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Reaction atlas · Big Bang nucleosynthesis

Radiative capture · Big Bang nucleosynthesis

1H(n,γ)2H

: proton + neutron → deuteron + gamma rayHow to read the notation

On this page

A neutron and a proton bind into a deuteron and give off a γ-ray. This is the first step of Big Bang nucleosynthesis: all later reactions start from the deuterium it makes.

In the first minutes after the Big Bang, neutrons and protons combined into deuterons almost as fast as energetic photons broke them apart again. Only when the Universe had cooled enough did deuterium survive, and the build-up of heavier nuclei could begin. The rate of this capture therefore sets when nucleosynthesis starts and how many neutrons are still left, which in turn fixes the amount of helium.

Facts

How well known
Calculated to about 1% at the energies of the Big Bang, with a theory checked against laboratory measurements.
Live evaluation
No live evaluation yet · Evaluations
Q-value · energy released
2.225 MeV
Thermal energy kT
about 26–69 keV, the energy of a gas at 300–800 million kelvin
By stellar site
  • 69 keVdeuterium bottleneck, 0.8 GK
  • 26 keVend of BBN, 0.3 GK
Why no Gamow window
A neutron feels no Coulomb barrier, so there is no Gamow window: the relevant energies are those of the thermal distribution itself, around kT.
Kind
Radiative capture

On the timeline

  1. 1948Alpher, Bethe and Gamow on the hot early Universe

How it was measured

1 measurement, 2000Show the list
  1. 2000

    Calculation from theory · up to about 1 MeV

    Pionless effective field theory calculation with M1 to NNLO and E1 to N4LO, constrained by the cold-neutron capture rate and by deuteron photodisintegration; 1% accuracy over the BBN range. [1]

Measurements (EXFOR)

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

78 datasets in 64 EXFOR entries, 1936–2020 · 23 without an energy range, not drawn

Temperature
Lowest energy in EXFOR
12.6 meV
Fink, 1936; SPEES et al., 1938; SCHULZ et al., 1945; Baker, 1958; Reier, 1961; BAYER et al., 1961; DLOUHY et al., 1962; Pal et al., 1965; BAYER et al., 1969; Cokinos et al., 1977; Lolich et al., 1980; MEADOWS et al., 1985; COX et al., 1986; Anderson et al., 2020 · σ · 13845.002
Maxwellian averages measured
1 sets
kT from 30 keV to 30 keV
Rate from energies not in EXFOR
37%
at kT = 68.9 keV, smooth estimate
1 meV100 meV10 eV1 keV100 keV10 MeVEnergy, or kT for a Maxwellian average (keV)kT = 68.9 keVσσ→Eₓdσ/dΩAyMACSother
  • Energies that matter at kT = 68.9 keV
  • 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 section2712.6 meV – 37.7 MeV
σ→Eₓpartial315 meV – 15 meV
dσ/dΩangular distribution99.62 MeV – 343 MeV
Aypolarization83 MeV – 225 MeV
MACSMaxwellian average130 keV – 30 keV
…other79.99 meV – 90.3 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

How well known, in detail: Calculated to about 1% at the energies of the Big Bang, with a theory tied to measurements of slow-neutron capture and of deuterons broken up by γ-rays.

At BBN energies the capture is dominated by the isovector M1 transition from the 1S0 continuum at the lowest energies and by isovector E1 capture from P waves at higher energies. The cross section is calculated in pionless effective field theory, with the M1 amplitude to next-to-next-to-leading order and the E1 amplitude to N4LO; one counterterm is fixed by the cold neutron capture rate and another by deuteron photodisintegration data. The stated accuracy is 1% for centre-of-mass energies up to about 1 MeV.

Evaluations

Compilations that combine the data into a recommended rate.

  • —B. D. Fields et al., JCAP 03, 010 (2020); erratum JCAP 11, E02 (2020) [2]

Related reactions

References

  1. 1.
  2. 2.

    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, 1H(n,γ)2H, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/1H-ng-2H.

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

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