Meson-Nucleus Bound States with Neural-Network Quantum States

Abstract

We present the first systematic calculations of $\ddot{I}•$-, $\hat{I}{\cdot }_c$-, and $J/\ddot{I}ˆ$-nucleus ground states up to mass number $A=12$ based on the HAL QCD meson-nucleon potentials at near-physical point. The $(A+1)$-body Schrödinger equation is solved with a neural-network variational Monte Carlo framework, generalized to incorporate mesonic degrees of freedom. Benchmarking on light nuclei from ${}^2$H to ${}^{12}$C yields ground-state energies consistent with experiment. Meson-nucleus bound states emerge at $A\ge 2$ for $\ddot{I}•$, $A\ge 4$ for $J/\ddot{I}ˆ$, and $A\ge 6$ for $\hat{I}{\cdot }_c$. The $\ddot{I}•$-nucleus systems exhibit the strongest binding, with binding energies reaching tens of MeV. The $J/\ddot{I}ˆ$-nucleus and $\hat{I}{\cdot }_c$-nucleus systems are weakly bound at the few-MeV and sub-MeV scale, respectively. The binding energy per nucleon deepens nearly linearly with $A$ for charmonium systems, whereas the $\ddot{I}•$-nucleus system exhibits a non-monotonic behavior peaking at ${}^4$He -- a distinctive hallmark of the short-range and strongly attractive $\ddot{I}•N$ interaction. The meson compresses the nucleon distribution relative to the parent nucleus, and evolves from a halo configuration to one embedded inside the nucleus with increasing $A$. Our results provide predictions for future experimental searches, and establish a quantitative bridge between lattice QCD meson-nucleon interactions and the emergent many-body phenomena in meson-nucleus bound states.

12 pages, 6 figures