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 listHide the list
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]
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]
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
- 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
- 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
| Quantity | Datasets | E_cm range (keV) |
|---|---|---|
| σcross section | 26 | 2.35 keV – 98.7 MeV |
| SS-factor | 12 | 2.35 keV – 1.48 MeV |
| dσ/dΩangular distribution | 68 | 900 eV – 49.7 MeV |
| Aypolarization | 18 | 10.5 keV – 133 MeV |
| Yyield | 2 | 250 keV – 79.2 MeV |
| …other | 13 | 2.4 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.
Open questions
- The normalization of the S-factor at BBN energies, where the evaluations differ.
Related reactions
References
- 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.
D. S. Leonard, H. J. Karwowski, C. R. Brune, B. M. Fisher, E. J. Ludwig
Phys. Rev. C 73, 045801 (2006) · 10.1103/PhysRevC.73.045801 · arXiv:nucl-ex/0601035
- 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.
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.
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.
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.
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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