Quantum entanglement in nuclear Cooper pair tunneling with $γ$-rays

While Josephson-like junctions, transiently established in heavy ion collisions ($τ_{coll}\approx10^{-21}$ 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 $γ$-rays of (Josephson) frequency $ν_J=Q_{2n}/h$ distributed over an energy range $\hbar/τ_{coll}$ is predicted.

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