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Jakub Skowronski
Reaction atlas · Proton–proton chains

Weak interaction · pp-I

1H(p,e+ν)2H

: proton + proton → deuteron + positron + neutrinoHow to read the notation

Well known
On this page

Two protons fuse into a deuteron, emitting a positron and a neutrino. This is the first and slowest step of the pp chain, and it sets the pace at which the Sun burns hydrogen.

For two protons to stick together, one of them must turn into a neutron while they are briefly close. That change goes through the weak interaction, the same force behind radioactive β decay, so it happens very rarely: a proton in the centre of the Sun waits billions of years on average before it takes part. This slowness is why the Sun lives so long. Almost every chain that turns hydrogen into helium in the Sun begins here, and the neutrinos it produces, called pp neutrinos, are the most numerous solar neutrinos reaching the Earth.

Facts

How well known
Far too slow ever to be measured in a laboratory, so the rate comes from theory; different calculations agree closely.
Live evaluation
No live evaluation yet · Evaluations
Reaction rates
Explore the rates →
Q-value · energy released
1.442 MeV
Q includes positron annihilation (2mec² = 1.022 MeV). Without it, 0.420 MeV is shared by the positron and the neutrino.
Gamow window
  • 6.1 ± 3.3 keVcentre of the Sun, 15.7 MK (pp-I)
Kind
Weak interaction

On the timeline

  1. 1938Bethe and Critchfield describe proton–proton fusion
  2. 1991SAGE, the first gallium experiment
  3. 1992GALLEX observes pp neutrinos at Gran Sasso
  4. 2014Borexino sees pp neutrinos

How it was measured

2 measurements, 1998–2013Show the list

  1. 1998

    Calculation from theory · solar energies

    Potential-model calculation with several high-precision nucleon-nucleon interactions, the axial two-body current tuned to the Gamow–Teller matrix element of tritium β decay; the overlap integral Λ2(0) lies between 7.05 and 7.06 for all interactions. [1]

  2. 2013

    Calculation from theory · 0–100 keV

    Chiral effective field theory with the N3LO two-nucleon potential, full electromagnetic interaction and weak-current constants fixed by the A = 3 binding energies, magnetic moments and tritium β decay; S- and P-wave contributions included. An erratum followed in 2019. [2]

Details

How well known, in detail: Known from theory only; potential-model and effective-field-theory calculations agree within their small uncertainties.

The cross section is far too small to measure in the laboratory at any energy, so S(0) is calculated. The calculation needs the overlap of the initial pp scattering state and the deuteron, both well constrained by nucleon-nucleon data, the axial coupling constant from neutron β decay, and two-body (meson-exchange) contributions to the weak axial current, which are fixed in modern calculations by the tritium β-decay rate. Potential-model calculations with several modern nucleon-nucleon interactions (Schiavilla et al. 1998) show a weak model dependence, and the chiral effective field theory calculation of Marcucci et al. (2013) agrees with them.

The Solar Fusion evaluations adopt a calculated S(0) whose uncertainty is smaller than that of the measured pp-chain rates, although the reaction has never been observed in the laboratory. The neutrinos it emits are observed directly: Borexino measured the pp-neutrino flux in 2014 (Bellini et al., Nature 512, 383), consistent with the solar-model prediction.

Peak energy E0 ± half the 1/e width, centre of mass, from the AME2020 masses.

Evaluations

Compilations that combine the data into a recommended rate.

  • —E. G. Adelberger et al., Rev. Mod. Phys. 83, 195 (2011) [3]
  • —B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [4]

Open questions

  • The size of two-body axial-current contributions at higher orders of effective field theory, which dominates the theoretical uncertainty.

Related reactions

References

  1. 1.

    R. Schiavilla, V. G. J. Stoks et al.

    Weak capture of protons by protons

    Phys. Rev. C 58, 1263 (1998) · 10.1103/PhysRevC.58.1263 · arXiv:nucl-th/9808010

  2. 2.

    L. E. Marcucci, R. Schiavilla, M. Viviani

    Proton-proton weak capture in chiral effective field theory

    Phys. Rev. Lett. 110, 192503 (2013); erratum Phys. Rev. Lett. 123, 019901 (2019) · 10.1103/PhysRevLett.110.192503 · arXiv:1303.3124

  3. 3.

    E. G. Adelberger et al.

    Solar fusion cross sections II: the pp chain and CNO cycles

    Rev. Mod. Phys. 83, 195 (2011) · 10.1103/RevModPhys.83.195

  4. 4.

    B. Acharya et al.

    Solar fusion III: New data and theory for hydrogen-burning stars

    Rev. Mod. Phys. 97, 035002 (2025) · 10.1103/8lm7-gs18 · arXiv:2405.06470

How to cite this page

J. Skowronski, 1H(p,e+ν)2H, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/1H-pp-2H.

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