron capture reactions from cross sections in the ENDF (National Nuclear Data Center, 2023a), JEFF (Nuclear Energy Agency, 2023), JENDL (Japan Atomic Energy Agency, 2023), ROSFOND (Inst Phys Power Engr, 2023), and CENDL (Chinese Institute of Atomic Energy, 2023) libraries. Comparisons [e.g., Zhang et al. (2022)] between these MACS and those generated from experiments [e.g., (Dillman (2023)] or from nuclear models [e.g., (Rauscher (2023a)] originating from nuclear astrophysics studies may improve the overall quality of all MACS collections.

For studies of the astrophysical r-process, it is critical to have reaction rates rather than MACS because of the wide range of temperatures present in neutron star mergers and core-collapse supernovae. It is also necessary to have neutron capture rates on thousands of neutron-rich unstable nuclei, which necessitates the use of nuclear models. NON-SMOKER (Rauscher, 2023a) was used to generate such rates for the JINA REACLIB library (Joint Institute for Nuclear Astrophysics, 2023a); TALYS (Koning, 2023a) was similarly used to generate rates for BRUSLIB (Goriely, 2023b). Recently, TALYS was used to generate the TENDL-Astrophysics database (Koning, 2023c), which contains neutron capture reaction rates on 8,892 isotopes with uncertainties generated from 288 models that combine different choices of input parameters—gamma strength functions, level densities, optical models, collective enhancements, width fluctuations, and mass models. The incorporation of uncertainties and the complete coverage of neutron-induced reactions on stable and neutron-rich isotopes make this library useful for quantitative investigations of s-process and r-process nucleosynthesis.

Weak nuclear reactions such as beta decays are very important for thermonuclear burning processes. For the r-process, these decays are critical input as they set the timescale of the burning and the final abundances [see, e.g., Langanke and Martínez-Pinedo (2003); Cowan et al. (2021)]. Beta-delayed single and multiple neutron emissions are also important as they alter the mass distribution of r-process abundances. Electron (positron) capture reactions are also needed for neutron-rich (proton-rich) nuclei. Where measurements of the beta- and positron-decay lifetimes of nuclei near stability exist, they are included in ENSDF (National Nuclear Data Center, 2023b); these values are often incorporated into thermonuclear rate libraries. For r-process simulations, however, thousands of weak rates on very neutron-rich nuclei are needed, and theoretical models are required to provide the needed data.

Important early theoretical studies of weak reactions in the nuclear astrophysics community were made by Fuller et al. (1980); Fuller et al. (1982a); Fuller et al. (1982b); Fuller et al. (1985). These collections included stellar weak interaction rates for intermediate-mass nuclei (up to mass 60) and are still used by some astrophysical simulation codes today (Timmes, 2023). Temperature dependences were soon added to tables of weak rates (Takahashi and Yokoi, 1987). Many other advances have followed, using a wide variety of theoretical approaches including microscopic models, shell-model Monte-Carlo, random phase approximation (RPA), quasiparticle RPA, relativistic RPA, finite-temperature relativistic nuclear field theory, and many more [see, e.g., Ferreira et al. (2014); Litvinova et al. (2020); Suzuki (2022); Goriely (2023a); Suzuki et al. (2023)]. While some tables of weak rates have been published in the literature [see, e.g., Takahashi and Yokoi (1987); Möller et al. (1997)], others have been folded into the major thermonuclear reaction rate libraries (described above) including JINA REACLIB (Joint Institute for Nuclear Astrophysics, 2023a), BRUSLIB (Goriely, 2023b), and others. The most recent global calculation, in Ney et al. (2020), employs a finite-amplitude method and quasiparticle RPA to calculate beta decays of nearly 4,000 neutron-rich nuclei; the beta decays and strength functions are available as a Supporting Material to the journal article (Ney et al., 2023).

Astrophysics simulations play a pivotal role in enabling studies of the cosmic creation of elements and the evolution and explosion of stellar systems. The two major aspects of these simulations, the hydrodynamics and the thermonuclear burning, are closely coupled: energy generated by thermonuclear burning alters the hydrodynamics (i.e., temperature and density), and updated hydrodynamics alters the reaction rates and subsequent thermonuclear burning. While the ideal simulation would fully couple these two aspects—a high resolution three-dimensional (3D) numerical hydrodynamical treatment coupled to a complete thermonuclear reaction network—this is not yet possible (even in 2D) due to the extreme computational resources required. For this reason, simulations emphasizing the hydrodynamic aspects utilize a truncated reaction network (e.g., an alpha-nuclei network); this provides, in a computationally possible manner, an approximation to the nuclear energy generation that dynamically modifies the hydrodynamic conditions at each time step. The current state-of-the-art in core-collapse supernova modeling has, notably, now reached high resolution 3D numerical hydrodynamics simulations with a 160 nuclide network (Sandoval et al., 2021). With computing power now reaching the exaflop (10¹⁸ floating point operations per second) scale (ORNL, 2023), it is exciting to imagine that coupling 3D hydrodynamics and full thermonuclear burning will perhaps be achieved for some systems within a decade.

