SoLid: Reactor Neutrino & Dark Sector

• SoLid is a very short-baseline reactor antineutrino experiment that uses a highly segmented detector to test for active–sterile neutrino oscillations and investigate the 5 MeV spectral distortion.
• Its advanced detector architecture features 12,800 PVT scintillating cells with 6LiF:ZnS neutron screens, enabling precise prompt–delayed signal separation and strong background rejection.
• The SoLid framework also extends to cosmology, modeling the dark sector as a relativistic elastic medium that transitions from matter-like behavior to a dark energy–like phase.

SoLid is primarily a very short-baseline reactor antineutrino experiment installed at the BR2 research reactor of SCK•CEN in Belgium, designed to probe the Reactor Antineutrino Anomaly, test oscillations into a light sterile neutrino state with a mass around the eV scale, and measure the $\overline{\nu}_e$ spectrum from $^{235}$U with particular sensitivity to the 5 MeV distortion. Its detector is a 1.6 ton, highly segmented system built from 12,800 scintillating cells that combine polyvinyltoluene (PVT) cubes with $^{6}$LiF:ZnS(Ag) neutron screens and are read out by wavelength-shifting fibers and silicon photomultipliers (SiPMs) (Manzanillas, 2019). In a distinct cosmological usage, “SoLid” also denotes a model in which the entire dark sector is treated as a relativistic elastic medium that behaves as pressureless matter at early times and as a solid dark-energy–like component at late times (Jiménez et al., 25 Jun 2026).

1. Reactor antineutrino experiment and scientific objectives

SoLid operates at the BR2 research reactor, a compact, high-flux research reactor whose fuel composition is dominated by $^{235}$U. Detector positions are between 6 and 9 m from the compact core, placing the experiment in the very-short-baseline regime relevant for eV-scale oscillations (Abreu et al., 2018). The experiment was designed around two coupled problems in reactor neutrino physics: the Reactor Antineutrino Anomaly (RAA) and the 5 MeV spectral distortion observed in previous reactor antineutrino experiments.

The RAA, together with the Gallium Anomaly (GA), is described at the $\sim 3\sigma$ level and could be interpreted as evidence for a 3+1 neutrino scenario. In that framework, SoLid searches for active–sterile oscillation signatures in the antineutrino energy spectrum as a function of baseline and energy. Its second central objective is a new, precise measurement of the $\overline{\nu}_e$ energy spectrum from $^{235}$U, intended to clarify the origin of the 5 MeV “bump” (Manzanillas, 2019).

These objectives impose stringent detector requirements. Fine spatial sampling is needed to measure position-dependent spectral distortions, while robust prompt–delayed identification is needed to reject reactor-induced and cosmogenic backgrounds. The detector design therefore couples heavy segmentation with a hybrid scintillation technology rather than a homogeneous liquid-scintillator geometry.

2. Detector architecture and inverse beta decay detection

The detector has five modules, each module contains ten planes, and each plane is a $16 \times 16$ array of SoLid cells, for a total of $5 \times 10 \times 16 \times 16 = 12{,}800$ cells. Each cell is a $5 \times 5 \times 5\ \text{cm}^3$ PVT cube with neutron screens attached. In the Phase-1 design, each cube has two $^{235}$0LiF:ZnS(Ag) screens, four $^{235}$1 grooves, and four double-clad wavelength-shifting fibers in perpendicular $^{235}$2–$^{235}$3 orientations; each fiber is coupled to one $^{235}$4 Hamamatsu MPPC on one end and a mirror on the other (Abreu et al., 2018).

The PVT scintillator cubes are EJ-200 elements with light yield $^{235}$5 optical photons/MeV, emission peak $^{235}$6 nm, decay time $^{235}$7 ns, and refractive index $^{235}$8. The $^{235}$9LiF:ZnS(Ag) screens are thin, about $^{6}$0, with light emission peak around 450 nm and a much slower decay, $^{6}$1. The PVT acts as the IBD target and positron calorimeter, while the $^{6}$2LiF:ZnS(Ag)) layer provides neutron capture and a delayed scintillation signal with a markedly different time structure (Abreu et al., 2018).

Detection is based on inverse beta decay,

$^{6}$3

The positron produces a prompt signal in PVT through ionization and, possibly, annihilation. The neutron thermalizes and is captured on $^{6}$4Li in the neutron screen, with the capture products depositing energy in the ZnS(Ag) phosphor. Because the same fiber–SiPM network collects both fast PVT scintillation and slow ZnS scintillation, prompt and delayed components are distinguished through waveform topology and pulse shape rather than by separate readout systems. A dedicated neutron trigger algorithm based on counting Peaks over Threshold (PoT) exploits the “sparkling” multi-peak ZnS time profile, in contrast to the single fast pulses from PVT (Manzanillas, 2019).

This architecture makes segmentation central to the experiment’s methodology. Signal topology is localized at cube scale, enabling powerful background rejection, but the same granularity forces calibration to be performed cell-by-cell and makes response homogeneity across 12,800 cells a primary technical problem.

