Tetraneutron Signatures in Light Nuclei

• The paper highlights experimental findings of narrow near-threshold peaks (E ≈ 0.8–2.37 MeV) from various reaction channels that signal possible tetraneutron resonances.
• Theoretical models, including no-core shell and Monte Carlo methods, predict resonances with widths around 1–2 MeV, challenging previous bound-state assumptions.
• Modern reaction mechanisms using missing-mass and invariant-mass techniques offer practical insights into extracting four-neutron correlations critical for nuclear structure research.

A tetraneutron in nuclear physics refers to a correlated system of four neutrons, potentially manifesting as a resonance or bound state in reactions involving light, neutron-rich nuclei. Despite decades of theoretical and experimental search, its existence, properties, and quantum numbers remain controversial. Core experimental campaigns with high-resolution missing-mass, knockout, transfer, and fragmentation reactions have yielded candidate signals—either as unbound resonance structures near threshold in nuclei such as $^8\mathrm{He}$, or as possible tightly bound configurations in specific transfer channels. Theoretical approaches employing ab initio, few-body, and energy-density functional methods indicate that any observable tetraneutron should appear as a resonance (not a bound state) at small positive energies above the four-neutron threshold. This article presents the principal experimental signatures, theoretical context, methodologies, and open questions regarding tetraneutron correlations in light nuclei, grounded entirely in published arXiv sources.

1. Experimental Signatures in Light Nuclei

High-sensitivity searches for tetraneutron signatures have been realized across multiple reaction classes:

• Transfer/Charge-Exchange: $^4\mathrm{He}(^8\mathrm{He}, ^8\mathrm{Be})4n$ at RIKEN (beam energies ∼186 MeV/nucleon), detecting missing-mass spectra from fully reconstructed α-particles in $^8\mathrm{Be}$ decays, yielding a near-threshold (resonance at $E=0.83 \pm 0.65_{\rm stat} \pm 1.25_{\rm syst}$ MeV, width $\Gamma \leq 2.6$ MeV) peak (Faestermann et al., 13 Jun 2025, Kezerashvili, 2016, Yang et al., 2019).
• Knockout: $^8\mathrm{He}(p, p′\alpha)4n$ at RCNP, leveraging high-resolution spectrometers to measure the outgoing α and proton, reconstructing the missing mass of the four-neutron system via

$$M_{\rm miss}^2 = (p_{^8\mathrm{He}} + p_p - p_\alpha - p_{p'})^2,$$

which provides a direct probe of the tetraneutron continuum. This technique revealed a pronounced peak at $E^* = 2.37 \pm 0.58$ MeV with $\Gamma = 1.75 \pm 0.37$ MeV (Faestermann, 2022, Faestermann et al., 13 Jun 2025, Yang et al., 2019).

• Fragmentation: $^{14}\mathrm{Be} \rightarrow ^{10}\mathrm{Be} + 4n$ at GANIL, searching for anomalous kinematic distributions in neutron-proton coincidences, with an upper decay energy limit of $E \leq 2.0$ MeV, though no explicit width extracted (Faestermann et al., 13 Jun 2025, Kezerashvili, 2016).
• Three-Proton Pickup: $^7\mathrm{Li}(^7\mathrm{Li}, ^{10}\mathrm{C}^*)4n$ at TUM provided evidence for a very narrow, potentially bound tetraneutron state, $E_B = 0.42 \pm 0.16$ MeV, width $\Gamma < 0.24$ MeV (Faestermann et al., 13 Jun 2025).
• Complementary Probes: Double-charge-exchange with pions on $^4\mathrm{He}$ (Kezerashvili, 2016) and photodisintegration ($\gamma,4n$ on $^{209}\mathrm{Bi}$), where enhanced cross-sections cannot be explained without correlated four-neutron emission (Faestermann et al., 13 Jun 2025).

Table: Selected Tetraneutron Candidate Observations

Reaction Channel	Resonance Energy (MeV)	Width (MeV)	Reference
$^8\mathrm{He}(p, p′\alpha)4n$	2.37 ± 0.58	1.75 ± 0.37	(Faestermann, 2022)
$^4\mathrm{He}(^8\mathrm{He}, ^8\mathrm{Be})4n$	0.83 ± 0.65 (stat) ± 1.25 (syst)	≤2.6	(Faestermann et al., 13 Jun 2025, Kezerashvili, 2016)
$^7\mathrm{Li}(^7\mathrm{Li}, ^{10}\mathrm{C}^*)4n$	−0.42 ± 0.16*	<0.24	(Faestermann et al., 13 Jun 2025)

*Negative sign denotes binding (i.e., a bound state); all other values are excitation energies above threshold.

