Ratio of the Gamow-Teller and Fermi Coupling Constants Determined from<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ft</mml:mi></mml:math>Values

Abstract

A comparison is made of the ratios of the squares of the Gamow-Teller and Fermi coupling constants, $\frac{{{C}_{\mathrm{GT}}}^{2}}{{{C}_{\mathrm{F}}}^{2}}$, calculated from the latest experimental $\mathrm{ft}$ values and the theoretical matrix elements for the "doubly closed shell\ifmmode\pm\else\textpm\fi{}one nucleon" mirror transitions and the ${0}^{+}$-${0}^{+}$ transitions. The $\mathrm{ft}$ value of the neutron derived from the recent half-life measurement of 11.7\ifmmode\pm\else\textpm\fi{}0.3 minutes leads to a value for $\frac{{{C}_{\mathrm{GT}}}^{2}}{{{C}_{\mathrm{F}}}^{2}}$ of 1.42\ifmmode\pm\else\textpm\fi{}0.06, which is in agreement with the ratio obtained from the correlation coefficient for the betaparticle momentum and the spin direction of the decaying neutron. The $\mathrm{ft}$ value for the decay of ${\mathrm{H}}^{3}$ is also in good agreement with this ratio if the Gamow-Teller matrix element for this transition does not differ appreciably from that predicted by the individual particle model. The $\mathrm{ft}$ value of the heavier mirror nuclei, ${\mathrm{O}}^{15}$, ${\mathrm{F}}^{17}$ and ${\mathrm{Ca}}^{39}$, are consistent with a considerably lower ratio. In particular, ${\mathrm{O}}^{15}$ and ${\mathrm{F}}^{17}$, for which the Gamow-Teller matrix elements are considered the most reliable because the magnetic moments of the daughter nuclei are especially close to the Schmidt limits, lead to a value for $\frac{{{C}_{\mathrm{GT}}}^{2}}{{{C}_{\mathrm{F}}}^{2}}$ of 1.16\ifmmode\pm\else\textpm\fi{}0.05. These results are consistent with recent theoretical considerations which suggest that meson exchange effects may give rise to appreciable corrections in the calculation of the matrix elements.