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Nuclear Data for Astrophysical Modeling

Nuclear physics has been playing an important role in modern astrophysics and cosmology. Since the early 1950's it has been successfully applied for the interpretation and prediction of astrophysical phenomena. Nuclear physics models helped to explain the observed elemental and isotopic abundances and star evolution and provided valuable insights on the Big Bang theory. Today, the variety of elements observed in stellar surfaces, solar system and cosmic rays, and isotope abundances are calculated and compared with the observed values. Consequently, the overall success of the modeling critically depends on the quality of underlying nuclear data that helps to bring physics of macro and micro scales together. To broaden the scope of traditional nuclear astrophysics activities and produce additional complementary information, I will investigate applicability of the U.S. Nuclear Data Program (USNDP) databases for astrophysical applications. EXFOR (Experimental Nuclear Reaction Data) and ENDF (Evaluated Nuclear Data File) libraries have large astrophysics potential; the former library contains experimental data sets while the latter library includes evaluated neutron cross sections. ENSDF (Evaluated Nuclear Structure Data File) database is a primary depository of nuclear structure and decay rates information. The decay rates are essential in stellar nucleosynthesis calculations, and these rates are evaluated using nuclear structure codes. The structure evaluation codes are pure mathematical procedures that can be applied to diverse data samples. A brief review of astrophysical nuclear data needs has been presented. Several opportunities and the corresponding computer tools have been identified. Further work will include extensive analysis of nuclear databases and computer procedures for astrophysical calculations.

Nuclear physics has been playing an important role in modern astrophysics and cosmology. Since the early 1950's it has been successfully applied for the interpretation and prediction of astrophysical phenomena. Nuclear physics models helped to explain the observed elemental and isotopic abundances and star evolution and provided valuable insights on the Big Bang theory. Today, the variety of elements observed in stellar surfaces, solar system and cosmic rays, and isotope abundances are calculated and compared with the observed values. Consequently, the overall success of the modeling critically depends on the quality of underlying nuclear data that helps to bring physics of macro and micro scales together. To broaden the scope of traditional nuclear astrophysics activities and produce additional complementary information, I will investigate applicability of the U.S. Nuclear Data Program (USNDP) databases for astrophysical applications. EXFOR (Experimental Nuclear Reaction Data) and ENDF (Evaluated Nuclear Data File) libraries have large astrophysics potential; the former library contains experimental data sets while the latter library includes evaluated neutron cross sections. ENSDF (Evaluated Nuclear Structure Data File) database is a primary depository of nuclear structure and decay rates information. The decay rates are essential in stellar nucleosynthesis calculations, and these rates are evaluated using nuclear structure codes. The structure evaluation codes are pure mathematical procedures that can be applied to diverse data samples. As an example, I will consider Hubble constant measurements. An extraordinary number of Hubble constant measurements challenges physicists with selection of the best numerical value. Data evaluation codes and procedures help to resolve this issue. The present work produces the most probable or recommended Hubble constant value of 66.2(77) (km/sec)/Mpc. This recommended value is based on the last 25 years of experimental research and includes contributions from different types of measurements. The current result implies (14.78±1.72) × 10 9 years as a rough estimate for the age of the Universe.

Introduction and Overview
In the last century, astronomy, astrophysics, and cosmology have evolved from observational and theoretical pursuits into more experimental science, with many stellar and planetary processes recreated in physics laboratories and extensively studied. Many astrophysical phenomena have been explained using the present understanding of nuclear physics processes, and the whole concept of stellar nucleosynthesis has been introduced. Further developments helped to identify the Big Bang, stellar, and explosive nucleosynthesis processes that are responsible for the currently-observed variety of elements and isotopes [Burbidge et al. 1957, 547, Cameron 1957. Today, nuclear physics is successfully applied to explain the variety of elements and isotope abundances observed in stellar surfaces, the solar system, and cosmic rays via network calculations and comparison with observed values.
A comprehensive analysis of stellar energy production, metallicity, and isotope abundances indicates a crucial role of proton, neutron, and light ion-induced nuclear reactions and α-, β-decay rates. These subatomic processes govern the observables and predict the star life cycle. Calculations of the transition rates between isotopes in a network strongly rely on theoretical and experimental cross section and decay rate values at stellar temperatures. Consequently, the general availability of nuclear data is of paramount importance in stellar nucleosynthesis research. Application of nuclear data codes and evaluation procedures to Hubble constant measurements shows a high potential of nuclear data analysis and mining techniques in astrophysics and cosmology.
This chapter will provide a review of theoretical and experimental nuclear reaction and decay data for stellar and explosive nucleosynthesis, as well as modern computation tools and methods. Examples of evaluated and compiled nuclear physics data will be given. Applications of nuclear databases and data evaluation methods for nucleosynthesis calculations and Hubble constant measurements evaluation, respectively, will be discussed.

