Logic Replicant
Empirical evidence · 08 / 09

Appendix: nucleosynthesis reactions

The known reactions included in the nucleosynthesis dataset: the four branches of the CNO cycle and three hot CNO cycles.

The nuclear reactions in the dataset, and what they are.

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What these reactions are

Stars heavier than the Sun burn hydrogen mostly through the CNO cycle: a carbon nucleus captures a proton, becomes nitrogen, then oxygen, and after a few steps returns to carbon, having turned four protons into a helium nucleus and released energy. Side branches and "hot" variants exist in massive stars, novae and X-ray bursts. Each arrow in the table below is one such step: what goes in, what comes out, and how much energy is released. Unstable nuclei decay on their own, and their half-lives are given.

Cycle sequences

The dataset covers fusion and fission of stable and unstable nuclei, with positrons e+, neutrons, gamma radiation γ, electron neutrinos νe and energy release (normally positive). Some cycles are listed partially to avoid repeating reactions already present in a preceding cycle. Equations 34–40 of the paper give the sequences:

CNO-I (starts and ends with 12C)
12C → 13N → 13C → 14N → 15O → 15N → 12C
CNO-II (minor branch of CNO-I, 0.04% of the time at the Sun's core)
15N → 16O → 17F → 17O → 14N → 15O → 15N
CNO-III (massive stars; starts when 17O becomes 18F)
17O → 18F → 18O → 15N → 16O → 17F → 17O
CNO-IV (forks from CNO-III when 18O produces 19F and a photon)
18O → 19F → 16O → 17F → 17O → 18F → 18O
HCNO-I (13N captures a proton instead of decaying)
12C → 13N → 14O → 14N → 15O → 15N → 12C
HCNO-II (17F captures a proton instead of decaying)
15N → 16O → 17F → 18Ne → 18F → 15O → 15N
HCNO-III (18F captures a proton instead of decaying)
18F → 19Ne → 19F → 16O → 17F → 18Ne → 18F

Table 2 of the paper

CycleReactionEnergy / half-life
CNO-I12C + 1H → 13N + γ+1.95 MeV
13N → 13C + e+ + νe+1.20 MeV (half-life 9.965 min)
13C + 1H → 14N + γ+7.54 MeV
14N + 1H → 15O + γ+7.35 MeV
15O → 15N + e+ + νe+1.73 MeV (half-life 122.24 s)
15N + 1H → 12C + 4He+4.96 MeV
CNO-II (partial)15N + 1H → 16O + γ+12.13 MeV
16O + 1H → 17F + γ+0.60 MeV
17F → 17O + e+ + νe+2.76 MeV (half-life 64.49 s)
17O + 1H → 14N + 4He+1.19 MeV
CNO-III (partial)17O + 1H → 18F + γ+5.61 MeV
18F → 18O + e+ + νe+1.656 MeV (half-life 109.771 s)
18O + 1H → 15N + 4He+3.98 MeV
CNO-IV (partial)18O + 1H → 19F + γ+7.994 MeV
19F + 1H → 16O + 4He+8.114 MeV
HCNO-I (partial)13N + 1H → 14O + γ+4.63 MeV
14O → 14N + e+ + νe+5.14 MeV (half-life 70.641 s)
HCNO-II (partial)17F + 1H → 18Ne + γ+3.92 MeV
18Ne → 18F + e+ + νe+4.44 MeV (half-life 1.672 s)
18F + 1H → 15O + 4He+2.88 MeV
HCNO-III (partial)18F + 1H → 19Ne + γ+6.41 MeV
19Ne → 19F + e+ + νe+3.32 MeV (half-life 17.22 s)
19F + 1H → 16O + 4He+8.11 MeV

Dataset: github.com/pedrocorral/nucleosynthesis-dataset. How it was augmented: Datasets.