Nuclear Fusion Pathways

A helium-4 nucleus contains two protons and two neutrons. Producing it from hydrogen requires reactions that bind particles together and convert two protons into neutrons. Once the associated electron and positron processes are included, the products have less total rest mass than the starting material.

The difference becomes energy according to E = mc². About 0.7% of the participating hydrogen mass is converted into energy. A useful overall balance, including positron–electron annihilation, is:[3]

This equation summarizes a network of separate reactions. In the hot core, the symbols refer to nuclei and free particles, rather than complete atoms.

How positively charged nuclei get close enough

Nuclei repel one another electrically. Higher temperatures increase their relative motion, while quantum tunneling gives them a chance to react at energies below the classical electrical barrier. Fusion rates reflect both the distribution of particle energies and the probability of a reaction at each energy.[2]

The probability still depends on the particular reaction. The first proton–proton reaction includes a weak-interaction conversion of a proton into a neutron, making a successful encounter exceptionally unlikely. This slow entrance helps explain how hydrogen burning can continue for billions of years.[1]

The simplest complete route is called pp I. It builds helium-3 first, then combines two helium-3 nuclei to make helium-4. The number of times each step occurs matters:

1. Step 01 · happens twice

   Make deuterium

   p + p → ²H + e⁺ + ν_e

   One proton becomes a neutron as the pair forms deuterium. A positron and an electron neutrino are emitted.

2. Step 02 · happens twice

   Build helium-3

   ²H + p → ³He + γ

   Each deuterium nucleus captures another proton. Repeating the first two steps produces two helium-3 nuclei.

3. Step 03 · happens once

   Complete helium-4

   ³He + ³He → ⁴He + 2p

   The two helium-3 nuclei react. Two protons return to the surrounding plasma.

Six protons enter these intermediate reactions, but two are returned. The net consumption is therefore four protons for one helium-4 nucleus. Positrons subsequently annihilate with electrons, adding to the released energy.[1], [3]

Three main branches, with different neutrino signatures

Helium-3 can instead react with an existing helium-4 nucleus to make beryllium-7. From there, electron capture leads into pp II, while proton capture leads into pp III. The branching probabilities depend on local conditions.

These are the three principal branches. Additional reactions include pep, an alternative way to form deuterium involving two protons and an electron, and the rare hep reaction between helium-3 and a proton. A full solar reaction network includes them as well.[1]

In the CNO cycles, heavier nuclei participate in a sequence of proton captures and radioactive decays. The principal loop, CNO I, is also called the CN cycle. A carbon-12 nucleus changes identity during the sequence and returns at the end.

1. ¹²C + p → ¹³N + γ

   Carbon-12 captures a proton.

2. ¹³N → ¹³C + e⁺ + ν_e

   Nitrogen-13 undergoes beta-plus decay.

3. ¹³C + p → ¹⁴N + γ

   Carbon-13 captures a proton.

4. ¹⁴N + p → ¹⁵O + γ

   Nitrogen-14 captures a proton: the bottleneck under ordinary stellar hydrogen-burning conditions.

5. ¹⁵O → ¹⁵N + e⁺ + ν_e

   Oxygen-15 undergoes beta-plus decay.

6. ¹⁵N + p → ¹²C + ⁴He

   A final proton capture releases helium-4 and restores carbon-12.

Four protons have been consumed, one helium-4 nucleus has been produced, and carbon is available for another loop. The ordinary cycle’s pace is largely controlled by nitrogen-14 capturing a proton.[1], [13]

The net fuel is hydrogen. Producing new carbon from helium requires a different reaction sequence, introduced later in this article.

Temperature changes the probabilities of nuclear reactions. Density affects how often particles encounter one another. Composition sets how much hydrogen and how many suitable catalyst nuclei are available. The balance between pp and CNO burning follows from these conditions throughout the burning region.

