Two-body cluster entangled structure in the $\mathcal{H}_1\otimes \mathcal{H}_2$ Hilbert space

TL;DR

This paper applies quantum entanglement analysis to nuclear cluster structures, transforming wave functions into particle basis to quantify entanglement and reveal its dependence on spatial configurations in $^8$Be.

Contribution

It introduces a wave function transformation method and spatially resolved entropy to analyze entanglement in nuclear cluster states, providing new insights into nuclear quantum correlations.

Findings

Entanglement correlates with cluster separation at femtometer scale.

As clusters approach each other, entanglement diminishes, approaching a separable state.

Spatially resolved entropy reveals entanglement dynamics during cluster separation.

Abstract

This study introduces a quantum information perspective to analyze the internal structure of atomic nuclei, focusing on the quantum entanglement between $\alpha$ clusters in the 0$^+$ state of $^8$Be. A wave function based on angular momentum coupling is developed to transform the two-cluster wave function from the conventional center of mass and relative coordinate basis ($\mathcal{H}_{R_{c.m.}} \otimes \mathcal{H}_r$) into the individual particle basis ($\mathcal{H}_1 \otimes \mathcal{H}_2$), which is essential for a precise quantification of entanglement. Within this method, the von Neumann entropy is employed to quantify the entanglement arising from the mixing of angular momentum channels. Additionally, we introduce the concept of spatially resolved entropy, which measures entanglement as a function of the radial separation between clusters. Our analysis reveals that the entanglement is strongly correlated with the spatial configuration at the femtometer scale. As the inter cluster separation vanishes, the system approaches a separable $S$-wave state, indicating that entanglement is dynamically generated during the spatial separation of the clusters. This research provides a new tool for investigating nonlocal quantum correlations in nuclear structure, complementing existing descriptions.