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Multi-neutron correlations in light nuclei via ab-initio lattice simulations

Shuang Zhang, Serdar Elhatisari, Ulf-G. Meißner

TL;DR

This work addresses the nature of multi-neutron correlations in light nuclei by performing ab initio lattice EFT calculations with an ensemble of chiral $N^3LO$ two- and three-nucleon forces and an uncertainty-quantified Bayesian analysis. The authors compute ground-state energies for $^{6}$H and $^{7}$H and extract a positive one-neutron separation energy for $^{7}$H, favoring direct $t+4n$ emission, while revealing core structures and surface dineutron clustering in $^{7}$H and $^{8}$He. Using two- and four-body correlation functions from pinhole samples, they identify a dominant extended symmetric $2n$–$2n$ geometry (~95%) and a smaller compact tetraneutron-like component (~5%) in $^{7}$H, along with corresponding spatial and angular patterns; $^{8}$He exhibits a similar hierarchy. The results offer a microscopic picture of emergent multi-neutron correlations, guiding interpretation of experiments probing tetraneutron configurations and informing the ongoing search for exotic multi-neutron clusters in neutron-rich light nuclei.

Abstract

The quest to understand multi-neutron systems has a long history, and recent experimental efforts aim to probe candidate four-neutron configurations in neutron-rich light nuclei such as ${}^8$He and ${}^7$H via quasi-free knockout reactions. However, the ground-state energies of the hydrogen isotopes ${}^6$H and ${}^7$H are not yet well constrained, with substantial discrepancies across experimental analyses and theoretical predictions. Using ab initio nuclear lattice effective field theory with an ensemble of 282 chiral two- and three-nucleon forces, we perform an uncertainty-quantified analysis of the ground-state energies of ${}^6$H and ${}^7$H. The marginal posteriors suggest single-neutron separation energy $S_n({}^{7}\text{H})=0.35^{+0.32}_{-0.32}$ MeV, disfavoring sequential ${}^{6}\mathrm{H}+n$ decay and pointing towards direct $t+4n$ emission. Intrinsic densities indicate triton- and $α$-like clusters in ${}^7$H and ${}^8$He, respectively. By computing two-body and reduced four-body correlation functions, we find that the valence neutrons in the surface region of these systems form compact dineutrons that predominantly organize into symmetric dineutron-dineutron configurations, with only a small but non-negligible fraction assembling into more compact tetraneutron-like substructures. In ${}^7$H, these components account for roughly 95% and 5% of the sampled four-neutron configurations, respectively, and ${}^8$He exhibits a similar hierarchy. For these configurations, we also extract the corresponding spatial and angular correlation patterns among the nucleons. These results provide nuclear-structure insights into the debate surrounding four-neutron clusters and complement ongoing experimental searches for tetraneutron signatures in light nuclei.

Multi-neutron correlations in light nuclei via ab-initio lattice simulations

TL;DR

This work addresses the nature of multi-neutron correlations in light nuclei by performing ab initio lattice EFT calculations with an ensemble of chiral two- and three-nucleon forces and an uncertainty-quantified Bayesian analysis. The authors compute ground-state energies for H and H and extract a positive one-neutron separation energy for H, favoring direct emission, while revealing core structures and surface dineutron clustering in H and He. Using two- and four-body correlation functions from pinhole samples, they identify a dominant extended symmetric – geometry (~95%) and a smaller compact tetraneutron-like component (~5%) in H, along with corresponding spatial and angular patterns; He exhibits a similar hierarchy. The results offer a microscopic picture of emergent multi-neutron correlations, guiding interpretation of experiments probing tetraneutron configurations and informing the ongoing search for exotic multi-neutron clusters in neutron-rich light nuclei.

Abstract

The quest to understand multi-neutron systems has a long history, and recent experimental efforts aim to probe candidate four-neutron configurations in neutron-rich light nuclei such as He and H via quasi-free knockout reactions. However, the ground-state energies of the hydrogen isotopes H and H are not yet well constrained, with substantial discrepancies across experimental analyses and theoretical predictions. Using ab initio nuclear lattice effective field theory with an ensemble of 282 chiral two- and three-nucleon forces, we perform an uncertainty-quantified analysis of the ground-state energies of H and H. The marginal posteriors suggest single-neutron separation energy MeV, disfavoring sequential decay and pointing towards direct emission. Intrinsic densities indicate triton- and -like clusters in H and He, respectively. By computing two-body and reduced four-body correlation functions, we find that the valence neutrons in the surface region of these systems form compact dineutrons that predominantly organize into symmetric dineutron-dineutron configurations, with only a small but non-negligible fraction assembling into more compact tetraneutron-like substructures. In H, these components account for roughly 95% and 5% of the sampled four-neutron configurations, respectively, and He exhibits a similar hierarchy. For these configurations, we also extract the corresponding spatial and angular correlation patterns among the nucleons. These results provide nuclear-structure insights into the debate surrounding four-neutron clusters and complement ongoing experimental searches for tetraneutron signatures in light nuclei.