These comparisons concern the reaction networks, not a universal dividing line between two classes of stars.[1], [2]

The Sun shows why a fixed temperature switch fails

The Sun’s modeled central temperature is about 15.7 million K, yet pp reactions still provide roughly 99% of its nuclear power, with CNO reactions contributing around 1%. Crossing 15 million K therefore does not, by itself, make a star CNO-dominated.[3], [4]

Higher-mass main-sequence stars generally develop hotter cores. In models with compositions similar to the Sun’s, CNO burning becomes important at masses moderately above the Sun’s. The precise crossover shifts with composition and evolution, and both networks can remain active.[5]

In astronomy, metallicity means the abundance of elements heavier than helium. It is broader than the CNO catalyst supply: two compositions with the same total metallicity need not contain identical amounts of carbon, nitrogen, and oxygen.

Strong temperature sensitivity concentrates CNO energy production toward the hottest central regions. Carrying that energy outward can require a steep temperature gradient, encouraging convection in the core. Such mixing redistributes helium and supplies additional hydrogen to the burning region.[5], [6]

The Sun instead has a mainly radiative interior, including its fusion-producing core, and a convective outer envelope. Still smaller stars can be fully convective. Energy generation and energy transport are related, but they are distinct physical processes.[3], [5]

The star adjusts its temperature, density, and size as these processes interact. A faster reaction rate at fixed conditions therefore does not translate directly into the same increase in a whole star’s luminosity. Stellar models must solve for the structure as well as the reactions.[3], [8]

Light escaping the Sun’s surface has been shaped by energy transport through its interior. Neutrinos interact so weakly that they usually escape directly, carrying information about the nuclear reactions that produced them.

The missing neutrinos revealed new physics

Early experiments detected fewer electron neutrinos than expected from solar models. SNO later measured interactions sensitive to the total flux of active neutrino flavors, as well as interactions sensitive to electron neutrinos.

The total agreed with solar expectations: many neutrinos had changed flavor during their journey. Neutrino oscillations explain why a detector sensitive mainly to electron neutrinos sees fewer than the Sun originally produced.[10]

Oscillations of the star itself provide a different kind of evidence. They constrain properties such as sound speed, which depend on temperature and composition. Inferring a core temperature therefore requires physical modeling rather than a direct thermometer reading.[3], [11]

For other stars, astronomers test fusion models chiefly through light, measured masses, and stellar oscillations. The detailed reaction-specific neutrino measurements described here come from the nearby Sun.

At stellar energies, many nuclear reactions are extremely rare in a laboratory. Background radiation can overwhelm their signals. Underground experiments reduce cosmic-ray background, allowing more sensitive measurements of selected reactions in both pp and CNO networks.[12]

LUNA’s studies of ¹⁴N + p → ¹⁵O + γ provide an important example. Measuring parts of this reaction helps constrain the bottleneck of ordinary CNO burning. Such work informs predictions of stellar evolution and solar neutrino production.[13]

The initial proton–proton reaction is exceptionally difficult: its probability is too small for a direct laboratory measurement. Its rate is determined from nuclear theory constrained by related physical information. Other reactions can be measured closer to stellar energies, with remaining extrapolations and uncertainties assessed explicitly.[1], [12]

A reaction network is one part of the calculation

Stellar evolution software such as MESA follows composition changes and energy generation together with gravity, pressure, and energy transport. Mixing can supply fresh fuel, and burning changes the material being mixed.

Researchers compare predicted luminosities, radii, lifetimes, and oscillation properties with observations. Reaction-rate uncertainties matter, alongside uncertainties in composition, opacity, convection, and other aspects of the model.[14]

As a core uses hydrogen, its composition and temperature evolve. The balance between pp and CNO reactions can change even before the main-sequence phase ends. Later, hydrogen can continue burning in a shell around a helium-rich core.

For a Sun-like star ascending the red-giant branch, CNO reactions become important in the hotter hydrogen-burning shell. The dominant route in the present-day solar core therefore does not define every later burning phase.[5], [6]

Nuclear reactions and stellar structure evolve together. Following both lets astronomers connect the light of a star today with its future changes—and with the material it may eventually return to its surroundings.