3. Calibration architecture and measured detector performance

SoLid’s calibration program is driven by the requirement that the energy scale and neutron detection efficiency be known in each cell with uncertainties smaller than 2% and 4%, respectively. To achieve this, the experiment uses an automated system called CROSS, a suite of radioactive gamma and neutron sources, channel-by-channel gain calibration, cell-by-cell light-yield calibration, and continuous monitoring with cosmic muons (Manzanillas, 2019).

CROSS is an automated mechanical setup in which a calibration arm inserts sources into gaps between modules while an actuator system moves detector modules relative to the arm, or vice versa. The source can be positioned so that the maximum distance to any cube is less than 35 cm. Full gamma calibration scans take about 1 day, full neutron calibration scans take about 3 days, and these campaigns are performed every reactor-OFF cycle, approximately every 2 months.

The primary gamma source for the energy scale is $^{6}$5Na. Because SoLid’s granularity suppresses visible photopeaks on a per-cube basis, the calibration uses the Compton edge of the 1.27 MeV gamma rather than full-energy absorption. Two independent methods are employed. In the Kolmogorov test method, a Geant4-deposited-energy spectrum is smeared under different assumptions for stochastic resolution and light yield, and the best agreement with data is selected using a Kolmogorov–Smirnov test. In the analytical fit method, a Klein–Nishina-based Compton electron spectrum is folded with a Gaussian detector response and fit directly to the measured spectrum. Both methods extract a PA-to-MeV conversion factor from the Compton edge position.

Linearity is cross-checked with $^{6}$6Bi, $^{6}$7Cs, and the gamma component of AmBe, spanning 0.57, 0.667, 1.06, and 4.4 MeV. The reported agreement between AmBe and $^{6}$8Bi with $^{6}$9Na is described as “excellent agreement,” supporting linearity in the relevant range for reactor $^{235}$0 spectra. Cosmic muon tracks provide daily monitoring and are reported to show a very stable detector response over time.

The calibration results give an average light yield across all 12,800 cells of

$^{235}$1

with a stochastic energy resolution of about

$^{235}$2

The plane-to-plane dispersion in light yield is smaller than 10%. For neutron detection, the experiment decomposes

$^{235}$3

where $^{235}$4 is estimated with Geant4 simulations and $^{235}$5 includes trigger and offline reconstruction. Neutron calibration with AmBe and $^{235}$6Cf yields a neutron reconstruction efficiency of about 75%, also with dispersion smaller than 10% across the 50 planes (Manzanillas, 2019).

4. Scintillation-light optimization and Phase-1 detector design

Before deployment of the 1.6 ton detector, SoLid carried out a systematic optimization of light collection and uniformity at the cube level. The reference point was the 288 kg SM1 prototype, which had a measured light yield of $^{235}$7 per cube and a stochastic resolution of $^{235}$8, insufficient for the Phase-1 requirement of

$^{235}$9

A dedicated $\sim 3\sigma$0Bi test bench was therefore built to compare detector configurations under controlled conditions. The key methodological feature was a thin plastic trigger scintillator that selected the 1 MeV conversion electrons, producing a Gaussian energy peak suitable for precise light-yield comparisons (Abreu et al., 2018).

The optimization showed that light collection depends on reflector choice, neutron-screen placement, fiber technology, number of fibers, and end-mirror reflectivity. Teflon tape gave the highest light yield in single-cube tests, 44 PA/MeV, but was rejected for mass construction because wrapping 12,800 cubes would be time-consuming and difficult to reproduce. Tyvek was selected because it could be cut and pre-folded in a stable pattern, and the thicker Phase-1 Tyvek grade improved light yield by about 10% relative to the SM1 Tyvek. Double-clad BCF-91A fibers trapped about 15% more light than single-clad fibers. Replacing the SM1 aluminium mirror with aluminised mylar gave a relative gain summarized as +7%. Increasing from two to four fibers per cube yielded the largest single gain, +43%.

The relative contributions reported for the Phase-1 design are summarized below.

Modification	Relative light-yield effect
Better cube machining	+10%
Thicker Tyvek wrapping	+10%
Double-clad fibres	+15%
Change in number and position of neutron screens	$\sim 3\sigma$1
Increasing fibres from 2 to 4 per cube	+43%
Better mirrors	+7%

These changes transformed the measured stand-alone cube performance from 18.6 PA/MeV in an SM1-like configuration to 51.6 PA/MeV in a Phase-1-like configuration. The expected Phase-1 detector performance was 52$\sim 3\sigma$22 PA/MeV per cube, and the mapped Phase-1 plane gave 51.6 to 54.5 PA/MeV with an average of 52.3 PA/MeV, corresponding to about 6% non-uniformity across the $\sim 3\sigma$3 plane. Using

$\sim 3\sigma$4

the experiment inferred that $\sim 3\sigma$5 is consistent with $\sim 3\sigma$6 stochastic energy resolution at 1 MeV. The final Phase-1 design therefore adopted well-machined EJ-200 cubes, pre-folded Tyvek 1082D wrapping, two $\sim 3\sigma$7LiF:ZnS(Ag) screens per cube, four double-clad BCF-91A fibers per cube, and aluminised mylar mirrors (Abreu et al., 2018).