Nucleosynthesis Models
Nucleosynthesis is an important physical phenomenon that is responsible for chemical elements and isotope abundances. It started in the early Universe and proceeds in the stars. The Big Bang nucleosynthesis is responsible for a relatively high abundance of the lightest primordial elements in the Universe from 1 H to 7 Li, and it precedes star formation and stellar nucleosynthesis. The general consistency between theoretically predicted and observed abundances of the lightest elements serves as a strong evidence for the Big Bang theory [Kolb & Turner, 1988, 1].
Presently-known varieties of nuclei and element abundances are shown in Fig. 1  Bang theory. These additional mechanisms have been pioneered by Eddington [Eddington 1920, 14] via introduction of a revolutionary concept of element production in the stars. Present nucleosynthesis models explain medium and heavy element abundances using stellar nucleosynthesis, consisting of burning (explosive) stages of stellar evolution, photo disintegration, and neutron and proton capture processes. These model predictions can be verified through star surface metallicity studies and comparison of calculated isotopic/elemental abundances with observed values, as shown in Fig. 2.
A detailed analysis of elemental abundances and radioactive decay rates shows several mechanisms for production of currently-observed chemical elements and isotopes. The slow-neutron capture (s-process) is responsible for creation of about 50 % of the elements beyond iron. In this region, neutron capture becomes dominant because of the increasing Coulomb barrier and decreasing binding energies. The s-process takes place in the Red Giants and AGB stars, where neutron temperature (kT ) varies from 8 to 90 keV. Further analysis of stable and long-lived nuclei indicates the large number of isotopes that lie outside of the s-process path peaks near A=138 and 208. In addition, the large gap between s-process nucleus 209 Bi and 232 Th, 235,238 U effectively terminates the s-process at 210 Po. Production of the actinide neutron-rich nuclei cannot be explained by s-process nucleosynthesis and requires introduction of a rapid neutron capture or r-process. The Fig. 1 data also indicate between 29 and 35 proton-rich nuclei that cannot be produced in the sor r-processes. A significant fraction of these nuclei originate from the γ-process [Boyd 2008, 1, Woosley & Howard 1978.
Nowadays, there are many well-established theoretical models of stellar nucleosynthesis [Boyd et al. 2009, 60, Burbidge et al. 1957; however, they still cannot reproduce the observed abundances due to many nuclear physics parameters that are not-well defined and stellar properties uncertainties. In this chapter, I will concentrate on the better known s-process nucleosynthesis. The flow of nuclear physics processes in the network calculations is defined by nuclear masses, reaction, and decay rates, and strongly correlated with stellar temperature and density. These calculations depend heavily on our understanding of temperature, density and chemical composition of stars, and the availability of high quality nuclear data.

Nucleosynthesis Data
There are many sources of stellar nucleosynthesis data that include KADoNiS, NACRE and REACLIB dedicated nuclear astrophysics libraries [Angulo et al. 1999, 3, Cyburt et al. 2010, 240, Dillmann et al. 2006, and the U.S. Nuclear Data Program databases.

