Skip to content
Jakub Skowronski
Skip to the map

Reaction atlas

The nuclear reactions that make stars shine

Where each reaction that powers stars and makes the elements sits on the chart of nuclides, how well it is known, and how it was measured.

↑ protons Z

neutrons N →

Line weight: key, major, minor reactionOther processesStable, radioactive

Hover over an arrow for its name and click it for the details, or click a square for the reactions of that nucleus. With a keyboard, Tab reaches the map and the arrow keys move along the reactions of the process on show.

How well each rate is known: More in the glossary

  • Well knownThe rate is known well enough for the stellar models that use it.
  • ImprovingRecent measurements have narrowed the rate; some uncertainty remains.
  • UncertainThe rate is uncertain enough to change the models that depend on it.
  • UnmeasuredNo direct data at the energies that matter; the rate rests on extrapolation or indirect methods.
How to read the map
protonsneutrons+ protonβ⁺+ neutron+ helium‑4stableradioactive
  • 1.Each square is an atomic nucleus. One step up adds a proton and makes the next element; one step to the right adds a neutron.
  • 2.Each arrow is a reaction or a decay. Straight up: a proton is captured. Two up and two right: a helium nucleus is captured. One down and one right: a β+ decay, in which a proton turns into a neutron.
  • 3.Squares filled in grey are stable nuclei; outlined squares are radioactive.
  • 4.The colour of an arrow tells which process it belongs to; the buttons above the map choose the process. Thicker lines are the more important reactions.
  • 5.Some arrows jump far. When two nuclei heavier than helium fuse, as in carbon burning, they form a highly excited nucleus that at once breaks up: 12C + 12C makes 24Mg*, which falls apart into 20Ne and an alpha particle or into 23Na and a proton. The arrow goes straight from 12C to the end product.

Reading a reaction

14N(p,γ)15O means: a nitrogen‑14 nucleus (the target) captures a proton (what goes in) and becomes oxygen‑15 (the product), giving off a gamma ray (what comes out). Every reaction is written the same way: target(in,out)product. More in the glossary

The kinds of arrow

  • (p,γ) a proton is captured: one up
  • (α,γ) a helium nucleus is captured: two up, two right
  • (p,α) a proton in, a helium nucleus out: one down, two left
  • (α,n) a helium nucleus in, a neutron out: two up, one right
  • (n,γ) a neutron is captured: one right
  • β+ a proton turns into a neutron: one down, one right
  • 12C + 12C two heavy nuclei fuse: a long jump

The proton–proton chains

How the Sun shines. Four protons become one helium nucleus through a chain of reactions that starts with the slowest process in the Sun, the fusion of two protons.

pp-I

The main branch in the Sun: two protons make a deuteron, the deuteron captures a proton to make 3He, and two 3He nuclei fuse to 4He.

centre of the Sun, 15.7 MK

  1. 1.1H(p,e+ν)2HWell known
  2. 2.1H(pe−,ν)2HWell known
  3. 3.2H(p,γ)3HeLUNAWell known
  4. 4.3He(3He,2p)4HeLUNAWell known

pp-II

3He captures a 4He nucleus to make 7Be, which captures an electron and becomes 7Li; 7Li and a proton give two 4He. Source of the 7Be solar neutrinos.

centre of the Sun, 15.7 MK

  1. 1.3He(α,γ)7BeLUNAImproving
  2. 2.7Be(e−,ν)7Lit½ 53.2 d
  3. 3.7Li(p,α)4HeWell known

pp-III

A rare branch: 7Be captures a proton to make 8B, whose decay emits the high-energy solar neutrinos first detected in the Homestake mine.

centre of the Sun, 15.7 MK

  1. 1.3He(α,γ)7BeLUNAImproving
  2. 2.7Be(p,γ)8BImproving
  3. 3.8B(β+ν)8Bet½ 772 ms

hep

The rarest termination: a 3He nucleus captures a proton and becomes 4He directly, through the weak interaction. It adds almost nothing to the Sun's energy, but emits the most energetic solar neutrinos.

centre of the Sun, 15.7 MK

  1. 1.3He(p,e+ν)4HeUnmeasured

Start here

A century of stellar fusion in 8 moments

From Eddington's guess in 1920 to measurements deep under a mountain: how we learned what makes the stars shine. The full timeline has 57 entries.

Three stories

  • 1

    The slowest reaction in the Sun

    Two protons fuse only if one of them turns into a neutron in the instant they touch. In the rate explorer's model of the Sun's centre, a proton waits about 6.1 billion years for that to happen. That is why the Sun is still shining. It is far too rare to measure in any laboratory: the rate comes from theory.

