Chart of the Nuclides

Purpose of this appendix

This appendix collects the nuclear data most often used throughout the book: the geometry of the chart of the nuclides, the nuclides that appear repeatedly in stellar nucleosynthesis, radioactive half-lives of astrophysical interest, and the public data sources used for quantitative work. It is not a complete nuclear database. More than three thousand nuclides are known experimentally, and most of them are radioactive. The aim here is selective: to provide a working reference for the processes discussed in the chapters.

For complete and current values of masses, half-lives, decay modes, levels, and evaluated nuclear properties, the primary reference is NNDC NuDat [Brookhaven National Laboratory] . Nuclear masses are conventionally taken from the Atomic Mass Evaluation, with AME2020 as the current reference in this text [Wang et al. 2021] . Reaction rates relevant to stellar calculations are commonly drawn from compilations such as NACRE-II [Xu et al. 2013] , JINA REACLIB, and process-specific databases such as KADoNiS for Maxwellian-averaged neutron-capture cross sections.

Geometry of the chart

The chart of the nuclides is the map on which nucleosynthesis is drawn. Each nuclide is placed by neutron number $N$ and proton number $Z$. Nuclides with the same $Z$ are isotopes of one element and lie along a horizontal sequence. Nuclides with the same $N$ are isotones. Nuclides with the same mass number $A = N + Z$ are isobars. Nuclear reactions and decays move material across this chart in characteristic directions.

The stable and long-lived nuclides form the valley of beta stability. For light nuclei, stability lies close to $N \approx Z$. For heavier nuclei, stability bends toward $N > Z$, because additional neutrons help offset the growing Coulomb repulsion between protons. Nuclei on the neutron-rich side of the valley tend to decay by $\beta^{-}$ emission. Nuclei on the proton-rich side tend to decay by $\beta^{+}$ emission or electron capture.

The outer boundaries are the drip lines. At the neutron drip line, adding another neutron no longer produces a bound nucleus; at the proton drip line, adding another proton is not energetically bound. The r process moves through neutron-rich territory toward the neutron drip line before beta decay brings material back toward stability. The rp process in X-ray bursts moves through proton-rich territory toward the proton drip line, with beta decays and waiting points controlling its progress.

The chart is structured by shell closures. The main magic numbers are

$$2,\ 8,\ 20,\ 28,\ 50,\ 82,\ 126.$$

Nuclei with magic $N$ or $Z$ have enhanced binding and often smaller neutron-capture cross sections. Doubly magic nuclei are especially important reference points: $^{4}\mathrm{He}$, $^{16}\mathrm{O}$, $^{40}\mathrm{Ca}$, $^{48}\mathrm{Ca}$, $^{56}\mathrm{Ni}$, $^{132}\mathrm{Sn}$, and $^{208}\mathrm{Pb}$ all appear repeatedly in nucleosynthesis because shell structure affects reaction flow.

The abundance peaks of heavy elements are a direct imprint of these closures. The s-process peaks near $A \approx 88$, $138$, and $208$ correspond to neutron magic numbers encountered near the valley of stability. The r-process peaks near $A \approx 80$, $130$, and $195$ are shifted because the r-process path crosses the same neutron shell closures at lower $Z$, far from stability, before beta decay returns the products to stable nuclei.

Nuclides by process

The following tables are working lists. Half-lives are rounded for reading use; they should not be used as a substitute for database values in calculations.

Big Bang Nucleosynthesis

Hydrogen burning

Helium and advanced burning

s process and branching points

r process

p nuclei and proton-rich products

Observable radioactivities

Decay modes

Astrophysical nucleosynthesis depends on both reaction rates and decay times. The relevant half-lives range from unbound nuclear resonances lasting far less than a femtosecond to nearly stable isotopes with half-lives longer than the age of the universe. Whether a nuclide behaves as active or effectively stable depends on the timescale of its environment.

The main decay modes are:

Laboratory half-lives are not always stellar half-lives. Dense plasma can change electron-capture rates. Thermal population of excited nuclear states can couple long-lived and short-lived isomers. Ionization can change bound-state beta decay in rare cases. Network calculations therefore use laboratory data as a baseline and apply stellar corrections when required.

Public nuclear data sources

NNDC / NuDat [Brookhaven National Laboratory] is the standard entry point for nuclear levels, half-lives, decay modes, radiation, and evaluated structure information. It is the first check for individual nuclides.

AME2020 [Wang et al. 2021] is the reference mass evaluation used for nuclear masses, mass excesses, and separation energies. It is essential for locating drip lines, Q-values, and reaction thresholds.

NACRE-II [Xu et al. 2013] compiles thermonuclear reaction rates for many reactions of astrophysical interest across the temperature ranges used in stellar models.

KADoNiS provides Maxwellian-averaged neutron-capture cross sections, especially at $kT = 30$ keV, and is widely used in s-process studies. Its methodology is closely connected to the s-process review by Kaeppeler et al. [Käppeler et al. 2011] .

JINA REACLIB provides reaction rates in a standard parameterized format used by many nuclear network codes, including stellar-evolution and explosive-nucleosynthesis calculations.

ENSDF is the evaluated nuclear structure file behind much of the level and decay information used by NNDC tools.

ENDF provides evaluated reaction cross sections used in nuclear applications and, for some regimes, in astrophysical network calculations involving neutron-induced reactions.