Astrophysical Libraries
The KADoNiS, NACRE and REACLIB dedicated nuclear astrophysics libraries are optimized for nuclear astrophysics applications and contain pre-selected data that are often limited to their original scope. In many cases, these data sources reflect the present state of nuclear physics, when experimental data are not always available or limited to a single measurement. Such limitation highlights the importance of theoretical calculations that are strongly dependent on nuclear models. In addition, nucleosynthesis processes are strongly affected by astrophysical site conditions. To enlarge the scope of traditional nuclear astrophysics calculations, I will investigate applicability of nuclear physics databases for stellar nucleosynthesis data mining. These databases were developed for nuclear science, energy production, and national security applications and will provide complementary and modelindependent results.
Nuclear Data for Astrophysics Modeling 5 Figure 3. Structure of an EXFOR compilation file.

Nuclear Reaction Data
The experimental and evaluated nuclear reaction data are archived in EXFOR and ENDF libraries, respectively.

EXFOR
The EXFOR database [Holden 2005, Otuka et al. 2014 contains an extensive compilation of experimental nuclear reaction data. The EXFOR library was started in 1967 at a meeting of the four major nuclear data centers: National Nuclear Data Center, Brookhaven National Laboratory, USA; NEA Databank, Paris, France; Nuclear Data Section, IAEA, Vienna, Austria; and Nuclear Power Engineering Institute, Obninsk, Russian Federation [Holden 2005]. This project was based on previously existing efforts, such as the Brookhaven Sigma Center Information Storage and Retrieval System (SCISRS). Currently, EXFOR is an international collaboration under the auspices of the International Atomic Energy Agency (IAEA), and scientists from the USA, France, Austria, Russian Federation, China, Hungary, India, Japan, Korea, and Ukraine contribute to it. EXFOR or EXchange FORmat file was established for information interchange between the four major data centers, and its file structure is shown in Fig. 3. The library consists of data entries that contain complete records of individual experiments. Each experiment may include multiple nuclear reaction data sets (subentries) and several research papers because EXFOR compilers group multiple publications from a particular experiment into a single entry. Another important feature of the library is that all experimental data are compiled as published, only obvious errors are corrected.
Historically, EXFOR was created in support of nuclear energy research and development activities. The initial database scope was limited to neutron-induced reactions in order to provide support for ENDF evaluations [Chadwick et al. 2011[Chadwick et al. , 2887. Later, the scope was extended to charged-particle and photon-induced reactions. Presently, neutron-, proton-, alpha-, and photon-induced reactions constitute 47.9, 19.8, 7.36 and 6.2 % of database content, respectively. The historic evolution of EXFOR content is shown in Fig.  4.
The EXFOR library contains a wealth of nuclear reaction data relevant to nucleosynthesis modeling because its present scope is broad and compilations are systematically per-  . Content evolution of the EXFOR database. Neutron reactions have been compiled systematically since the discovery of the neutron, while charged particle and photon reactions have been covered less extensively.
formed in the last 50 years. To illustrate this point I will consider EXFOR data on the neutron capture and production reactions that play an essential role in s, r and p processes, respectively. The analysis of data shown in Fig. 5 indicates that the most frequently-used neutron capture targets are gold, uranium and tin, while neutron-rich tin, gold and uranium are materials of choice for photo-neutron reaction studies. Further examination of data history provides indication of two trends: large numbers of nuclear reaction measurements in the 1970's [Pritychenko 2015, 1781] and a recent increase in (n,γ) and (γ,n) reactions. The last trend shows clear proof of nucleosynthesis research impact on the nuclear reaction field in the last 15 years. Direct results on Maxwellian-averaged cross sections and astrophysical reaction rates are also compiled in EXFOR.
The EXFOR project has a very advanced Web interface (http://www.nndc.bnl.gov/exfor) [Zerkin et al. 2005, 586] that provides direct access to data and evaluation tools, such as an inverse reaction calculator which is based on the nuclear reaction reciprocity theorem. It allows extracting a reaction cross section if an inverse reaction is known. For 1 + 2 → 3 + 4 and 3 + 4 → 1 + 2 processes the cross section ratio is where E 12 , E 34 are kinetic energies in the c.m. system, J is angular momentum, and δ 12 =δ 34 =0. The EXFOR project is a primary source of experimental nuclear reaction data for many potential applications, such as neutron cross section evaluations. Next, I will discuss a relationship between EXFOR and ENDF databases.
Nuclear Data for Astrophysics Modeling