  • 2

    The step that sets the CNO pace

    In stars heavier than the Sun, carbon, nitrogen and oxygen help turn hydrogen into helium. The slow step is nitrogen-14 capturing a proton: in the core of a 15 M☉ star a nitrogen-14 nucleus waits about 4900 years. Measurements reach down to 70 keV; the centre of the Sun needs about 27 keV.

  • 3

    Why underground

    At the energies stars use, a target may see a few reactions a day, fewer than the counts that cosmic rays leave in a detector at the surface. Under 1.4 km of rock at Gran Sasso, LUNA counts in near silence. In EXFOR, 83 datasets on 20 reactions of the atlas come from there, and for 15 of them they are still the lowest energies ever measured.

Guided paths

From a question to what we still don't know, a few steps at a time.

Why these reactions matter, and why they are measured underground

Stars shine because light nuclei fuse into heavier ones. Fusion in stars made most of the elements from carbon up to iron; most of those beyond iron were made instead by neutron captures, slow ones mainly in red giants and rapid ones in stellar explosions and neutron-star mergers. To model a star, or to read the composition of an old one, we need to know how fast each of these reactions runs at the temperature inside it: its reaction rate.

That rate is hard to measure. Nuclei repel each other electrically, and at stellar temperatures they have far too little energy to overcome the repulsion. They fuse only by quantum tunnelling, and only within a narrow band of energies, the Gamow window, where the nuclei are fast enough and still numerous enough. In the Sun the window for 14N + p lies near 27 keV (a keV, a kilo-electronvolt, is the energy an electron gains across 1000 volts). The chance that a reaction happens is measured by its cross section, an effective target area. At 70 keV, the lowest energy at which this reaction has been measured, the cross section is 0.24 picobarn, or 2.4 × 10−37 cm².

Even an intense beam then produces only a trickle of reactions, and at the surface of the Earth cosmic rays make far more counts than that in any γ-ray detector. In the early 1990s the LUNA collaboration therefore moved its accelerator under the Gran Sasso mountain in Italy, where 1.4 km of rock cuts the flux of cosmic-ray muons about a millionfold. Several reactions of the pp chains and the CNO cycles have since been measured there at, or close to, the energies at which the Sun runs them.

Each reaction turns one nucleus into another, and in a star they link up into chains and cycles: a reaction network. This atlas collects the reactions that matter most. For each it says what the reaction does, why it matters, how it has been measured and what is still uncertain. The map places them on the chart of nuclides, with protons counted upwards and neutrons across; choose a process to follow its path.

Schematic cross-section of the Gran Sasso mountain. Cosmic-ray muons coming from above stop in the rock; only about one in a million reaches the underground halls, about 1400 m below the summit, where the LUNA 400 kV accelerator and the 3.5 MV machine of the Bellotti Ion Beam Facility (BIBF) send their beams onto targets surrounded by detectors.Gran Sassorock1≈ 1400 m2345motorway tunnel
  1. At the surface, cosmic rays make a steady rain of muons, which leave signals in any γ-ray detector.
  2. About 1400 m of rock (3800 m water equivalent) stop all but about one muon in a million.
  3. LUNA 400 kV: proton and helium beams for hydrogen burning, since the early 2000s.
  4. The 3.5 MV machine of the Bellotti Ion Beam Facility (BIBF), inaugurated in 2023: proton, helium and carbon beams for helium and carbon burning.
  5. The beam hits a target; a detector around it counts the γ-rays or particles from the few reactions.

Schematic, not to scale.

LUNA results in the atlas

LUNA on the timelineMy part in LUNA, since 2020

Reactions in the atlas with at least one measurement published by the LUNA collaboration, with the years of those measurements.

Timeline

Theory, experiments, observations and laboratories, from 1920 to today, each entry with its reference.

The s-process

How slow neutron captures carry iron to lead: the path on the chart of nuclides, its branch points, and how the captures are measured.

Reaction rates, live

How fast each reaction runs in a star, and what changes when a rate does. Calculated in your browser.

Methods and laboratories

How a cross section at stellar energies is measured, directly or indirectly, and where.

Open questions

What the field still argues about, who holds which view, and what would settle it.

The data

The whole atlas as one JSON file: 75 reactions, 353 references, with Q-values and Gamow windows computed from AME2020.

How to cite this atlas

J. Skowronski, Reaction atlas, version 2026-10-12, https://jskowron.eu/atlas.

Cite the version you used; the date is the last change to the content.

The text and the data, including data.json, are released under the CC BY 4.0 licence: you may reuse them, with credit. Licence: CC BY 4.0

LUNA marks LUNA work throughout the atlas. Q-values from the AME2020 mass evaluation, half-lives from NUBASE2020.