Spin correlation in two-proton emission from $^6$Be

TL;DR

This paper theoretically investigates spin correlations in two-proton emission from $^6$Be, revealing nonlocal quantum correlations that depend on nuclear interactions, and proposes using two-proton emitters to test entanglement in nuclear systems.

Contribution

It introduces a time-dependent three-body model to evaluate spin correlations in $^6$Be decay, demonstrating nonlocal quantum effects beyond classical limits.

Findings

The spin correlation indicator |S| ≈ 2.65 exceeds local-hidden-variable limits.

Short-lived $2p$ states show weaker spin correlations.

Core-proton interactions do not diminish the observed correlations.

Abstract

This paper presents a theoretical evaluation of spin correlation in the two-proton ($2p$) radioactive emission. The three-body model of $^{6}$Be with the proton-proton interaction, which is adjusted to reproduce the experimental energy release, is utilized. Time-dependent calculation is performed to compute the coupled-spin state of the emitted two protons. The spin-correlation function $S$ as the Clauser-Horne-Shimony-Holt (CHSH) indicator is evaluated as $|S| \cong 2.65$. Namely, the $2p$-spin correlation beyond the limit of local-hidden-variable (LHV) theory is suggested. This correlation is sensitive to the proton-proton interaction. The short-lived (broad-width) $2p$~state has the weaker spin correlation. In parallel, the core-proton interactions do not harm this correlation during the time-dependent decaying process. The CHSH measurement can be a novel probe into the effective nuclear interaction inside finite systems. Two-proton emitters can provide a testing field for identical-particle entanglement.