²H(p,γ)³He · Reaction atlas

A deuteron captures a proton and becomes ³He, giving off a γ-ray. In the Sun this follows the fusion of two protons almost at once. After the Big Bang it was one of the three reactions that destroyed deuterium, and the one least known before LUNA.

Deuterium, the nucleus made of one proton and one neutron, was formed in the first minutes after the Big Bang. How much of it survived depends on two things: the density of ordinary matter in the Universe and the speed of the reactions that burn it. This reaction is one of them. Astronomers measure the deuterium left in distant, almost pristine gas clouds; if the burning rate is known, that measurement gives the matter density, which can then be compared with the value from the cosmic microwave background, the light left over from the Big Bang. In stars the reaction is so fast that it never limits the pp chain, but it burns the deuterium of young stars before they start to burn hydrogen.

Facts

How well known: Since the LUNA measurement of 2020 the rate at the energies of the Big Bang is known to about 3%. Small differences remain with theoretical calculations and with the data at higher energies.
Live evaluation: No live evaluation yet · Evaluations
Reaction rates: Explore the rates →
Q-value · energy released: 5.493 MeV
Gamow window: 6.7 ± 3.5 keVcentre of the Sun, 15.7 MK (pp-I)
92 ± 92 keVdeuterium bottleneck, 0.8 GK (Big Bang nucleosynthesis)
48 ± 41 keVend of BBN, 0.3 GK (Big Bang nucleosynthesis)
Kind: Radiative capture

On the timeline

2020LUNA measures deuterium burning for cosmologyLUNA

How it was measured

7 measurements, 1997–2024, 3 at LUNAShow the list

1997
Triangle Universities Nuclear Laboratory, Durham NC
Direct measurement at the surface · below 80 keV
Cross sections, S-factors and analyzing powers with polarized and unpolarized beams; the extracted S(0) was about 25% below the value then used in astrophysics, and the vector analyzing power proved sensitive to meson-exchange currents. [1, 2]
2002
LUNA 50 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · down to 2.5 keV
Windowless gas target and segmented 4π BGO detector; first data inside and below the solar Gamow peak, with about 10% accuracy. [3]
2016
Calculation from theory · BBN range
Ab initio calculation with the AV18 and Urbana IX interactions and relativistic corrections to the one-body current; S-factor about 10% above the adopted fits. [4]
2019
Jožef Stefan InstituteJožef Stefan Institute
Direct measurement at the surface · 47–210 keV
Deuterated titanium targets and two HPGe detectors at 90° and 135°; cross sections and angular distributions in good agreement with the ab initio calculation. [5]
2020
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · BBN range
High-purity D₂ gas target, intense proton beam and a HPGe detector, after a commissioning campaign that brought the systematic uncertainty below 3%. The new rate gives the baryon density to 1.6%, in agreement with the CMB. [6, 7]
2021
HZDR Tandetron, Dresden-RossendorfHelmholtz-Zentrum Dresden-Rossendorf
Direct measurement at the surface · 265–1094 keV
Solid TiD targets, HPGe detectors at 55° and 90°, target deuterium content measured in situ and by elastic recoil detection; the data favour an S-factor higher than earlier fits in this range. [8]
2024
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · energies from 30 to 280 keV
Angular distribution of the capture γ-rays inferred from the shape of the γ spectrum of a single HPGe detector facing an extended D₂ gas target, and compared with ab initio predictions. [9]

Measurements (EXFOR)

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

50 datasets in 26 EXFOR entries, 1962–2021 · 7 without an energy range, not drawn

Temperature

centre of the Sun, T₉ = 0.0157 (15.7 MK)deuterium bottleneck, T₉ = 0.8 (800 MK)end of BBN, T₉ = 0.3 (300 MK)

Lowest energy in EXFOR: 2.18 keV; Bystritsky et al., 2010 · S · F1083.004
Distance from the Gamow peak: 0.65 Gamow widths below; E₀ = 6.7 keV, window 3.22–10.2 keV
Rate from energies not in EXFOR: 0.06%; at T₉ = 0.0157, smooth estimate · 0.06% of it lies below the lowest energy in EXFOR

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
Quantity	Datasets	E_cm range (keV)
σcross section	9	2.52 keV – 7.91 MeV
SS-factor	10	2.18 keV – 1.09 MeV
σ→Eₓpartial	1	95 MeV – 127 MeV
dσ/dΩangular distribution	14	10 keV – 316 MeV
Aypolarization	7	10 keV – 316 MeV
…other	2	3.33 MeV – 127 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.

