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Reaction atlas · Big Bang nucleosynthesis

Fusion · Big Bang nucleosynthesis

3He(d,p)4He

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

On this page

3He and a deuteron fuse into 4He and a proton. After the Big Bang it converted part of the 3He into 4He.

The reaction is the mirror of deuterium–tritium fusion and, like it, is very fast at the energies of the early Universe. It removes 3He and deuterium and adds to 4He. In the laboratory it has been a favourite case for studying how the electrons around the target nuclei make fusion easier at low energy.

Facts

How well known
Measured with small uncertainty at the energies of the Big Bang. The only open question is how much the atomic electrons of the target raise the measured rate at the lowest energies.
Live evaluation
No live evaluation yet · Evaluations
Q-value · energy released
18.353 MeV
Gamow window
  • 180 ± 130 keVdeuterium bottleneck, 0.8 GK (Big Bang nucleosynthesis)
  • 92 ± 56 keVend of BBN, 0.3 GK (Big Bang nucleosynthesis)
Kind
Fusion

How it was measured

3 measurements, 2000–2005, 1 at LUNAShow the list
  1. 2000

    LUNA 50 kVLaboratori Nazionali del Gran Sasso (INFN)

    Direct measurement underground · 4.2–13.8 keV

    d(3He,p)4He with a 3He beam on a deuterium gas target; the stopping power of 3He in D2 agrees with the standard compilation, and the screening potential Uₑ = 132 ± 9 eV is twice the atomic-physics estimate. [1]

  2. 2001

    100 kV accelerator, Ruhr-Universität Bochum

    Direct measurement at the surface · 5–60 keV (d beam) and 10–40 keV (3He beam)

    Both 3He(d,p)4He and d(3He,p)4He, with the LUNA setup; Uₑ = 219 ± 7 eV and 109 ± 9 eV, above the atomic-physics values of 120 and 65 eV. [2]

  3. 2005

    Trojan Horse method · from 600 keV down to astrophysical energies

    Trojan Horse measurement through the three-body reaction 6Li(3He,pα)4He at 5 and 6 MeV; the bare S-factor was extracted in the modified plane-wave Born approximation, and the screening potential derived from it is consistent with the adiabatic limit. [3]

Measurements (EXFOR)

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

96 datasets in 43 EXFOR entries, 1951–2016 · 2 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
5.01 keV
Aliotta et al., 2001 · S · A0228.002
Distance from the Gamow peak
0.68 Gamow widths below
E₀ = 178 keV, window 49.9–306 keV
Rate from energies not in EXFOR
< 0.01%
at T₉ = 0.8, smooth estimate
1 keV10 keV100 keV1 MeV10 MeV100 MeVEnergy, or kT for a Maxwellian average (keV)E₀ = 178 keVσSdσ/dΩAyMACSlowest in EXFOR 5.01 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 section143.8 keV – 23.9 MeV
SS-factor113 keV – 339 keV
dσ/dΩangular distribution3236 keV – 159 MeV
Aypolarization3636 keV – 159 MeV
MACSMaxwellian average14.77 keV – 9.54 keV
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 cross section is dominated by the 3/2+ resonance in 5Li, the mirror of the 5He state that governs d+t. At the lowest energies the measured S-factor rises above the bare-nucleus trend because the atomic electrons of the target screen the Coulomb barrier. The LUNA 50 kV accelerator measured d(3He,p)4He down to 4.2 keV and found a screening potential of 132 ± 9 eV, twice the atomic-physics estimate of 65 eV.

Measurements of both 3He(d,p)4He and d(3He,p)4He at a 100 kV accelerator in Bochum, with the LUNA setup, gave screening potentials of 219 ± 7 eV and 109 ± 9 eV, again well above the atomic-physics values of 120 eV and 65 eV. The Trojan Horse method, which gives the bare S-factor without screening, yielded a screening potential consistent with the adiabatic limit.

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.

  • —P. Descouvemont et al., At. Data Nucl. Data Tables 88, 203 (2004) [4]
  • —H.-S. Bosch, G. M. Hale, Nucl. Fusion 32, 611 (1992); correction Nucl. Fusion 33, 1919 (1993) [5]

Open questions

  • The electron-screening potential extracted from the lowest-energy direct data, which exceeds the adiabatic estimate, while the Trojan Horse analysis finds a value consistent with it.

Related reactions

References

  1. 1.

    H. Costantini et al. (LUNA Collaboration)

    Stopping power, electron screening and the astrophysical S(E) factor of d(3He,p)4He

    Phys. Lett. B 482, 43 (2000) · 10.1016/S0370-2693(00)00513-XLUNA

  2. 2.

    M. Aliotta, F. Raiola, G. Gyürky et al.

    Electron screening effect in the reactions 3He(d,p)4He and d(3He,p)4He

    Nucl. Phys. A 690, 790 (2001) · 10.1016/S0375-9474(01)00366-9

  3. 3.

    M. La Cognata et al.

    Bare-nucleus astrophysical factor of the 3He(d,p)4He reaction via the "Trojan horse" method

    Phys. Rev. C 72 (2005), issue 6

  4. 4.

    P. Descouvemont, A. Adahchour, C. Angulo, A. Coc, E. Vangioni-Flam

    Compilation and R-matrix analysis of Big Bang nuclear reaction rates

    At. Data Nucl. Data Tables 88, 203 (2004) · arXiv:astro-ph/0407101

  5. 5.

    H.-S. Bosch, G. M. Hale

    Improved formulas for fusion cross-sections and thermal reactivities

    Nucl. Fusion 32, 611 (1992); correction Nucl. Fusion 33, 1919 (1993)

How to cite this page

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

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

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