Coherent nuclear scattering: a small detector, a tiny recoil

The whole nucleus scatters as one

When the momentum transfer is too small to resolve the individual nucleons, their weak scattering amplitudes can add coherently. In the Standard Model, most of a nucleus's weak charge comes from its neutrons. Squaring the summed amplitude can give a higher rate than treating each nucleon as a separate scatterer.

What matters is the wavelength set by the momentum transfer. As the momentum transfer grows, the nuclear form factor reduces the coherence, so a larger nucleus does not give an unlimited boost at every neutrino energy or recoil angle.

Elastic means the nucleus stays in its ground state and simply recoils as a whole. The neutrino leaves with most of its energy. Because this is a neutral-current process, it is sensitive to the active flavors, but no outgoing electron, muon or tau reveals which flavor arrived.

Sources: [1] · [2] · [3]

A heavy target takes little kinetic energy

Energy and momentum conservation limit how much energy a light neutrino can give a nucleus at rest. The recoil is largest when the neutrino bounces straight back. When the nucleus's mass energy is far above the neutrino energy, the maximum recoil grows as the square of the neutrino energy and falls as the nuclear mass increases.

So a reactor antineutrino of several MeV can leave a nuclear recoil below one keV, even though the interaction rate is enhanced. The exact maximum depends on the isotope and the neutrino energy. The formula below treats the neutrino as massless and the nucleus as isolated and at rest; the response of the atoms and the detector material comes later.

A heavier nucleus can raise the weak charge but pushes more recoils below the detector threshold. Choosing a target means balancing rate, recoil spectrum, achievable threshold and background. Detector mass alone does not decide how much useful exposure you get.

Sources: [1] · [3] · [2]

The detector sees only part of the recoil energy

A nuclear recoil and an electron recoil that deposit the same energy need not give the same light or charge. Part of a nuclear recoil's energy goes into moving atoms, which the detector does not measure. This reduction, often called quenching, has to be calibrated and given an uncertainty.

A threshold quoted in electron-equivalent energy therefore cannot be used directly as a nuclear-recoil threshold. Near threshold, trigger efficiency, noise rejection and the tail of the detector response strongly shape the accepted spectrum. These effects have to be built into the predicted signal; one overall scale factor cannot correct for them.

Neutrons also cause nuclear recoils, and electronic noise can mimic small pulses. Shielding, dedicated neutron measurements, pulse-quality checks and comparisons of source timing or source on and off each test for a different fake. A low threshold helps only when the origin and stability of these tiny signals are understood.

Sources: [2] · [3] · [4]

An accelerator and a reactor check the signal in different ways

In 2017 COHERENT reported a 6.7-standard-deviation signal from a 14.6-kilogram cesium-iodide scintillator at the Oak Ridge Spallation Neutron Source. The source makes pulses of pions that stop and decay, so the neutrinos arrive with a known energy and timing pattern. That pattern helps separate them from steady backgrounds and from neutrons made by the beam.

In 2025 CONUS+ reported in Nature a 3.7-standard-deviation signal from germanium detectors at the Leibstadt reactor in Switzerland. The analysis used 119 days of reactor-on data and inferred 395 plus or minus 106 signal events; the Standard Model predicts 347 plus or minus 59.

Both numbers come from fits after background subtraction; no individual recoil is known for certain to be a neutrino. The reactor experiment compares reactor-on and reactor-off data, a different test from accelerator pulse timing. Because the two results use different energies and target materials, their agreement is an independent physical check.

Sources: [2] · [3]

What coherent scattering can be used for

Comparing the measured rate and spectrum with the Standard Model can limit how the nucleus responds to the weak force, or test for additional interactions. Such limits depend on the source flux, the neutron distribution, quenching and the detector threshold. Using several targets and source types helps tell a real change in the interaction from an error in the detector response.

The same process matters for dark-matter experiments sensitive enough to see nuclear recoils from solar neutrinos. Those recoils are a physical background with their own energy and time distribution; they do not make every further dark-matter measurement impossible.

Compact reactor monitors are a possible application. Whether one is practical depends on the exposure needed, the shielding, calibration with the reactor off and stable operation; observing the interaction does not settle that. Coherent scattering opens a new way to measure, and its practical uses and its tests of fundamental physics each need their own evidence.

Sources: [3] · [1] · [5]

Primary sources & revision

1. Freedman · Coherent effects of a weak neutral current (1974)
2. COHERENT Collaboration · Observation of coherent elastic nuclear scattering (2017)
3. CONUS+ Collaboration · Direct reactor coherent scattering (Nature 2025)
4. COHERENT Collaboration · CsI low-energy nuclear-recoil response (2021/2022)
5. PandaX Collaboration · Solar boron-8 nuclear-recoil indication (2024)

First published 2026-10-11; last revised 2026-10-11. Original explanatory text and diagrams by Sandbox Physics. Illustrations are schematic; no experimental event records are reproduced here. This is an independent educational publication, not an official Nobel or experiment collaboration publication.