Distinct classes of observed signals can be summarized as narrow, low-energy peaks typical of bound or quasi-bound ground-state candidates, and broader features (widths ∼1–2 MeV) compatible with unbound four-neutron resonance or continuum structures.

2. Theoretical Models and Resonance Predictions

Microscopic calculations of the tetraneutron rely on various formulations:

• No-Core Shell Model plus Continuum (NCSMC, SS-HORSE extension): Employs hyperspherical harmonics, outgoing-wave boundary conditions, and analytic continuation to extract resonance poles. Using JISP16 or Daejeon16 NN interactions (designed to mimic certain 3N-force effects), ab initio calculations predict $E_r \approx 0.8$–2.6 MeV and $\Gamma \approx 1.4$–2.4 MeV for the tetraneutron (Shirokov et al., 2024).
• No-Core Gamow Shell Model (NCGSM): Expands the many-body wavefunction in a Berggren ensemble, treating bound, resonant, and continuum states uniformly. Even with maximally correlated four-neutron continuum (full DMRG), widths remain $\Gamma \gtrsim 3.7$–6 MeV, exceeding most experimental upper bounds (Fossez et al., 2016).
• Green’s-Function Monte Carlo and Quantum Monte Carlo: Standard NN+3N (chiral, AV18) Hamiltonians generally preclude bound tetraneutron or narrow resonance poles, requiring altered or phenomenological T=3/2 three-neutron forces for binding (Faestermann et al., 13 Jun 2025, Shirokov et al., 2024, Kezerashvili, 2016).
• Energy Density Functional Approaches: The Giessen EDF study supports the existence of a highly dilute, halo-like tetraneutron bound at ∼0.14 MeV only for extreme radii (rms ∼45 fm), implying that such a state could evade observation in reactions favoring compact configurations (Faestermann et al., 13 Jun 2025).

Key resonance formula:

$$\sigma_{\rm res}(E) \propto \frac{\Gamma/2}{(E - E^*)^2 + (\Gamma/2)^2}$$

Resonances in the four-neutron S-matrix thus appear as $S(E)$ poles at $E_p = E_r - i\Gamma/2$, recoverable from the energy dependence of the missing-mass or invariant-mass spectra.

3. Reaction Mechanisms and Signature Extraction

Modern experiments utilize complete kinematics and high-efficiency multi-neutron arrays (NeuLAND, NEBULA, stilbene-based) with missing (invariant) mass or missing-invariant-mass reconstructions. The missing-mass squared is written as:

$$M^2_{\rm miss} = (P_{\rm initial} - \sum_{i} P_{i,\,{\rm detected}})^2$$

Experimental analyses fit the reconstructed excitation spectra with Breit–Wigner line shapes, extract the statistical significance above modeled continuum backgrounds (e.g., by Monte Carlo or event-mixing), and systematically assess uncertainties from detector resolution, energy calibration, and kinematic acceptance (Faestermann, 2022, Yang et al., 2019).

Angular and momentum correlations have emerged as critical observables; genuine four-neutron resonances are expected to yield distinctive low-relative-momentum enhancements and specific Jacobi-coordinate patterning, distinguishable from phase-space or sequential decay backgrounds (Yang et al., 2019).

Finally, “missing-invariant-mass” methods, which allow reconstruction even with only 3/4 neutrons detected, have enabled a substantial gain—order of magnitude ×20—in sensitivity to near-threshold tetraneutron production (Yang et al., 2019).

4. Microscopic Structure and Correlations

Ab initio nuclear lattice effective field theory calculations for $^8\mathrm{He}$, $^7\mathrm{H}$, and associated hydrogen isotopes provide explicit spatial and angular correlations of neutron clusters in the nuclear surface (Zhang et al., 21 Dec 2025). The dominant configuration in both systems is a symmetric dineutron–dineutron arrangement (∼95% probability), with only a small (∼5%) component realizing a compact, “genuine” tetraneutron-like (four-body) substructure.

