Competition between particle-hole and particle-particle correlations in forbidden electron capture: The case of Te-123

The K-electron capture half-life of Te-123 has been recently measured to be 2.4 x 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 quasiparticle 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 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 one to reproduce the experimental findings.