Four-Neutron Configurations

• Four-neutron configurations are neutral clusters of four neutrons that may form near-threshold bound states or broad resonances, depending on NN and few-nucleon interactions.
• Experimental studies using knockout, transfer, fragmentation, and photodisintegration reactions reveal distinct missing-mass peaks and energy-width signatures indicative of tetraneutron dynamics.
• Ab initio and continuum models underscore the role of dineutron correlations and final-state interactions, suggesting that observed enhancements may arise from nonresonant continuum effects rather than a true S-matrix pole.

Four-neutron configurations, often called “tetraneutron” states, are neutral, spin-isospin-pure systems composed solely of four neutrons. These configurations occupy a boundary region in nuclear structure physics where the interplay between few-body correlations, the Pauli principle, and the details of the nucleon–nucleon (NN) and few-nucleon interactions manifests in both continuum and near-threshold phenomena. The central question is whether four neutrons can generate a bound or resonant quasi-stable cluster, or whether observable enhancements in four-neutron emission spectra are entirely attributable to continuum correlations and reaction mechanisms.

1. Experimental Evidence and Reaction Approaches

A variety of experimental strategies have been deployed in attempts to observe four-neutron configurations, utilizing knockout, transfer, fragmentation, and photodisintegration reactions, each with distinct kinematic signatures and systematics. Major categories include:

• Knockout Reactions: For example, the $(p, \alpha)$ reaction off ${}^{8}$He at 150–156 MeV/u, where a proton removes an $\alpha$ particle and the missing-mass spectrum of the remaining four neutrons is reconstructed event-by-event. This technique enables a direct mapping of the tetraneutron excitation energy through precise four-momentum conservation. A statistically significant near-threshold peak at $E^*=2.37(58)$ MeV with width $\Gamma=1.75(37)$ MeV was reported, interpreted as a resonant tetraneutron state (Faestermann, 2022).
• Double-Charge Exchange and Pickup: For instance, the ${}^{7}$Li(${}^{7}$Li,${}^{10}$C)4$n$ reaction demonstrated a candidate bound tetraneutron with $E_B=0.42(16)$ MeV and an upper limit on the width $\Gamma<0.24$ MeV. In contrast, ${}^4$He(${}^8$He,$\,{}^8$Be)4$n$ double-charge exchange yielded a threshold resonance at $E_r=0.83(65)(125)$ MeV, $\Gamma<2.6$ MeV (Faestermann et al., 13 Jun 2025).
• Fragmentation and Photodisintegration: Fragmentation of ${}^{14}$Be and photodisintegration of heavy targets have produced events consistent with multineutron emission but remain affected by backgrounds (e.g., in-flight decay, detector pileup).
• Kinematically Complete Final-State Detection: Modern experiments utilize large solid-angle spectrometers, neutron–gamma discrimination, and full kinematic reconstruction to resolve four-neutron events and extract excitation energy spectra.

These observables, summarized in the table below, reflect significant diversity across setups:

Reaction/Facility	Excitation Energy (MeV)	Width (MeV)	Interpretation
${}^8$He($p$,$\alpha$)4$n$ (RIKEN)	2.37(58)	1.75(37)	Broad resonance
${}^7$Li(${}^7$Li,${}^{10}$C)4$n$	–0.42(16)	<0.24	Bound state?
${}^4$He(${}^8$He,$\,{}^8$Be)4$n$	0.83(65)(125)	<2.6	Near-threshold
${}^2$H(${}^8$He,$^6$Li)4$n$ (Dubna)	3.5(0.7)	—	Hump, unresolved

Signal patterns cluster into two categories: a very narrow, possibly bound state near threshold, and a broader resonance at 2–3 MeV. In many cases, sequential neutron decay is kinematically suppressed, suggesting direct four-neutron emission as the dominant process (Zhang et al., 21 Dec 2025).