In contrast, there are two categories of simulations with modest computational requirements: those that combine an approximate 1D analytical hydrodynamics calculation with a full thermonuclear burn simulation, and “post-processing” codes that calculate a full thermonuclear burn over an static (imported) hydrodynamics profile. These simulations can routinely track compositional changes over thousands of nuclear species.

For each of these three categories of simulations, thermonuclear reaction rate libraries provide critical nuclear physics input. Most codes having a preferred rate library format of either pointwise rates or analytical rate formulae. Additionally, some codes have a default rate library that is hardwired, others enable rate library substitutions after a fair amount of effort, and still others make it easy to rapidly change rate libraries. Below, we describe a variety of astrophysical simulation codes that are available to the community.

The Modules for Experiments in Stellar Astrophysics (MESA) (Paxton et al., 2011; MESA Collaboration, 2023) is a widely used set of open source libraries for computational stellar astrophysics. It features a 1D stellar evolution module that couples hydrodynamics and nucleosynthesis using adaptive mesh refinement, and has separate modules for nuclear reaction rates, equations of state, and more. The default thermonuclear reaction rate library for MESA is a custom combination of 300 rates from CF88, NACRE, and others; there is an option to use rates from the JINA REACLIB collection as well.

The NUGRID post-processing nucleosynthesis code (Denissenkov et al., 2014; NUGRID Collaboration, 2023) has the capability of processing the multi-zone output of 1D stellar evolution codes such as MESA (Paxton et al., 2011; MESA Collaboration, 2023), and enables a dynamical adjustment of the size of the network depending on the composition. NUGRID has a reaction library that combines pointwise reaction rates from numerous sources including NACRE (Angulo et al., 1999), CF88 (Caughlan and Fowler, 1988), BRUSLIB (Goriely, 2023b), an early version of JINA REACLIB (Joint Institute for Nuclear Astrophysics, 2023a), and other sources. NUGRID also has an associated jupyter-based platform and python scripts.

XNet (Hix, 2023) is a fully-implicit post-processing nucleosynthesis code. It can be run in standalone mode or coupled to a hydrodynamics package. For the latter, XNet has been coupled to FLASH (Fryxell et al., 2000; Dubey et al., 2009) and CHIMERA (Bruenn et al., 2020) for studies of core collapse supernova simulations [see, e.g., Sandoval et al. (2021) mentioned above], as well as to other codes to study other phenomena. XNet uses thermonuclear rates from JINA REACLIB as a default, and can track ∼5,000 nuclide abundances for r-process studies. As described below, XNet has also been integrated into the Computational Infrastructure for Nuclear Astrophysics (CINA) (Smith, 2023) in a manner that enables rapid customization of input reaction rate libraries.

The Portable Routines for Integrated nucleoSynthesis Modeling (PRISM) nucleosynthesis code (Sprouse et al., 2020; Sprouse et al., 2021) is a modern code used for a novel “nucleosynthesis tracing” technique. PRISM relies primarily on theoretical reaction rates of r-process nuclei calculated with the statistical Hauser-Feshbach code CoH (Kawano et al., 2016).

SkyNet (Lippuner and Roberts, 2017) is another new nuclear reaction network code. It is written in a modular fashion and features significant attention to neutrino-induced nucleosynthesis. This code uses as default reactions from JINA REACLIB (Joint Institute for Nuclear Astrophysics, 2023a) and from other sources.

Torch (Timmes, 1999; Timmes, 2023) is an older general reaction network that is set for a 513 isotope network by default; this network can be expanded to include more species as needed. The default nuclear reactions are from a combination of an early version of REACLIB (Joint Institute for Nuclear Astrophysics, 2023a), NON-SMOKER (Rauscher, 2023a), and other sources.

The WinNet (Winteler, 2013) code is an updated version of the BasNet (Thielemann et al., 2011) reaction network; neither of these two codes are publicly distributed. WinNet can track over 5,800 nuclides, contains reactions from NON-SMOKER and many other sources, and has been used for studies of the r-process in core-collapse supernovae and in neutron star mergers [e.g., Korobkin et al. (2012)].

The Webnucleo nuclear reaction network (Meyer, 2012; Meyer, 2023) is a modular system for nucleosynthesis calculations available both in jupyter notebooks and in downloadable source code. This system accepts user-specified pointwise reaction rates as default inputs. The pynucastro library (Smith AI. et al., 2023) is a new open-source python library that enables interactive creation and exploration of nuclear reaction networks. The networks built with this system can be exported for use in large-scale simulation codes.

Significant effort is required to prepare the thermonuclear reaction libraries that are the key nuclear input for all the simulations discussed above. Of all the necessary steps, the most critical are the calculation of resonant cross sections from the properties of near-threshold levels and the numerical integration of energy-dependent cross sections to form temperature-dependent thermonuclear reaction rates. These processing steps are well known and are discussed in books [e.g., Clayton (1984); Rolfs and Rodney (1988); Iliadis (2015)] as well as in many journal articles. For this reason, many nuclear astrophysics research groups have built, but rarely distribute, their own codes for such calculations. It should be noted, however, that some details (e.g., numerical integration routines) can produce differences in outputs from different codes.