5. Homogeneity, systematics, and experimental significance

The detector’s segmentation is both its principal advantage and its main calibration burden. Variations in cube light yield, SiPM gain, fiber alignment, optical coupling, neutron-screen coupling, and edge geometry all act at cell level. SoLid’s calibration strategy responds by equalizing response with per-cell constants and by periodically remeasuring the detector under reactor-OFF conditions. This is necessary because SoLid runs at the surface and SiPM gains are temperature dependent (Manzanillas, 2019).

On the optical side, the dedicated test bench identified a dominant run-to-run systematic uncertainty of about 5% on light-yield measurements, arising from cube handling and positioning, fiber positioning, temperature fluctuations, and MPPC over-voltage variations. Optical cross-talk between neighboring cubes was found to be small and manageable: in 90% of events, the neighbor saw less than 10% of the light from the source cube, with no noticeable signal in the next-to-next cube. This result, together with four readout channels per cube, supported the claim that cross-talk could be disentangled in reconstruction (Abreu et al., 2018).

The significance of these calibrations is directly tied to the sterile-neutrino search. A well-controlled energy scale is needed to reconstruct the $\sim 3\sigma$8 spectrum and to prevent detector-response variations from aliasing into apparent spectral distortions. Likewise, neutron-efficiency non-uniformities matter because SoLid’s oscillation signature is a coupled deformation in energy and position. Miscalibrated efficiencies could mimic or obscure oscillation patterns. The calibration results therefore function not merely as detector characterization but as constraints on a major class of instrumental systematics (Manzanillas, 2019).

Within the landscape of very short baseline reactor experiments, SoLid differs from liquid-scintillator designs such as STEREO, DANSS, NEOS, and segmented liquid detectors like PROSPECT by emphasizing solid PVT cubes, very fine segmentation, and hybrid PVT/$\sim 3\sigma$9LiF:ZnS(Ag) technology for robust prompt–neutron separation. The optimization studies suggest that this architecture can achieve light collection and resolution competitive with more homogeneous designs while retaining unusually strong topology-based background rejection (Abreu et al., 2018).

6. “SoLid” as a unified solid dark sector

In cosmology, “SoLid” denotes a different construct: a unified description of dark matter and dark energy in terms of a single dark component modeled as a relativistic elastic medium. The medium is described by three scalar fields $\overline{\nu}_e$0 that label comoving volume elements, with dynamics encoded in a Lagrangian $\overline{\nu}_e$1, where $\overline{\nu}_e$2 measures compression or volume change and $\overline{\nu}_e$3 measure shear. On an FLRW background with

$\overline{\nu}_e$4

one finds

$\overline{\nu}_e$5

so the background evolution depends on $\overline{\nu}_e$6, while the shear invariants become crucial at perturbative level (Jiménez et al., 25 Jun 2026).

The total action is

$\overline{\nu}_e$7

with dark-sector energy density and pressure

$\overline{\nu}_e$8

The specific realization discussed is a generalized Chaplygin-type solid. At background level, it reproduces a generalized Chaplygin gas equation of state, while its perturbation sector is solid rather than fluid. The fluid-to-solid transition is controlled by

$\overline{\nu}_e$9

with $^{235}$0 giving an early-time fluid-like phase with $^{235}$1, and $^{235}$2 producing a late-time solid phase with

$^{235}$3

The full equation of state is

$^{235}$4

The defining solid property is the dependence of $^{235}$5 on $^{235}$6 and $^{235}$7, which yields a nonzero shear modulus, propagating transverse phonons, anisotropic stress, and a gravitational-wave mass term. The transverse and longitudinal sound speeds are

$^{235}$8

In the accelerated slow-roll solid phase,

$^{235}$9

so the solid contribution stabilizes a regime that would be unstable in a pure fluid. The stated stability conditions are $16 \times 16$0, $16 \times 16$1, and $16 \times 16$2.

This perturbative structure yields several late-time observables. Tensor modes satisfy

$16 \times 16$3

with

$16 \times 16$4

In the scalar sector, the effective growth equation contains both a reduction of the effective gravitational coupling,

$16 \times 16$5

and pressure support from $16 \times 16$6, so structure growth is suppressed at late times. The anisotropic stress of the solid also generates a gravitational slip,

$16 \times 16$7

with sub-Hubble slip parameter

$16 \times 16$8

Because the solid phase emerges only at low redshift, these effects are designed to leave high-redshift cosmology essentially unmodified.

The model is presented as an EFT of a relativistic medium rather than a microscopic theory. Its stated advantages are that it decouples the background equation of state from the perturbation sound speed, thereby avoiding the strong acoustic oscillations that afflict perfect-fluid generalized Chaplygin models, and that it predicts correlated late-time signatures in growth, lensing, slip, and gravitational waves. Its stated open issues are the need to tune elastic parameters so that $16 \times 16$9 remains small yet positive, the absence of a microscopic origin for the solid, persistence of the coincidence problem, and the fact that a full confrontation with data through MCMC has not been performed (Jiménez et al., 25 Jun 2026).