2. Ab Initio Theoretical Models

Several ab initio approaches have been applied to the four-neutron problem, providing rigorous benchmarks with controllable approximations:

• Quantum Monte Carlo (QMC) in External Traps: Calculations using local chiral interactions at N$^2$LO confine four neutrons in a Woods-Saxon potential, extrapolating the energy to zero well-depth to infer resonance energies. These yield $E_{4n}=2.1\pm 0.2$ MeV, indicating a dilute, short-lived resonance; the trineutron resonance is consistently found lower, $E_{3n}=1.1\pm0.2$ MeV (Gandolfi et al., 2016).
• No-Core Shell Model with Continuum (NCSM/HORSE/J-Matrix): Direct diagonalization in extensive HO bases followed by HORSE analytic continuation predicts a resonance at $E_r \approx 0.8$ MeV, $\Gamma \approx 1.4$ MeV using JISP16 forces, with configuration analysis indicating a mainly $p$-wave continuum structure and absence of compact clusterization (Shirokov et al., 2016).
• Gamow Shell Model and DMRG: Calculations with chiral N$^3$LO and JISP16 interactions, incorporating scattering boundary conditions, consistently produce very broad resonances $E_r\approx 6.5$–$7.3$ MeV, $\Gamma\approx 3.7$–4 MeV, inconsistent with narrow experimental signals. Importantly, the maximal isospin configuration of 4$n$ severely suppresses the role of three- and higher-body forces in these results (Fossez et al., 2016).
• Adiabatic Hyperspherical and Momentum-Space AGS Equations: Both coordinate- and momentum-space four-body frameworks, driven by realistic NN and 3N forces, fail to identify any tetraneutron pole near the real axis at the physical interaction strengths. Instead, these models demonstrate a generic near-threshold enhancement in the density of states due to long-range, universal $1/R^3$ interactions, not associated with any true resonance (Higgins et al., 2020, Higgins et al., 2020, Deltuva, 2018).
• Quartet and Cluster-Based Methods: Application of quartet-based models in valence spaces (e.g., $sd$-shell) reveals that strongly correlated four-neutron wave functions account for nearly all low-energy correlations. These form the building blocks for shell-model descriptions and exhibit configuration mixing controlled by antisymmetrization and angular-momentum coupling structures (Sambataro et al., 2015).

Collectively, ab initio theories, using accepted nuclear forces adjusted for few-nucleon observables, do not support a physical tetraneutron bound or low-lying narrow resonant state, though moderately broad resonance-like structures in the MeV range can be accommodated by some models.

3. Reaction Mechanism Effects and Continuum Correlations

Recent work has emphasized the possibility that signal enhancements in four-neutron spectra may not indicate true quasistationary tetraneutron states but instead arise from final-state correlations and nonresonant continuum dynamics:

• Dineutron–Dineutron Correlations: The close-to-unitary $nn$ $^1$S$_0$ channel promotes spatially compact dineutron clusters. Knockout of a core ($\alpha$ or triton) from a halo nucleus like ${}^8$He or ${}^7$H leaves a correlated four-neutron system, which, upon evolving under the bare $nn$ interaction, produces a low-energy enhancement in missing-mass spectra. Calculated strength functions under such scenarios quantitatively reproduce the experimental peak location, width, and tail structure without requiring a true resonance (Lazauskas et al., 2022).
• Density of States Enhancement: The dominant adiabatic four-body potential for neutrons lacks a trapping region but exhibits a long-range $a/R^3$ attraction, leading to a $1/\sqrt{E}$ divergence in the density of states near threshold. The associated Wigner–Smith time delay amplifies continuum yields for low relative energies, explaining observed experimental cross sections through universal near-threshold physics (Higgins et al., 2020, Higgins et al., 2020).
• Final-State Interactions and Pauli Focusing: In five-body decays (core+4$n$), strong Pauli antisymmetrization (“Pauli focusing”) channels multi-neutron emission into symmetry-allowed configurations, resulting in nontrivial and diagnostic angular and energy correlations. Distinct “fingerprints” in two-dimensional energy/angle distributions can be attributed to the leading shell-model configurations of the precursor and exploited experimentally (Sharov et al., 2018).

