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Competition Between Particle-Hole and Particle-Particle Correlations in Forbidden Electron Capture: the Case of $^{123}$Te

M. Bianchetti·M. R. Quaglia·G. Colo`·P. M. Pizzochero·R. A. Broglia·P. F. Bortignon
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Abstract

The K-electron capture half-life of $^{123}$Te has been recently measured to be $t^K_{exp}=2.4\times 10^{19}$ yr, and constitutes the longest half-life ever measured in a single $β$-transition of any nuclear species. We have calculated this second unique forbidden transition within the framework of the proton-neutron quasi-particle random phase approximation, making use of Skyrme-type effective interactions. A strong cancellation effect between particle-hole and particle-particle correlations is found. The model, without any renormalization of the force, provides a lower limit for the K-electron capture half-life of $\sim 10^{17}$ yr, which unambiguously rules out the old experimental values of $10^{13} - 10^{14}$ yr. A few percent increase of the particle-particle matrix elements of the Skyrme interaction allows to reproduce the experimental findings.

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M. Bianchetti, M. R. Quaglia, G. Colo`, P. M. Pizzochero, R. A. Broglia, P. F. Bortignon. 1997-06-24. Competition Between Particle-Hole and Particle-Particle Correlations in Forbidden Electron Capture: the Case of $^{123}$Te. https://doi.org/10.1103/physrevc.56.r1675

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