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arXiv:2303.10529

Diproton correlation and two-proton emission from proton-rich nuclei

Oishi, Tomohiro

Published Mar 19, 2023• 0 citations
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Abstract

Open-print version of dissertation thesis. This thesis focuses on the relation between the diproton correlation and the two-proton emission with quantum entanglement. For this purpose, I developed a time-dependent three-body (proton-proton-core) model, where one Cooper pair of protons move inside the mean-field potential. The time-dependent calculation based on the three-body model provides an intuitive way to describe the quantum dynamics of the entangled fermionic pair. It has been shown that, by considering the Cooper-pairing correlation in the initial state of the two protons, (i) the experimental 2p-decay width of Be-6 is well reproduced, and (ii) the two protons are emitted mainly as a diproton-like cluster with the spin-singlet configuration in the early stage of the emission. Hence, the two-proton emission can provide an access to the diproton correlation. This thesis presented the first step to theoretically investigate the diproton correlation as well as quantum entanglement in the time-dependent radioactive emission. [NOTE] In this open-print version, several Figures were inevitably eliminated, because of the copyright and/or file-size problems. Several minor corrections have been done, but without changing the scientific discussions, results, and conclusions from the original version in 2014.

DOI
10.48550/arxiv.2303.10529

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Open-print version of dissertation thesis. This thesis focuses on the relation between the diproton correlation and the two-proton emission with quantum entanglement. For this purpose, I developed a time-dependent three-body (proton-proton-core) model, where one Cooper pair of protons move inside the mean-field potential. The time-dependent calculation based on the three-body model provides an intuitive way to describe the quantum dynamics of the entangled fermionic pair. It has been shown that, by considering the Cooper-pairing correlation in the initial state of the two protons, (i) the experimental 2p-decay width of Be-6 is well reproduced, and (ii) the two protons are emitted mainly as a diproton-like cluster with the spin-singlet configuration in the early stage of the emission. Hence, the two-proton emission can provide an access to the diproton correlation. This thesis presented the first step to theoretically investigate the diproton correlation as well as quantum entanglement in the time-dependent radioactive emission. [NOTE] In this open-print version, several Figures were inevitably eliminated, because of the copyright and/or file-size problems. Several minor corrections have been done, but without changing the scientific discussions, results, and conclusions from the original version in 2014.
We show that a two-proton emitter with a diproton-correlated initial state can act as a source of spin-correlated proton pairs. Using a time-dependent three-body model, we investigate the two-proton emission of 16^{16}16Ne (14^{14}14O+2p+2p+2p) and analyze the spin correlation of the emitted protons. We find that, when the emission proceeds as a democratic three-body process from an initial state containing a spin-singlet diproton correlation, the emitted protons exhibit a pronounced spin-correlation pattern exceeding the local-hidden-variable bound. This spin correlation closely resembles that of a pure spin-singlet pair. In contrast, this pattern is lost when the process is dominated by the sequential emission or when the initial diproton correlation is absent. These results demonstrate that a certain class of two-proton emitters can deliver spin-entangled proton pairs, and their spin correlation reflects the diproton correlation embedded in the initial state.
This paper presents a theoretical evaluation of spin correlation in the two-proton (2 p ) 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 calculations are 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 | ≅ 2.65 . Namely, the 2 p -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) 2 p 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 the identical-particle entanglement.
By employing the time-dependent approach, we investigate a quantum tunneling decay of many-particle systems. We apply it to a schematic one-dimensional three-body model with a heavy-core nucleus and two valence protons. We calculate the decay width for two-proton emission from the survival probability, which well obeys the exponential decay law after a sufficient time. The effect of the correlation between the two emitted protons is also studied by observing the time evolution of the two-particle density distribution. It is shown that the pairing correlation significantly enhances the probability for the simultaneous diproton decay.
The decay process of the schematic one-dimensional three-body system is considered. A time-dependent approach is used in combination with a one-dimensional three-body model, which is composed of a heavier core nucleus and two nucleons, with the aim of describing its evolution in two-nucleon emission. The process is calculated from the initial state, in which the three ingredient particles are confined. In this process, two different types of emission can be found: the earlier process includes the emission of spatially correlated two-nucleon pair, like a dinucleon, whereas, at a subsequent time, all the particles are separated from each other. The time-dependent method can be a suitable option to investigate the meta-stable and/or open-quantum systems, where the complicated many-body dynamics should necessarily be taken into account.
Abstract The emission of two correlated fermions from a nuclear, or, in general, quantum meta-stable system is a poorly known, but fundamental problem: the interaction between the fermions can significantly affect the tunneling process. The behaviour of spin-singlet or spin-triplet emission has not been fully studied. In this article, the one-dimensional tunneling process of two fermions of the same kind is investigated. We solve the time-dependent Schrödinger equation for the two-fermion (2F) state, which is initially confined inside the square-well-plus-barrier potential. The interaction between the two fermions is schematically described by a short-range square-well attractive potential. A noticeable difference between the spin-singlet and triplet emissions is shown. Their tunneling probability, which is evaluated from the time-dependent survival probability, depends on the total spin, even if the effective-barrier height is fixed to be equivalent. Also, a spatial correlation of two fermions appears (vanishes) in the spin-singlet (triplet) case. The total-spin dependence of 2F emission can be attributed to the anti-symmetrization condition: it allows (prohibits) degenerate pairing, where two fermions can occupy the same spatial orbit, in the spin-singlet (triplet) case. This degenerate pairing makes the spin-singlet 2F state more long-lived than the spin-triplet one, even under the equivalent conditions. Only in the spin-singlet channel, the short-range 2F attraction enhances the degenerate-pair component, providing the difference between correlated and uncorrelated emissions. On the other hand, the spin-triplet emission cannot profit from the 2F interaction, due to the Pauli principle. These conclusions are independent of the physical scales.
We discuss the peculiarities of scattering in a three-proton system induced by the presence of an entangled proton-proton Bell-like state in the initial configuration. We formulate the problem using the standard spin formalism of nuclear physics in order to follow in detail the reaction pathways leading to the teleportation of a quantum-mechanical state within this system. By performing numerical simulations of the system and calculations based on a realistic nucleon-nucleon potential, we evaluate the relevant spin observables and search for a simple, experimentally feasible signal that could provide clear evidence of quantum teleportation. For the case in which proton 2, belonging to the entangled proton pair 23, interacts with hydrogen target 1, thereby triggering the teleportation process, we find clear evidence of teleportation through measurements of the final polarization of proton 3', even for small values of the polarization of target proton 1. The dominant component of this polarization is transferred almost entirely from target proton 1 to proton 3 in the angular region characterized by strong entanglement. For an unpolarized target proton 1, quantum teleportation is no longer possible. The only unambiguous signature of the residual quantum correlations would be provided by measurements of the spin correlations within the strongly entangled final-state proton pair 1'2'. Indirect evidence may also be obtained from measurements of the polarization of proton 2' in the final state, although the corresponding effectis relatively weak.