ENDF
ENDF is a core nuclear reaction database containing evaluated (recommended) cross sections, spectra, angular distributions, and fission product yields, thermal neutron scattering, photo-atomic and other data, with an emphasis on neutron-induced reactions. ENDF library evaluations are based on theoretical calculations adjusted to experimental data with an exception of neutron resonance region, where priority is given to experimental data. ENDF evaluations consist of complete neutron reaction data sets for particular isotope or element (ENDF material). They cover all neutron reaction channels within the 10 −5 eV -20 MeV energy range. All these data sets are stored in the internationally-adopted ENDF-6 format that is maintained by Cross Section Evaluation Working Group and publicly available at the National Nuclear Data Center (NNDC) website (http://www.nndc.bnl.gov/endf). Neutron cross sections for astrophysical range of energies, such as the 56 Fe(n,γ) reaction shown in Fig. 6 Recent releases of evaluated nuclear reaction libraries have created a unique opportunity of applying these data for non-traditional applications, such as s-process nucleosynthesis [Pritychenko 2010, 197]. The feasibility study of the evaluated neutron cross sections for s-process nucleosynthesis is presented below. The Maxwellian-averaged cross section can be expressed as where k and T are the Boltzmann constant and temperature of the system, respectively, and E is an energy of relative motion of the neutron with respect to the target. Here, E L n is a neutron energy in the laboratory system and m 1 and m 2 are masses of a neutron and target nucleus, respectively.
The astrophysical reaction rate for network calculations is defined as where T 9 is temperature expressed in billions of Kelvin, N A is an Avogadro number. T 9 is related to the kT in MeV units as follows 11.6045 × T 9 = kT (4) It is commonly known that for the equilibrium s-process-only nuclei product of σ Maxw γ (kT ) and solar-system abundances (N (A) ) is preserved [Rolfs & Rodney 1988, 1] The stellar equilibrium conditions provide an important test for s-process nucleosynthesis in mass regions between neutron magic numbers N=50, 82, 126 [Arlandini et al.
Nuclear Data for Astrophysics Modeling 9 1999, 886]. To investigate this phenomenon, I will consider ENDF/B-VII.1 library cross sections. These data were never fitted for nuclear astrophysics models and are essentially model-independent.
The product values of the ENDF/B-VII.1 σ Maxw γ (30keV ) times solar abundances [Anders & Grevesse 1989, 197] are plotted in Fig. 7. They reveal that the ENDF/B-VII.1 library data closely replicate a two-plateau plot [Rolfs & Rodney 1988, 1] and provide a powerful testimony for stellar nucleosynthesis. The predictive power of stellar nucleosynthesis calculations depends heavily on neutron cross section values and their covariance matrices. To understand the unique isotopic signatures from the presolar grains, ∼1 % cross section uncertainties are necessary [Käppeler 2011, 390]. Unfortunately, present experimental and theoretical errors are often much higher.

Nuclear Structure and Decay Data
Analysis of the s-process path in the Kr-Rb-Sr region indicates that cross section data alone cannot explain the present-day variety of elements and isotopes. The data in Fig. 8 clearly show that decay information is absolutely essential in stellar nucleosynthesis modeling.

ENSDF
The best source of decay data is the ENSDF database [Burrows 1990, 595, ENSDF 2016, and the Kr-Rb-Sr data sets are shown in Table 1. ENSDF contains evaluated structure and decay data sets for over 3000 nuclides as shown in Fig. 1, and it is predominantly a USNDP product with some contributions from Europe and Asia. The ENSDF library is essentially based on evaluation of experimental data, and all data for a given mass chain or nuclide are re-evaluated on a 10-12 year basis. It uses the mathematical procedures and codes to deduce the evaluated or recommended values. ENSDF decay data sets contain the following information [Burrows 1990, 595]:

