³He(α,γ)⁷Be · Reaction atlas

A ³He nucleus captures a ⁴He nucleus (an alpha particle) and becomes ⁷Be, giving off a γ-ray. It opens the branches of the pp chain that emit the ⁷Be and ⁸B solar neutrinos, and it made most of the lithium after the Big Bang.

In the Sun, a ³He nucleus either fuses with another ³He or captures an alpha particle through this reaction. The share that goes this way fixes the number of ⁷Be and ⁸B neutrinos, which detectors such as Borexino and Super-Kamiokande count. It is the largest nuclear uncertainty in the predicted fluxes of those neutrinos. After the Big Bang the ⁷Be made here later decayed to ⁷Li, so the reaction also sets the predicted amount of primordial lithium. That prediction is higher than the amount of lithium seen in old stars, a mismatch called the lithium problem.

Facts

How well known: Known to a few per cent at solar energies, but only by extending measurements made at higher energies: no experiment has yet reached the energies at which the reaction runs in the Sun.
Live evaluation: Plot the data · ⁷Be →
Reaction rates: Explore the rates →
Q-value · energy released: 1.587 MeV
Gamow window: 23 ± 6.5 keVcentre of the Sun, 15.7 MK (pp-II)
315 ± 170 keVdeuterium bottleneck, 0.8 GK (Big Bang nucleosynthesis)
165 ± 75 keVend of BBN, 0.3 GK (Big Bang nucleosynthesis)
Product ⁷Be: radioactive, t_½ = 53.2 d
Kind: Radiative capture

On the timeline

2007Borexino detects ⁷Be solar neutrinos in real time

How it was measured

10 measurements, 2004–2023, 4 at LUNAShow the list

2004
Weizmann Institute accelerator laboratoryWeizmann Institute of Science
Activation · 420–950 keV
Activation with a ³He gas cell; S(0) = 0.53 ± 0.02 ± 0.01 keV b, from a set of energies at a time when earlier activation data covered only one or two energies each. [1]
2006
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Activation · 127, 148 and 169 keV
Windowless gas target, high beam intensity and low-background γ counting of the ⁷Be produced; cross sections with 4% total uncertainty. [2]
2007
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Activation · 106 keV
Activation point at 106 keV, closer to the solar Gamow energy than any earlier measurement; σ = 0.567 ± 0.029 (stat) ± 0.016 (syst) nb. [3]
2007
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · 93, 106 and 170 keV
Prompt γ-rays and ⁷Be activity measured simultaneously; the two methods agree, branching ratios between the two γ transitions measured to 5–8%, extrapolated S(0) = 0.560 ± 0.017 keV b. [4]
2007
CENPA, University of WashingtonCenter for Experimental Nuclear Physics and Astrophysics, University of Washington
Direct measurement at the surface · 0.33–1.23 MeV
Small gas cell, prompt γ-rays and ⁷Be activity; the two methods agree, and a fit with the Kajino model gives S(0) = 0.595 ± 0.018 keV b. [5]
2008
LUNA 400 kVLaboratori Nazionali del Gran Sasso (INFN)
Direct measurement underground · beam energies 220, 250 and 400 keV
Full account of the LUNA prompt-γ experiment and its systematic uncertainties, together with the activation results, and S-factor extrapolations with two theoretical models. [6]
2009
ERNA recoil separatorCIRCE laboratory, Caserta (at Ruhr-Universität Bochum until 2009)
Inverse kinematics and recoil separators · around and above 1 MeV
Direct detection of the ⁷Be recoils with the ERNA separator, with coincident γ-rays; above 1 MeV the cross section differs from earlier results in absolute value and energy dependence. [7]
2013
Nuclear Science Laboratory, Notre DameUniversity of Notre Dame
Direct measurement at the surface · about 0.3–1.5 MeV
Prompt γ-ray measurement with the HIPPO helium-jet gas target over a wide energy window. [8]
2019
Atomki, DebrecenInstitute for Nuclear Research (Atomki)
Activation · 4.0–4.4 MeV
Thin-window ³He gas cell; a constant cross section of about 10.5 μb near the ⁷Be proton separation threshold and an upper limit of 45 neV on the strength of a resonance there. [9]
2023
Atomki, DebrecenInstitute for Nuclear Research (Atomki)
Activation · above the ⁷Be proton separation threshold
Activation with a thin-window ³He gas cell, extending the capture data into the energy range of the known ⁷Be levels, where only one narrow data set (4.0–4.4 MeV) existed before. [10]

Measurements (EXFOR)

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

44 datasets in 22 EXFOR entries, 1959–2023 · 5 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: 92.9 keV; Costantini et al., 2008 · σ · O1709.002.1
Distance from the Gamow peak: 5.4 Gamow widths above; E₀ = 23.1 keV, window 16.6–29.5 keV
Rate from energies not in EXFOR: 100%; at T₉ = 0.0157, smooth estimate · 100% 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	21	92.9 keV – 8.31 MeV
SS-factor	12	9.88 keV – 2.8 MeV
σ→Eₓpartial	4	93.3 keV – 1.3 MeV
…other	2	107 keV – 1.27 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 (44)Compound nucleus ⁷Be

Try it: an R-matrix evaluation

This system has a live AZURE2 model on this site: change the energies and widths of its levels and see how the fit to the data and the extrapolation to stellar energies change.

