Observation of a correlated free four-neutron system

The study investigates whether pure neutron systems can exist as bound or resonant states, focusing on the four-neutron (tetraneutron) system. Prior knowledge establishes that the dineutron is unbound by about 100 keV and a trineutron is unlikely, though some recent theory suggests possible three-neutron resonance. The tetraneutron has long been a candidate for a multi-neutron system potentially existing as a weakly bound or very short-lived unbound resonant state. Previous experiments with stable beams and various reactions (including fission, pion-induced double-charge exchange, and transfer reactions) found no definitive signal. A 2002 breakup of 14Be into 10Be + 4n hinted at a bound tetraneutron, but theory indicated a bound state would require unrealistic modifications to nuclear forces; the finding is also consistent with a near-threshold resonance with Er ≤ 2 MeV. A 2016 DCX experiment with a high-energy 8He beam indicated a resonance at Er = 0.8 ± 1.4 MeV with Γ ≤ 2.6 MeV but could not exclude a bound state due to large uncertainties. The present work aims to provide a decisive observation using a reaction mechanism that can strongly populate a correlated four-neutron system and enable precise missing-mass reconstruction.

• Early searches targeted possible bound tetraneutrons in uranium fission, yielding null results.
• Pion-induced double-charge-exchange reactions, particularly 4He(π−, π+)4n, and transfer reactions such as 4He(d, 6Li), also did not yield positive signals.
• The 2002 breakup of 14Be into 10Be + 4n suggested a bound state; subsequent theory concluded a bound tetraneutron is incompatible with realistic nuclear forces, though a near-threshold resonance (Er ≤ 2 MeV) remained possible.
• In 2016, using a radioactive 8He beam in the 8He(4He, 8Be) DCX channel, an indication of a resonance at Er = 0.8 ± 1.4 MeV with Γ ≤ 2.6 MeV was reported but remained inconclusive.
• Theoretical landscape is divided: Green’s function Monte Carlo and QMC approaches support a near 2 MeV resonance (broad or with unspecified width), whereas NCSM/NCGSM predictions vary widely; some calculations argue a resonance requires modified nuclear forces, and others predict a non-resonant low-energy enhancement of states.

• Reaction and production mechanism: Quasi-elastic knockout of an alpha (4He) core from a high-energy 8He projectile on a proton target: 8He(p, p4He), in inverse kinematics at large momentum transfer. The 8He nucleus has an alpha core plus four valence neutrons with small 4n center-of-mass motion; sudden removal of the alpha core produces a localized four-neutron system with low relative energy and large overlap with a tetraneutron state.
• Kinematics: Backward-angle proton–alpha scattering in the center-of-mass (θc.m. ≥ 160°) maximizes momentum transfer between the proton and alpha while leaving the 4n spectators near recoil-less, minimizing final-state interactions with charged fragments.
• Facility and beam: Conducted at RIKEN RIBF with the SAMURAI spectrometer. Primary 18O beam on Be target; secondary 8He beam separated with BigRIPS and delivered at 156 MeV/u to a 5-cm liquid hydrogen target.
• Beam tracking and ID: Upstream scintillators for charge and momentum identification and drift chambers for tracking event-by-event.
• Detection of charged fragments: Three silicon-strip detector planes before the magnet provided tracking, dE, and vertex reconstruction; fragments were bent through SAMURAI (1.25 T field). A drift chamber at the focal plane and scintillator walls provided timing and energy-loss; alpha and proton were identified via energy deposition and position, and their momenta reconstructed precisely.
• Neutron detection: Forward-angle neutron detector arrays were present, but due to low p–4He elastic cross section at backward angles (<1 μb) and low neutron detection efficiency, coincidence detection of more than two neutrons was not feasible; neutron detection was used only for a consistency check of recoil-less production.
• Channel selection and missing mass: Events with identified incoming 8He, outgoing alpha, and proton define the 8He(p, p4He) channel. The 4n energy spectrum is reconstructed via missing mass using energy–momentum conservation: the missing four-vector Pmiss = P8He + Ptarget − P4He − Pp, and E4n = Emiss − Pmiss − 4 mn. Bound 4n would appear at E4n < 0; resonances at E4n > 0.
• Benchmark with 6He: A companion 6He measurement under similar conditions validated the missing-mass analysis. The 2n relative energy spectrum matched theory (COSMA-based) after convolution with acceptance/resolution, yielding a missing-mass resolution of about 1 MeV (sigma) nearly constant over energy; systematic uncertainties on absolute energy and width were 0.4 MeV and 0.27 MeV, respectively.
• Modeling the 4n spectrum: The non-resonant 4n continuum was computed using a source-term approach in the Schrödinger equation with the 8He ground-state wave function in a five-body COSMA approximation. The continuum shape depends on the 4n hyperradius ρ4n; ρ4n ≈ 5.6 fm (consistent with COSMA 4He radius) produces a broad distribution centered around ~30 MeV, matching data.
• Fit model: The measured spectrum was modeled as f(E4n) = a fres(E4n) + b fcon(E4n) + c fbkg(E4n), with a Breit–Wigner resonance fres, non-resonant continuum fcon (parameterized by hyperradius), and background fbkg from quantified competing processes. The dominant background is a two-step process producing 6He followed by p–4He quasi-elastic scattering; its contribution was simulated and normalized using measured cross sections to 2.6% of events (c fixed). The full fit was convolved with experimental acceptance and detector response (acceptance maximal for 20–40 MeV).
• Statistics: 422 events in the 8He(p, p4He) channel were collected. A χ2 minimization provided resonance parameters; the peak significance exceeded 5σ.