Sr
• Parent level energy, J π , T 1/2 and Q-value for the parent ground-state to daughter ground-state decay.
• Branching ratio for the decay mode and normalization factors for converting the relative emission probabilities for γ-ray and β-or electron capture to absolute emission probabilities.
• γ-ray and E0 transition energies, emission probabilities, multipolarities and mixing ratios and the total and partial internal conversion coefficients.
These ENSDF decay data play an important role at stellar nucleosynthesis branch points where β-decay and neutron capture rates are At these points, the stellar thermal environment may complicate the situation even further by changing β-decay rates and affecting the process path. Branching is particularly important for unstable isotopes such as 134 Cs. This isotope can either decay to 134 Ba, if neutron year to 30 days over the temperature range of (100-300)×10 6 K. These variations are due to differences between decay rates of neutral and highly-ionized atoms [Takahashi & Yokoi 1987, 375]. In many cases where experimental data are not available, nuclear theory may provide complete data sets for stellar nucleosynthesis calculations [Möller et al. 1995, 185, Möller et al. 1997.

Data Evaluation Codes and Procedures
Over the last 65 years, the USNDP has accumulated a wealth of experimental knowledge and a diverse range of data analysis and evaluation techniques. The nuclear reaction data evaluations often use EMPIRE, TALYS and Atlas collection of nuclear reaction model codes [Herman et al. 2007, 2655, Koning et al. 2008, 211, Mughabghab 2006, 1] that are frequently calibrated to fit experimental data [Otuka et al. 2014, 272]. The model codes are essential for neutron cross section calculations of short-lived radioactive nuclei where experimental data are not available. The structure and decay data evaluations are often based on direct evaluation of experimental results. ENSDF data evaluation philosophy includes collection of the best available data from each type of experiment and nuclide in a concise and well-documented manner [Burrows 1990, 595]. The emphasis in nuclear data evaluation is on conservative analysis of the structure and decay properties obtained from experimental evidence, well-founded systematics, or theory. The propagation of uncertainties is often problematic due to the large amount of data, the correlations between uncertainties, and insufficient information provided by authors. These problems are further complicated by the need for correct propagation of large uncertainties, asymmetric uncertainties, limits, and ranges. A recent NNDC review of data uncertainties [Brown et al. 2015, 034020] provides a complete description of this topic.
Over the years many of these problems have been addressed, covariance formalism has been developed for ENDF libraries [Chadwick et al. 2011[Chadwick et al. , 2887, and new computer codes were introduced. The data analysis and evaluation codes are pure mathematical procedures that can be applied to diverse data samples. In this chapter, I will discuss a nontraditional application of nuclear data evaluation codes for Hubble constant experimental data sets evaluation.

Hubble Constant Experimental Data Sets
The Hubble constant and its present-day numerical value are very important for modern astrophysics and cosmology [Boyd 2008, 1, Dolgov et al. 1988. For many years, researchers have been improving accuracy of the constant [Livio & Riess 2013, 41]. Fig. 9 shows the time evolution of Hubble research in the last 100 years, and the original effort can be traced to as early as 1916 [Huchra 2015]. The large number of measurements creates a certain degree of confusion about Hubble constant numerical value, and scientists often rely on recently-published results [Olive et al. 2014, 090001]. The precision of Hubble constant measurements has improved enormously over the years; however, it is not always prudent to reject older results in favor of the latest findings. Consequently, it makes perfect sense to analyze all available results, evaluate the data, and extract the recommended value.