Open the ⁷Be evaluation →

Details

The capture proceeds by external direct capture to the ⁷Be ground state and to its first excited state at 429 keV, so the cross section can be measured either by detecting the prompt γ-rays or by counting the ⁷Be activity afterwards (activation). Before 2006 the two approaches disagreed on the extrapolated S(0). The LUNA campaign at the 400 kV accelerator used a windowless ³He gas target and measured both observables at the same time, down to 93 keV, with agreement between them; the activation results reached a 4% total uncertainty.

Surface experiments at the Weizmann Institute, Seattle and Notre Dame, and the ERNA recoil separator, then covered the energies from about 0.3 MeV upwards and constrained the energy dependence needed to extrapolate to the solar Gamow window. Above 1 MeV the ERNA data differ from earlier results in both normalization and slope. Activation measurements at Atomki extended the data to the ⁷Be proton separation threshold and, in 2023, above it, into the region of the known ⁷Be levels.

Solar Fusion III recommends S(0) = 0.561 ± 0.018 (exp) ± 0.022 (theory) keV b; the theoretical uncertainty has grown since Solar Fusion II and is now comparable to the experimental one. BBN analyses with the current rates conclude that a nuclear-physics solution of the lithium problem is highly unlikely.

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) [11]
—B. Acharya et al., Rev. Mod. Phys. 97, 035002 (2025) [12]
—P. Descouvemont et al., At. Data Nucl. Data Tables 88, 203 (2004) [13]
—C. Iliadis, A. Coc, Astrophys. J. 901, 127 (2020) [14]

Open questions

The energy dependence of the S-factor between 100 keV and 1 MeV, which controls the extrapolation to the solar Gamow window.
The disagreement in slope and normalization above 1 MeV between recoil-separator and γ-ray data.

Discussed on the open-questions page

The S-factor of ³He(α,γ)⁷Be at zero energy

Related reactions

References

1.
B. S. Nara Singh, M. Hass, Y. Nir-El, G. Haquin
New precision measurement of the ³He(⁴He,γ)⁷Be cross section
Phys. Rev. Lett. 93, 262503 (2004) · 10.1103/PhysRevLett.93.262503 · arXiv:nucl-ex/0407017
2.
D. Bemmerer et al. (LUNA Collaboration)
Activation measurement of the ³He(α,γ)⁷Be cross section at low energy
Phys. Rev. Lett. 97, 122502 (2006) · 10.1103/PhysRevLett.97.122502 · arXiv:nucl-ex/0609013LUNA
3.
Gy. Gyürky et al. (LUNA Collaboration)
³He(α,γ)⁷Be cross section at low energies
Phys. Rev. C 75, 035805 (2007) · 10.1103/PhysRevC.75.035805LUNA
4.
F. Confortola et al. (LUNA Collaboration)
Astrophysical S factor of the ³He(α,γ)⁷Be reaction measured at low energy via detection of prompt and delayed γ rays
Phys. Rev. C 75, 065803 (2007) · 10.1103/PhysRevC.75.065803 · arXiv:0705.2151LUNA
5.
T. A. D. Brown, C. Bordeanu, K. A. Snover et al.
³He + ⁴He → ⁷Be astrophysical S factor
Phys. Rev. C 76, 055801 (2007) · 10.1103/PhysRevC.76.055801 · arXiv:0710.1279
6.
H. Costantini et al. (LUNA Collaboration)
The ³He(α,γ)⁷Be S-factor at solar energies: the prompt γ experiment at LUNA
Nucl. Phys. A 814, 144 (2008) · 10.1016/j.nuclphysa.2008.09.014 · arXiv:0809.5269LUNA
7.
A. Di Leva et al.
Stellar and primordial nucleosynthesis of ⁷Be: measurement of ³He(α,γ)⁷Be
Phys. Rev. Lett. 102, 232502 (2009); erratum Phys. Rev. Lett. 103 (2009) · 10.1103/PhysRevLett.102.232502
8.
A. Kontos, E. Uberseder, R. deBoer, J. Görres, C. Akers, A. Best, M. Couder, M. Wiescher
Astrophysical S factor of ³He(α,γ)⁷Be
Phys. Rev. C 87, 065804 (2013) · 10.1103/PhysRevC.87.065804
9.
T. Szücs, G. G. Kiss, Gy. Gyürky, Z. Halász, T. N. Szegedi, Zs. Fülöp
Cross section of ³He(α,γ)⁷Be around the ⁷Be proton separation threshold
Phys. Rev. C 99, 055804 (2019) · 10.1103/PhysRevC.99.055804
10.
Á. Tóth, T. Szücs et al.
Experimental determination of the ³He(α,γ)⁷Be reaction cross section above the ⁷Be proton separation threshold
Phys. Rev. C 108, 025802 (2023) · 10.1103/PhysRevC.108.025802 · arXiv:2307.10218
11.
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
12.
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
13.
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
14.
C. Iliadis, A. Coc
Thermonuclear reaction rates and primordial nucleosynthesis
Astrophys. J. 901, 127 (2020) · arXiv:2008.12200

How to cite this page

J. Skowronski, ³He(α,γ)⁷Be, in Reaction atlas, 2026-10-12, https://jskowron.eu/atlas/3He-ag-7Be.

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