For $^7\mathrm{H}$, the single-neutron separation energy is found to be

$$S_n(^7\mathrm{H}) = 0.35_{-0.32}^{+0.32}\;\mathrm{MeV}$$

implying (at 1σ) preference for direct t+4n decay over sequential $^6\mathrm{H} + n$ emission and suggesting that knockout and break-up channels directly probe the four-neutron system.

Detailed analysis of two- and four-body correlation functions, e.g., $\rho_2(r, r', \theta)$ and

$$\rho_4(\theta_1, \varphi_1, \theta_2, \varphi_2; \Theta, \zeta)$$

(where brackets denote ensemble averaging in quantum Monte Carlo), show that dineutron pairs localize near the nuclear surface ($r_{nn} \sim 2.2$–3.7 fm), and that rare compact four-body geometries can be correlated with specific angular (torsion, opening angle) distributions, providing a potential experimental discriminant for true tetraneutron formation (Zhang et al., 21 Dec 2025).

5. Comparative Analysis, Systematics, and Controversies

Experimental data cluster into two subpopulations: extremely narrow, near-threshold peaks (interpreted as possibly bound ground-state tetraneutrons) and broader structures (widths 1–2 MeV) consistent with unbound resonances or correlated continuum enhancements. The (p,pα) knockout (Faestermann, 2022), transfer (Faestermann et al., 13 Jun 2025), and double-charge-exchange (Kezerashvili, 2016) experiments largely corroborate the presence of a resonance near 1–3 MeV above the 4n threshold. The sharply differing resonance widths, resonance energy systematics, and selectivity for reaction mechanisms suggest—a plausible implication is—that both a weakly bound $0^+$ ground state and a $2^+$ continuum state may exist, with transfer reactions favoring ground-state population, while knockout/fragmentation accesses the unbound resonance (Faestermann et al., 13 Jun 2025).

Ab initio treatments consistently find that no bound tetraneutron exists with chiral NN+3N interactions. While specific frameworks (e.g., JISP16, Daejeon16, or NN interactions softened by V_low-k/SRG) can place a resonance in the 0.8–2.6 MeV range with moderate width, the most sophisticated continuum-coupled calculations indicate width parameters ($\Gamma > 3.7$ MeV) incompatible with claims of a “narrow” resonance (Fossez et al., 2016, Shirokov et al., 2024).

Dispersive Casimir–Polder four-body interactions have been estimated and found to be negligibly small (∼10⁻⁹ MeV at 1 fm separation), incapable of contributing significantly to tetraneutron binding or resonance energy—a plausible implication is their inclusion is theoretically complete but physically irrelevant in experimental tetraneutron phenomenology (Hussein et al., 2017).

6. Astrophysical and Nuclear Matter Implications

Inclusion of a tetraneutron resonance at $E_{4n} = 2.37$ MeV, $\Gamma = 1.75$ MeV in relativistic mean-field models of light-component nuclear matter notably impacts the equilibrium distribution of light clusters in low-temperature, neutron-rich environments. Specifically, enhanced proton and α-particle abundances (factors 3–5 at $Y_p = 0.1, T = 4$ MeV), decreased free-neutron fractions, and altered equilibrium constants are predicted. These changes may influence electron-capture and neutrino opacity in core-collapse supernovae, modify matter ejection and nucleosynthesis in neutron-star mergers, and, at lower densities, affect heavy-ion collision cluster yield patterns (Pais et al., 2023).

7. Open Questions and Future Prospects

Key open problems include:

• Unambiguous identification of quantum numbers and the possible coexistence of a bound $0^+$ ground state and higher-lying $2^+$ continuum state in the four-neutron system.
• Determination of the relevant reaction mechanisms and selectivity for populating different four-neutron configurations.
• Extension of ab initio methods to capture strongly non-compact, halo-like tetraneutron states as envisioned by EDF approaches.
• Direct measurement and reconstruction of two- and four-neutron correlation observables (relative momenta, opening angles, torsion) in multi-neutron knockout and decay events.
• Systematic mapping of isospin-analogue resonances in A=4,8,12,16 systems via competitive α-transfer, missing-mass, and γ-spectroscopy channels (Shirokov et al., 2024, Yang et al., 2019).

Future campaigns at RIBF, ACCULINNA-2, and new-generation neutron-detection facilities, combined with high-statistics and high-resolution kinematic measurements, are anticipated to resolve current ambiguities and decisively constrain the allowed structure of light multi-neutron systems (Faestermann et al., 13 Jun 2025, Yang et al., 2019).