The consensus across this body of work is that many of the experimental “tetraneutron” signatures can arise from reaction-induced continuum enhancements and specific symmetry-induced correlations, rather than genuine four-body S-matrix poles.

4. Bound vs. Resonant Tetraneutron: Interpretation of Discrepant Signals

The variation in experimental results—some observing narrow, possibly bound states, others broad resonances—has led to a two-component interpretative scheme (Faestermann et al., 13 Jun 2025):

1. Ground-State Scenario: In certain reactions (slow compound pickup, e.g., ${}^7$Li(${}^7$Li,${}^{10}$C)4$n$), where all four neutrons can be coupled to $s_{1/2}$ and $p_{3/2}$ orbitals with $J^\pi=0^+$, selective population of an extremely weakly bound tetraneutron state is plausible. Hartree–Fock–Bogoliubov energy density functional theory in a large cavity marginally binds 4$n$ at very low density, but such solutions have extraordinary spatial extent and dilute character.
2. First Excited Resonant State: Knockout or fast-transfer reactions off neutron-rich halos preferentially leave four valence neutrons in $p_{3/2}$ orbitals, favoring a $2^+$ excitation at $E^*\sim2.5$–3 MeV. This matches the systematics for $N=4$ even-even nuclei and is consistent with observed broader resonance peaks.

This dual scenario places the theoretical challenges into sharper relief: binding four neutrons, even at extreme spatial dilution, is not supported by standard many-body methods without modification of NN (or 3N) interactions. Artificially increasing T=3/2 3N forces to create a tetraneutron near threshold is incompatible with established spectroscopy of neighboring nuclei and nucleon scattering observables (Hiyama et al., 2016).

5. Multi-neutron Correlations and Internal Structure

Ab initio lattice effective field theory (NLEFT) simulations enable direct sampling of multi-neutron correlation functions in light nuclei, allowing the identification and quantification of genuine four-neutron substructures:

• Dominance of Dineutron–Dineutron Modes: For both ${}^7$H and ${}^8$He, approximately 95% of four-neutron configurations in the surface/halo regions are symmetric dineutron–dineutron geometries. Only $\sim$5% exhibit compact, interlaced tetraneutron-like correlations. The intrinsic densities and reduced correlation functions provide detailed spatial and angular benchmarks, which can inform the theoretical interpretation and the design of future experiments (Zhang et al., 21 Dec 2025).
• Experimental Implication: The overwhelming dominance of dineutron–dineutron backgrounds implies that even if compact tetraneutron states exist, their experimental signature will be heavily diluted unless kinematic and angular cuts are optimized for their unique geometric features.

6. Outlook and Open Questions

The modern synthesis of experimental and theoretical work suggests:

• Threshold signals vs. S-matrix poles: Observable peaks in four-neutron final states may often be attributed to nonresonant density-of-states enhancements and final-state correlations. Absence of a low-lying four-body resonance pole is a robust result in many ab initio approaches with realistic forces.
• Potential for a physical tetraneutron: Only energy density functional models with extreme dilute boundary conditions provide even a marginally bound solution, and this requires further empirical validation and theoretical scrutiny.
• Experimental priorities: Improved statistics in reactions favoring s-wave four-neutron configurations, precise angular and energy correlation measurements, and comprehensive reaction model analysis are essential for disentangling continuum backgrounds from possible genuine tetraneutron contributions.
• Theory frontiers: Systematic studies of four-neutron observables with controlled variation of 3N and 4N force terms, as well as benchmarking of computationally intensive continuum calculations, remain necessary to resolve the observed experimental discrepancies.

In conclusion, four-neutron configurations remain at the intersection of complex reaction dynamics, few-body quantum correlations, and the limits of nuclear binding. While broad resonance-like features in the unbound continuum are reproducible in several models, evidence for a sharp, physically isolated tetraneutron state is at best circumstantial and remains one of the outstanding enigmas in low-energy nuclear physics (Faestermann, 2022, Faestermann et al., 13 Jun 2025, Gandolfi et al., 2016, Hiyama et al., 2016, Lazauskas et al., 2022, Zhang et al., 21 Dec 2025).