Quantum entanglement in nuclear Cooper pair tunneling with $\gamma$-rays

TL;DR

This paper explores quantum entanglement in nuclear Cooper pair tunneling during heavy ion collisions, predicting gamma-ray emission at Josephson frequency related to two-neutron transfer and estimating the nuclear Cooper pair's correlation length.

Contribution

It introduces a novel analysis of nuclear Cooper pair tunneling, linking quantum entanglement effects to gamma-ray emission and providing estimates of the nuclear Cooper pair's correlation length.

Findings

Prediction of gamma-ray emission at Josephson frequency.

Estimation of the nuclear Cooper pair's correlation length.

Identification of the tunneling cross section's dependence on nucleon separation.

Abstract

While Josephson-like junctions, transiently established in heavy ion collisions ($\tau_{coll}\approx10^{-21}$ s) between superfluid nuclei --through which Cooper pair tunneling ($Q$-value $Q_{2n}$) proceeds mainly in terms of successive transfer of entangled nucleons-- is deprived from the macroscopic aspects of a supercurrent, it displays many of the special effects associated with spontaneous symmetry breaking in gauge space (BCS condensation), which can be studied in terms of individual quantum states and of tunneling of single Cooper pairs. From the results of studies of one- and two- neutron transfer reactions carried out at energies below the Coulomb barrier we estimate the value of the mean square radius (correlation length) of the nuclear Cooper pair. A quantity related to the largest distance of closest approach for which the absolute two-nucleon tunneling cross section is of the order of the single-particle one. Furthermore, emission of $\gamma$-rays of (Josephson) frequency $\nu_J=Q_{2n}/h$ distributed over an energy range $\hbar/\tau_{coll}$ is predicted.