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Reaction atlas · Big Bang nucleosynthesis

Fusion · Big Bang nucleosynthesis

2H(d,n)3He

: deuteron + deuteron → helium‑3 + neutronHow to read the notation

On this page

Two deuterons fuse into 3He and a neutron. Together with its twin reaction, which gives tritium and a proton, it is one of the main ways deuterium was destroyed after the Big Bang.

The deuterium left over from the Big Bang is a sensitive measure of the density of ordinary matter in the Universe. Three reactions decide how much deuterium burned: proton capture on deuterium and the two branches of deuteron–deuteron fusion. After the proton-capture rate was measured precisely at LUNA, the deuteron–deuteron rates became an important part of the remaining uncertainty.

Facts

How well known
Several data sets exist, but the choice of evaluation changes the predicted primordial deuterium abundance noticeably.
Live evaluation
No live evaluation yet · Evaluations
Q-value · energy released
3.269 MeV
Gamow window
  • 105 ± 98 keVdeuterium bottleneck, 0.8 GK (Big Bang nucleosynthesis)
  • 55 ± 43 keVend of BBN, 0.3 GK (Big Bang nucleosynthesis)
Kind
Fusion

How it was measured

3 measurements, 1995–2014Show the list
  1. 1995

    Direct measurement at the surface · 1.6–130 keV

    Both d+d channels measured with beams from 30, 100 and 450 kV accelerators. The ratio of the two cross sections stays close to unity at low energy, so no Oppenheimer–Phillips effect was seen, and the electron-screening enhancement of d(d,p)t below 10 keV is larger than atomic-physics models predict. [1]

  2. 2006

    TUNL Low-Energy Beam Facility, Durham NC

    Direct measurement at the surface · 110–650 keV (laboratory)

    Total cross sections of both channels from a simultaneous fit of angular distributions and normalization data, with about 2% uncertainty and a 1% scale error; the resulting rates are about 7% above NACRE. [2]

  3. 2014

    Trojan Horse method · BBN energies

    Trojan Horse determination of the bare S-factors of both channels, free of electron screening, and new reaction rates for BBN. [3]

Measurements (EXFOR)

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

145 datasets in 75 EXFOR entries, 1936–2025 · 6 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
3.25 keV
Bystritsky et al., 2008; Bystritsky et al., 2012; Bystritsky et al., 2012 · S · A0726.002.1
Distance from the Gamow peak
0.52 Gamow widths below
E₀ = 105 keV, window 6.96–204 keV
Rate from energies not in EXFOR
< 0.01%
at T₉ = 0.8, smooth estimate
100 eV1 keV10 keV100 keV1 MeV10 MeV100 MeVCentre-of-mass energy (keV)E₀ = 105 keVσSdσ/dΩAyYotherlowest in EXFOR 3.25 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 section262.35 keV – 98.7 MeV
SS-factor122.35 keV – 1.48 MeV
dσ/dΩangular distribution68900 eV – 49.7 MeV
Aypolarization1810.5 keV – 133 MeV
Yyield2250 keV – 79.2 MeV
…other132.4 keV – 2.5 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 d+d reaction proceeds through two mirror channels of nearly equal strength, 3He + n and 3H + p. Both have been measured with accelerators over the BBN energy range and down to a few keV, where electron screening in laboratory targets becomes visible, and with the Trojan Horse method. The evaluations differ in how they weight and normalize these data sets, and analyses after the LUNA d(p,γ)3He result examine the effect of the d+d rates and of their evaluation on the predicted primordial deuterium abundance.

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]
  • —O. Pisanti et al., JCAP 04, 020 (2021) [6]
  • —B. D. Fields et al., JCAP 03, 010 (2020); erratum JCAP 11, E02 (2020) [7]

Open questions

  • The normalization of the S-factor at BBN energies, where the evaluations differ.

Related reactions

References

  1. 1.

    U. Greife, F. Gorris, M. Junker, C. Rolfs, D. Zahnow

    Oppenheimer-Phillips effect and electron screening in d+d fusion reactions

    Z. Phys. A 351, 107 (1995) · 10.1007/BF01292792

  2. 2.

    D. S. Leonard, H. J. Karwowski, C. R. Brune, B. M. Fisher, E. J. Ludwig

    Precision measurements of 2H(d,p)3H and 2H(d,n)3He total cross sections at Big Bang nucleosynthesis energies

    Phys. Rev. C 73, 045801 (2006) · 10.1103/PhysRevC.73.045801 · arXiv:nucl-ex/0601035

  3. 3.

    A. Tumino et al.

    New determination of the 2H(d,p)3H and 2H(d,n)3He reaction rates at astrophysical energies

    Astrophys. J. 785, 96 (2014)

  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)

  6. 6.

    O. Pisanti, G. Mangano, G. Miele, P. Mazzella

    Primordial deuterium after LUNA: concordances and error budget

    JCAP 04, 020 (2021) · 10.1088/1475-7516/2021/04/020 · arXiv:2011.11537

  7. 7.

    B. D. Fields, K. A. Olive, T.-H. Yeh, C. Young

    Big-Bang Nucleosynthesis after Planck

    JCAP 03, 010 (2020); erratum JCAP 11, E02 (2020) · 10.1088/1475-7516/2020/03/010 · arXiv:1912.01132

How to cite this page

J. Skowronski, 2H(d,n)3He, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/2H-dn-3He.

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

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