Hubble Constant Data Evaluation
The volume of Hubble constant measurements far exceeds other experimental quantities in nuclear physics [Pritychenko 2015, 075103] and supplies a large input sample for USNDP codes. Previously, similar situations have been encountered in nuclear and particle physics and resolved with data evaluations. Nuclear data evaluations and their policies are well described in literature [Pritychenko et al. 2016, 1, ENSDF 2016. Frequently, the evaluations Nuclear Data for Astrophysics Modeling 13 are completely based on or adjusted to available experimental data. These adjustments and specialized mathematical statistics techniques can be applied for nuclear, particle, or any other data sets. In this work, I would follow standard nuclear data evaluation procedures to deduce the recommended value. Current evaluation input data are mostly based on the NASA/HST Key Project on the Extragalactic Distance Scale compilation [Huchra 2015] and recent results. A visual inspection of historical Hubble Constant measurements, as shown in Fig. 9, is instrumental in the data analysis. It suggests that one may safely reject all measurements prior to 1970. It is common knowledge that Hubble constant measurements heavily rely on the accuracy of astronomic distance determination.
Older results, such as those reported by A. Sandage and G. de Vancouleurs, suffered from inaccurate measurements [Livio & Riess 2013, 41]. Therefore, the rejection of all results prior to 1990 could provide a complimentary benchmark value of the Hubble constant. In the present data analysis, the experimental data have been separated into two groups, with 1970 and 1990 time cuts, and further reduced using the following policies: • Rejection of repeated results (multiple publication of the same result).
These experimental data sets have been processed with the latest version of the visual averaging library [Birch & Singh 2014, 106]. The library program includes limitation of relative statistical weight (LWM), normalized residual (NRM), Rajeval technique (RT), and the Expected Value (EVM) statistical methods to calculate averages of experimental data with uncertainties. The experimental data sets were processed, and evaluated values with reduced χ 2 <2 were typically accepted as reasonable data fits. The current evaluation incorporates statistical methods based on the inverse squared value of the quoted uncertainties, a procedure that is consistent with the general methodology used in treatment of data for the ENSDF database [ENSDF 2016] and Particle Data Group [Olive et al. 2014, 090001].

Hubble Results and Discussion
Two sets of recommended values are displayed in Fig. 10, and the combined numerical values are shown in Table 2. The Hubble constant combined central values extracted by means of different mathematical techniques are in good agreement, while uncertainties need further discussion.  In recent years, an effort has been made to calculate the Hubble constant median statistics [Chen & Ratra 2011, 1]. The median statistics approach differs substantially from nuclear or particle data evaluation procedures. At the same time, it provides a complementary value of 68±5.5 (or ±1) (km/sec)/Mpc, where the errors are the 95% statistical and systematic (or statistical) errors, that can be compared with the present results.
The knowledge of Hubble constant value has multiple implications in science. As an example, a rough estimate of the age of the Universe can be deduced using the standard methodic [Wikipedia 2015]. The adopted value of 66.2(77) (km/sec)/Mpc implies (14.78±1.72)×10 9 years estimated value for the age of Universe. The last result is consistent with the recently published value of (13.798±0.037)×10 9 years [Ade et al. 2013, A1].
The analysis of Hubble constant measurements has been performed using standard US-NDP codes and procedures. An evaluated data set of most probable values of Hubble constant has been deduced and shown in Table 2. These values are consistent with other available results. An accurate constant value is instrumental for many potential applications. The recommended value of the constant is completely based on experimental measurements, and further, more precise observations, would lead to a more accurate determination of it.

Further Analysis of Astrophysical Data Sets
In the near future, data analysis and evaluation codes could be applied to experimental nuclear reaction data in order to produce data sets of cross section values and uncertainties complementary to astrophysical libraries [Angulo et al. 1999, 3, Cyburt et al. 2010, 240, Dillmann et al. 2006.

Conclusion
A brief review of astrophysical modeling data needs has been presented with an emphasis on nucleosynthesis modeling. The scope of the traditional nuclear astrophysics activities has been extended to the USNDP nuclear databases, codes, and methods. The EXFOR and ENDF libraries are extensively investigated in the context of neutron cross sections for s-process nucleosynthesis. Further analysis shows that decay rates are essential in stellar nucleosynthesis calculations, and these rates have been evaluated for ENSDF database using nuclear structure codes.
The nuclear data evaluation codes and procedures have been applied to Hubble constant measurements. This approach results in the most probable or recommended Hubble constant value of 66.2(77) (km/sec)/Mpc and implies (14.78±1.72) × 10 9 years as a rough estimate for the age of the Universe.
The current analysis of astrophysical nuclear data needs indicates a strong potential of USNDP databases for astrophysical applications. Further work may produce results in complementary to astrophysics libraries data sets. These data could play a crucial role in stellar nucleosynthesis modeling and other potential applications.