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Reaction atlas · Proton–proton chains

Fusion · pp-I

3He(3He,2p)4He

: helium‑3 + helium‑3 → helium‑4 + proton + protonHow to read the notation

Well knownMeasured at LUNA
On this page

Two 3He nuclei fuse into one 4He nucleus and release two protons. This closes the main branch of the pp chain in the Sun.

Once 3He has been made, it can meet another 3He nucleus or a 4He nucleus. The first path ends the pp-I chain and produces no further neutrinos; the second opens the pp-II and pp-III branches, which emit the 7Be and 8B solar neutrinos. The competition between the two therefore sets how many of these neutrinos the Sun emits. In the 1990s the reaction was also measured to test the idea that an unknown low-energy resonance could explain the solar neutrino deficit.

Facts

How well known
Measured down to the energies at which the reaction runs in the Sun. The remaining uncertainty comes from the correction for the atomic electrons of the target, which make the reaction easier in the laboratory than it is for bare nuclei, and from the energy spectrum of the emitted protons.
Live evaluation
No live evaluation yet · Evaluations
Reaction rates
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Q-value · energy released
12.860 MeV
Gamow window
  • 22 ± 6.3 keVcentre of the Sun, 15.7 MK (pp-I)
Kind
Fusion

On the timeline

  1. 1994LUNA, the first underground acceleratorLUNA
  2. 1999LUNA measures 3He + 3He inside the solar Gamow peakLUNA

How it was measured

5 measurements, 1996–2017, 3 at LUNAShow the list
  1. 1996

    LUNA 50 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · down to about 21 keV

    First data inside the solar Gamow peak, no evidence for a low-energy resonance; tentative S(0) = 5.1 ± 0.1 MeV b after the screening correction. [1]

  2. 1998

    LUNA 50 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · down to 20.76 keV

    Full analysis of the first LUNA campaign; electron screening observed clearly for this reaction, larger than expected, and dominating the uncertainty of the bare S(0) = 5.40 MeV b. [2]

  3. 1999

    LUNA 50 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · down to 16.5 keV

    New detector setup; data down to the lower edge of the solar Gamow peak, with no sign of the narrow resonance proposed to reduce the 7Be and 8B neutrino fluxes. [3]

  4. 2004

    RCNP, OsakaResearch Center for Nuclear Physics, Osaka University

    Direct measurement at the surface · 30–50 keV

    Doubly charged 3He beam free from molecular interference; S-factor in the gap left by LUNA, with smaller statistical and systematic errors than earlier data. [4]

  5. 2017

    OMEGA laserLaboratory for Laser Energetics, University of Rochester

    Laser and inertial-confinement plasmas · low centre-of-mass energy, plasma

    Proton spectra from 3He+3He fusion in high-energy-density plasmas; the measured shape is proposed as a benchmark for the analysis of low-resolution accelerator data. [5]

Measurements (EXFOR)

Every dataset EXFOR holds for this reaction, drawn by the energies it covers, against the energies a star uses.

21 datasets in 10 EXFOR entries, 1966–2004

centre of the Sun, T₉ = 0.0157 (15.7 MK)

Lowest energy in EXFOR
17 keV
Bonetti et al., 1999 · S · A0379.002
Distance from the Gamow peak
Inside the window
E₀ = 22.1 keV, window 15.8–28.4 keV
Rate from energies not in EXFOR
7.3%
at T₉ = 0.0157, smooth estimate · 7.3% of it lies below the lowest energy in EXFOR
10 keV100 keV1 MeV10 MeV100 MeVCentre-of-mass energy (keV)E₀ = 22.1 keVσSdσ/dΩlowest in EXFOR 17 keV
  • Gamow window, hatched where no measurement reaches
  • Outlined bars are shown but not counted (the rule is under “How these numbers are made”).
  • A diamond is a dataset at a single energy. Bars running off the right edge continue to higher energies.
The datasets of the gap map, by quantity
The datasets of the gap map, by quantity
QuantityDatasetsE_cm range (keV)
σcross section629.8 keV – 12 MeV
SS-factor816.5 keV – 2.96 MeV
dσ/dΩangular distribution799.8 keV – 4.55 MeV
How these numbers are made

Lowest measured energy, everywhere in the data explorer: the lowest centre-of-mass energy at which a dataset in EXFOR measures the reaction itself (cross section, S-factor, angular distribution, yield or resonance strength), judged point by point. A point counts when it is a value, not an upper or lower limit, when it lies at least one standard deviation above zero, and when its energy is physical: at least 1 keV for charged particles, and not below the threshold of an endothermic reaction. Not counted: extrapolated, calculated, evaluated or derived values; superseded, deleted or preliminary data; ratios; a single S-factor value, which in EXFOR is a fit result; and indirect methods (Trojan horse, Coulomb dissociation, ANC, surrogate reactions), recognized from EXFOR's method and analysis codes, their text and the title. Frame and unit errors of EXFOR are corrected first, and values the literature shows to be upper limits are read as limits, from a list that gives the evidence for each. Datasets that reach the same energy within 0.5% are all credited, earliest first. Rate from energies not in EXFOR: the share of the rate integrand at that temperature outside the energy ranges the counted datasets cover (from their lowest measured point to their highest), with a constant S-factor (σ ∝ S(E₀)/E · e^−2πη, so the integrand is e^(−E/kT − 2πη)); for a neutron capture, σ ∝ 1/v. Resonances make the real integrand lumpy, so read it as a smooth baseline.

Details

The two-proton exit channel makes the reaction measurable by detecting the energetic protons in silicon telescopes, which LUNA did with the 50 kV accelerator and a windowless 3He gas target. The data reached below the centre of the solar Gamow peak and excluded a narrow resonance there. The low-energy data show a rise of the S-factor due to electron screening by the atomic electrons of the target, larger than expected; the screening correction is the main uncertainty on the bare-nucleus S(0).

Measurements with a doubly charged 3He beam at Osaka, free of molecular-beam contamination, filled the energy gap above the LUNA range. Plasma experiments at laser facilities measured the proton spectrum, whose shape matters when low-resolution detectors are used.

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) [6]
  • —B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [7]

Open questions

  • The origin of the electron-screening enhancement, which is larger than expected.
  • The shape of the three-body proton spectrum and its effect on detection efficiencies.

Related reactions

References

  1. 1.

    C. Arpesella et al. (LUNA Collaboration)

    Measurement of the 3He(3He,2p)4He cross section within the solar Gamow peak

    Phys. Lett. B 389, 452 (1996)LUNA

  2. 2.

    M. Junker et al. (LUNA Collaboration)

    Cross section of 3He(3He,2p)4He measured at solar energies

    Phys. Rev. C 57, 2700 (1998) · 10.1103/PhysRevC.57.2700 · arXiv:nucl-ex/9707003LUNA

  3. 3.
  4. 4.

    N. Kudomi, M. Komori, K. Takahisa, S. Yoshida, K. Kume, H. Ohsumi, T. Itahashi

    Precise measurement of cross section of 3He(3He,2p)4He by using 3He doubly charged beam

    Phys. Rev. C 69, 015802 (2004) · 10.1103/PhysRevC.69.015802 · arXiv:astro-ph/0306454

  5. 5.
  6. 6.

    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

  7. 7.

How to cite this page

J. Skowronski, 3He(3He,2p)4He, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/3He-3He2p-4He.

Cite the date you used; it is the last change to this page.

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