Non-coherent character of isoscalar pairing probed with Gamow-Teller strength: New insight into $^{14}$C dating $\beta$ decay

TL;DR

This study examines the phase coherence of isoscalar pairs in nuclei through Gamow-Teller strengths, revealing that isoscalar pairs lack phase coherence, which impacts nuclear decay processes like $^{14}$C dating.

Contribution

It provides new insights into the non-coherent nature of isoscalar pairing in nuclei, contrasting with isovector pairing, and explains the suppression of certain Gamow-Teller transitions.

Findings

Gamow-Teller matrix elements are always constructive under pairing Hamiltonians.

Observed GT strengths are hindered in two-hole configurations like $^{14}$C.

Isoscalar pairs lack phase coherence, affecting nuclear decay processes.

Abstract

We investigate the phase coherence of isoscalar pairs from the $B({\rm GT};0^+_1\,T\!=\!1 \to 1^+_1\,T\!=\!0)$ values in two-particle configurations of $A=6$, 18, and 42 nuclei and two-hole configurations of $A=14$ and 38 ones. We find that these Gamow-Teller (GT) matrix elements are always constructive and thus enlarged under isovector- and isoscalar-pairing Hamiltonians, whereas the observed GT strengths are strongly hindered for the two-hole configurations, including the famous $^{14}$C dating $\beta$ decay. This indicates that the actual isoscalar pair, unlike the isovector pair, has no definite phase coherence, which can work against forming isoscalar-pair condensates.