Analog-antianalog isospin mixing in ⁴⁷K β decay and time-reversal symmetry

The neutron β decays to its isobaric analog state, the proton, as does tritium. Many other isotopes undergo β^- decay to states of same spin and parity I^π, but because of the extra Coulomb energy at higher Z, decay to the isobaric analog state is energetically forbidden. So the Gamow-Teller operator dominates, while the Fermi operator linking isobaric analog states is only allowed if some low-lying final state of same I^π is mixed by an isospin-breaking interaction with the excited isobaric analog. We see such isospin breaking in an I^π=1/2⁺ state in the ⁴⁷Ca nucleus 80% fed by the β decay of I^π=1/2^{+ 47}K. Interference between Gamow-Teller and isospin-suppressed Fermi amplitudes produces a small asymmetry of the progeny recoil direction with respect to the initial nuclear spin, which we measure with TRIUMF's Neutral Atom Trap for beta decay (TRINAT).

Our preliminary result from a weighted average of recoil and beta asymmetries is M_F/M_GT=-0.096±0.037, implying a Coulomb mixing matrix element 72±29 keV, an order of magnitude larger than measured in other β asymmetry measurements in nearby nuclei. Since ⁴⁷Ca and ⁴⁷K are near closed shells, that single known ⁴⁷Ca 1/2⁺ state (J.K. Smith PRC 2020) may contain a large fraction of the antianalog configuration and its predicted 190 keV mixing matrix element with the analog [Auerbach, Loc NPA 2022].

Sensitivity to time reversal-odd parity-even (TOPE) inherently isovector [Simonius PRL 1997] N-N interactions through a β-ν-spin correlation is thought to be enhanced in these systems, as they are referenced to Coulomb rather than strong interactions [Barroso, Blin-Stoyle PLB 1973], while in this ⁴⁷Ca case the nuclear matrix elements of such an isovector TOPE interaction may also escape fragmentation.