All measurements (50)Compound nucleus ³He

Details

Two energy ranges matter. The solar Gamow window lies at a few keV, where the LUNA 50 kV accelerator measured the cross section with about 10% accuracy well below the solar Gamow peak. For Big Bang nucleosynthesis (BBN) the relevant centre-of-mass energies range from tens to a few hundred keV, where before 2020 the data had large uncertainties and an ab initio calculation (Marcucci et al. 2016) predicted an S-factor about 10% above the adopted fits.

The capture is dominated by E1 and M1 transitions to the ³He ground state; polarization observables measured at TUNL below 80 keV are sensitive to meson-exchange currents. The LUNA 400 kV measurement with a windowless D₂ gas target and a HPGe detector reached a systematic uncertainty below 3% and settled the rate in the BBN range. With it the BBN-derived baryon density has a 1.6% uncertainty and agrees with the value from the cosmic microwave background (CMB).

Measurements at higher energy, with TiD targets, constrain the energy dependence above the BBN window.

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) [10]
—B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [11]
—P. Descouvemont et al., At. Data Nucl. Data Tables 88, 203 (2004) [12]
—O. Pisanti et al., JCAP 04, 020 (2021) [13]
—B. D. Fields et al., JCAP 03, 010 (2020); erratum JCAP 11, E02 (2020) [14]

Open questions

The residual tension between the measured S-factor and ab initio calculations at a level of a few per cent.
The energy dependence above the BBN window, where the TiD-target data of 2021 lie above earlier fits.

Discussed on the open-questions page

Primordial deuterium and the baryon density

Related reactions

References

1.
L. Ma, H. J. Karwowski, C. R. Brune et al.
Measurements of ¹H(d⃗,γ)³He and ²H(p⃗,γ)³He at very low energies
Phys. Rev. C 55, 588 (1997) · 10.1103/PhysRevC.55.588
2.
G. J. Schmid et al.
The ²H(p⃗,γ)³He and ¹H(d⃗,γ)³He reactions below 80 keV
Phys. Rev. C 56, 2565 (1997) · 10.1103/PhysRevC.56.2565
3.
C. Casella et al. (LUNA Collaboration)
First measurement of the d(p,γ)³He cross section down to the solar Gamow peak
Nucl. Phys. A 706, 203 (2002) · 10.1016/S0375-9474(02)00749-2LUNA
4.
L. E. Marcucci, G. Mangano, A. Kievsky, M. Viviani
Implication of the proton-deuteron radiative capture for Big Bang Nucleosynthesis
Phys. Rev. Lett. 116, 102501 (2016) · 10.1103/PhysRevLett.116.102501 · arXiv:1510.07877
5.
I. Tišma, M. Lipoglavšek, M. Mihovilovič et al.
Experimental cross section and angular distribution of the ²H(p,γ)³He reaction at Big-Bang nucleosynthesis energies
Eur. Phys. J. A 55, 137 (2019) · 10.1140/epja/i2019-12816-1
6.
V. Mossa et al. (LUNA Collaboration)
Setup commissioning for an improved measurement of the D(p,γ)³He cross section at Big Bang Nucleosynthesis energies
Eur. Phys. J. A 56, 144 (2020) · 10.1140/epja/s10050-020-00149-1 · arXiv:2005.00002LUNA
7.
V. Mossa et al. (LUNA Collaboration)
The baryon density of the Universe from an improved rate of deuterium burning
Nature 587, 210 (2020) · 10.1038/s41586-020-2878-4LUNA
8.
S. Turkat et al.
Measurement of the ²H(p,γ)³He S factor at 265–1094 keV
Phys. Rev. C 103, 045805 (2021) · 10.1103/PhysRevC.103.045805 · arXiv:2104.06914
9.
K. Stöckel et al. (LUNA Collaboration)
Novel approach to infer the ²H(p,γ)³He angular distribution: experimental results and comparison with theoretical calculations
Phys. Rev. C 110, L032801 (2024) · 10.1103/PhysRevC.110.L032801LUNA
10.
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
11.
B. Acharya et al.
Solar fusion III: New data and theory for hydrogen-burning stars
Rev. Mod. Phys. 97, 035002 (2025) · 10.1103/8lm7-gs18 · arXiv:2405.06470
12.
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
13.
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
14.
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(p,γ)³He, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/2H-pg-3He.

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

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