Paper Structure

This paper contains 13 sections, 9 equations, 8 figures, 2 tables.

Table of Contents

  1. Results:
  2. Supplemental Material
  3. Uncertainty quantification of chiral forces
  4. Evaluation of observables with pinhole configurations
  5. Intrinsic densities
  6. Schematic illustration of four-neutron correlations in $^{7}$H
  7. Extrapolation in Euclidean time
  8. Finite-volume effects
  9. Experimental information on $^{6}$H and $^{7}$H
  10. Two-neutron correlations in $^{6}$He and $^{3}$H
  11. Intrinsic densities, two-neutron correlations, and dineutron sizes in $^{8}$He and $^{7}$H
  12. Opening angle $\theta$ and $\varphi$ dependence in four-neutron correlation of $^{7}$H
  13. Internal angular and radial distributions from the four-neutron correlations in $^{7}$H

Figures (8)

  • Figure 1: Calculated and experimental g.s. energies of $^{6,7}$H, and the 0$^{+}$ and 0$_2$$^{+}$ state energies of $^{8}$He. Colored markers overlaid on the corresponding curves indicate the calculated energies versus Euclidean time $\tau$, with statistical uncertainties. The curves represent the $\tau$-extrapolation fits, and horizontal dashed lines denote the extrapolated $\tau\!\to\!\infty$ energies with their statistical uncertainties. Experimental data Aleksandrov:1984H6Belozyorov:1986H456Gurov:2003pvCaamano:2008zzA1:2025mjfKorsheninnikov:2000He7uniqueCaamano:2007zzNikolskii:2010zzBezbakh:2019dvhCaamano:2020Muzalevskii:2020svp are shown as symbols labeled "EXP" in the legend. Inset: The red circles represent the g.s. energies of $^{6,7}$H from non-implausible prior samples obtained via history matching Elhatisari:2022zrb, including uncertainties. Posterior samples are shown as pale blue points, with dashed lines indicating the 1$\sigma$ and 2$\sigma$ credible intervals. The dashed black line denotes the condition $E(^{6}\mathrm{H}) = E(^{7}\mathrm{H})$. Marginal distributions are shown along each axis, with medians indicated by ticks and thick and thin bars representing the 1$\sigma$ and 2$\sigma$ credible intervals, respectively.
  • Figure 2: (a) Intrinsic nucleon (blue) and proton (red) densities of the $^7$H ground state, visualized as slices at $x=0$ and $x=\pm 2.5$ fm. The red dashed line marks the maximal spatial extent of the identified triton cluster. (b) Two-neutron correlation density of all neutrons in the $^7$H ground state, with $r$ defined relative to the c.m. of the core. (c) Two-neutron correlation density of the four valence neutrons, with $r$ defined with respect to the c.m. of the $^7$H.
  • Figure 3: Four-neutron geometry and correlations. (a) Joint probability density $p(\Theta,\zeta)$ of the inter-pair opening angle $\Theta$ and torsion angle $\zeta$ in $^{7}$H. (b) Comparison of the inter-dineutron opening-angle probability density $p(\Theta)$ in $^{7}$H and $^{8}$He under the same intra-angle selection, $\theta_{1,2}\le60^\circ$ and $|\varphi_{1,2}-90^\circ|\le10^\circ$, where we classify configurations with $\Theta<90^\circ$ as compact and $\Theta>90^\circ$ as extended for discussion. (c-f) Conditional internal angular and radial correlations for configurations selected at $\Theta\approx69^\circ$ (compact) and $\Theta\approx141^\circ$ (extended). Here $\theta_{1,2}$ denote the intra-pair opening angles of the two selected $nn$ pairs, and $r_{1,2}$ denote the distances from the c.m. of each pair to the $^{7}$H c.m. Angles are shown in degrees, while $p(\Theta,\zeta)$ and $p(\Theta)$ are reported per radian squared and per radian, respectively.
  • Figure S1: Schematic illustration of the angular coordinates used to characterize the four-neutron correlations in $^{7}$H.
  • Figure S2: Calculated two-neutron correlation densities of $^{6}$He and $^{3}$H. In $^{6}$He, the correlation is evaluated for the two valence neutrons, providing a benchmark for our correlation-analysis procedure. The $^{3}$H result serves as a reference for comparison with the multi-neutron correlations in $^{7}$H.
  • ...and 3 more figures