Another important processing step is the fitting of temperature-dependent rates to analytical formulae. Such fits are challenging because reaction rates can vary by up to 30 orders of magnitude or more over astrophysical temperature ranges (see, e.g., Figure 2). Fits of rates to the REACLIB analytical formulation are, for example, discussed in Cyburt et al. (2010). Other important processing steps include creating inverse reaction rates from forward rates and checking that they obey the principle of detailed balance, converting cross sections to S-factors, numerically interpolating codes to generate thermonuclear rates at any temperature from pointwise rate tables, downloading and extracting data from standard databases [e.g., ENDF (National Nuclear Data Center, 2023a), ENSDF (National Nuclear Data Center, 2023b)], and more.

A number of these processing steps are contained within CINA (Nesaraja et al., 2005a; Nesaraja et al., 2005b; Smith, 2005; Smith et al., 2006; Smith, 2023). This software system is a unique online cloud-computing data “pipeline” that provides a simple graphical user interface (GUI) to guide users step-by-step in processing and using nuclear data in astrophysical simulations. Operating since 2004, CINA enables users to work with nuclear data, with thermonuclear reaction rates, and with nucleosynthesis simulations. For nuclear data, users can upload, manipulate, and save reaction cross sections. For thermonuclear rates, users can: convert cross sections or S-factors into thermonuclear reaction rates via numerical integration; modify, parameterize (i.e., fit to the REACLIB analytic formula), and save rates into rate libraries; and combine libraries to form custom collections that can run in nucleosynthesis simulations. For simulations, users can: upload custom hydrodynamic profiles; set up and execute post-processing nucleosynthesis simulations with the XNet code (Hix, 2023); run multi-zone simulations and compute zone-weighted final abundances; set up batch modes of runs over multiple rate libraries and hydrodynamic profiles; rapidly change nuclear physics inputs (i.e., reaction rates) and determine astrophysical impacts; run automated sensitivity studies for determining input (rate) vs output (abundance) correlations; save and visualize simulations with customizable plots and animations; analyze and annotate simulations; quantify uncertainties in predicted final abundances; and compare multiple simulation results. Information in CINA, including large custom rate libraries and simulation outputs, can easily be shared between users within the system as well as exported. CINA’s GUI is platform independent and runs on any machine with Java installed; the system is free to use and all users receive free disk space to store their runs. Since it is a remotely-executed cloud computing service, CINA requires users to have an active internet connection, but does not require any compilation, libraries, licenses, special environments, or user updates in order to operate. CINA utilizes the JINA REACLIB (Joint Institute for Nuclear Astrophysics, 2023a) database as the default rate library, but enables users to quickly create, save, share, and use customized rate libraries from within the GUI.

The nuclear equation of state (EOS) describes the characteristics (e.g., compressibility) and the dynamics of nuclear matter in ultra-dense systems such as neutron stars, core-collapse supernovae, and neutron star mergers (Oertel et al., 2017). In Sumiyoshi et al. (2020), considerations of the influence of neutron-rich matter, hyperons and quark matter, and hadron-to-quark transitions in EOS studies are reviewed. Because the EOS is needed, especially for supernova simulations, at finite temperature and various lepton fractions, the results are usually presented in a tabular fashion, and many studies [e.g., Shen (2014); Shen et al. (2020)] have produced, analyzed, and compared the impact of different EOS tables on neutron stars and related systems. While not all EOS reported in the literature are publicly distributed, an online archive of many EOS tables may be found at Shen (2023a). The EOS tables for some particular studies are also posted online [e.g., Shen (2023b); Lattimer (2023)].

In the synthesis of the heaviest elements in core-collapse supernovae and neutron star mergers, the series of neutron captures on n-rich unstable nuclei, the r-process, leads to the formation of nuclei that undergo fission [see, e.g., Côté et al. (2018)]. When fission causes these heavy nuclei break apart, this effectively prevents even more massive nuclei from being formed; it therefore helps determine the “endpoint” of the r-process. From as early as the 1930s [e.g., Bohr and Wheeler (1939)], the fission process has been a focus of a segment of the nuclear physics community. Despite much effort, the complex mechanism of fission has made it very challenging to model (Schunck and Robledo, 2016). For this reason, fission has rarely been incorporated in astrophysical simulations even though it plays a critical role in the decay of heavy nuclei. In Goriely (2015), the effects of fission recycling (where fission products undergo subsequent neutron captures leading to fission), fission fragment distributions, and the capture of prompt fission neutrons were investigated. The results of some fission models relevant for nuclear astrophysics are posted online: BRUSLIB (Goriely, 2023b) provides fission information for 1,000 isotopes with Z ranging from 90 to 110, and Goriely (2009) provides similar information. More recently, the Fission In R-process Elements (FIRE) collaboration (Côté et al., 2018; FIRE Collaboration, 2023) was formed to focus on integrating advanced models of spontaneous, neutron-induced, and β-delayed fission into rapid neutron capture (r-process) nucleosynthesis codes and examining the subsequent astrophysical impacts. A set of their fission yields are distributed at FIRE Collaboration (2022).