• A pronounced low-energy peak is observed in the 4n missing-mass spectrum at E4n ≈ 2 MeV atop a broad non-resonant continuum (centered around ~30 MeV). The spectrum is well described by a Breit–Wigner resonance plus a continuum and a small background contribution.
• Fitted resonance parameters (acceptance- and resolution-convolved fit):
  • Energy: E4n = 2.37 ± 0.38(stat.) ± 0.44(sys.) MeV.
  • Width: Γ = 1.75 ± 0.22(stat.) ± 0.30(sys.) MeV.
  • Corresponding lifetime: τ = (3.8 ± 0.8) × 10^−22 s.
• Statistical significance: well beyond 5σ for the peak.
• Relative population probability (resonant vs non-resonant continuum), after deconvolution and using the fit model: Pn = 18.7 ± 2.3% (COSMA model expectation ~30% for hyperradius ρ4n = 5.6 fm; fit favors ρ4n = 5.0 ± 0.1 fm, implying a smaller resonant population).
• Background from two-step processes (6He production followed by p–4He scattering): estimated at 2.6% of total events and included in the fit; shifts/broadens the 6He-like distribution to lower energies.
• Experimental resolution and systematics from 6He benchmark: missing-mass resolution ~1 MeV (sigma); systematic uncertainty on absolute energy 0.4 MeV and on width 0.27 MeV; acceptance varies with energy and is maximal for 20–40 MeV.
• Event statistics: 422 events in the selected 8He(p, p4He) channel; p–4He elastic cross section at backward angles is <1 μb, limiting statistics.

The observation of a statistically significant peak near E4n ≈ 2.4 MeV addresses the long-standing question of whether a tetraneutron can exist as a resonant state. The measured energy and width are consistent with a short-lived unbound tetraneutron resonance, aligning with earlier experimental indications from DCX (Er = 0.8 ± 1.4 MeV, Γ ≤ 2.6 MeV) and with some ab initio theory (e.g., QMC predicting Er ≈ 2.1(2) MeV). The reaction mechanism—sudden removal of the alpha core at large momentum transfer—maximizes overlap with a correlated 4n configuration and minimizes final-state interactions with charged fragments, enabling a clean missing-mass reconstruction. The agreement between the measured non-resonant continuum and source-term COSMA calculations (broad peak around 30 MeV) supports the physical plausibility of the continuum model and the extraction of the resonance parameters. Nevertheless, theoretical predictions remain diverse: while some frameworks (QMC, certain NCSM/NCGSM variants) accommodate a near-threshold resonance with varying widths, others argue such a resonance would require modifications to nuclear forces, or predict a non-resonant low-energy enhancement instead. Definitive theoretical discrimination will require ab initio treatments including continuum effects. Experimentally, the present result establishes a robust benchmark for nuclear-force models in neutron-rich systems and motivates complementary measurements with different reaction mechanisms and direct neutron detection to probe correlations and decay dynamics.

This work reports a firm experimental observation of a resonance-like structure consistent with an unbound tetraneutron state near threshold. Using a high-energy inverse-kinematics alpha-knockout reaction with a radioactive 8He beam and precise missing-mass reconstruction, a peak at E4n = 2.37 ± 0.38(stat.) ± 0.44(sys.) MeV with width Γ = 1.75 ± 0.22(stat.) ± 0.30(sys.) MeV (τ ≈ 3.8 × 10^−22 s) was measured with significance exceeding 5σ. The non-resonant continuum shape agrees with theoretical expectations based on the 8He ground-state structure. These results provide a key benchmark for theories of nuclear forces in extreme neutron-rich conditions. Future directions include experiments employing different reaction mechanisms and coincident detection of all four neutrons to elucidate correlations and decay pathways, as well as more sophisticated ab initio calculations that explicitly include continuum coupling to clarify the origin of the observed low-energy peak.

• Limited statistics (422 events) due to very small p–4He elastic cross section at backward angles (<1 μb), constraining precision.
• Neutron detection inefficiency precluded coincident detection of more than two neutrons; the analysis relies on missing-mass reconstruction without full 4n coincidence, limiting direct access to neutron–neutron correlations and decay modes.
• Experimental acceptance is energy dependent (maximal between 20–40 MeV), necessitating convolution/deconvolution that can introduce model dependence.
• Background from two-step processes, though small (~2.6%), required modeling and subtraction.
• Systematic uncertainties in absolute energy (0.4 MeV) and width (0.27 MeV) remain.
• Theoretical ambiguity persists: different ab initio and model-based predictions vary, and some suggest non-resonant low-energy enhancements that cannot yet be ruled out solely from the present spectrum.