Meson-exchange enhancement in first-forbidden $\beta$ -transitions: the case of $^{50}$K and $^{38}$Ca

The $\beta$- decay of $^{50}$K and $^{38}$Ca have been investigated with the main motive of determining more accurately the first-forbidden $\beta$- branches, in particular the rank-zero, $\Delta$J = 0, $\,\beta$ -transitions. $^{50}$K and $^{38}$Ca have been produced by fragmentation of U and Ti targets respectively, with a 1 GeV proton beam and subsequent on-line mass separation. For $^{50}$K, $\gamma$-ray spectroscopy, as well as delayed neutron spectroscopy by time of flight, were carried out to obtain a detailed decay scheme to 20 (bound and unbound) levels in $^{50}$Ca. The level structur e of $^{50}$Ca can be compared to recent calculations which incorporate 1p1h excitations from the f$_{7/2}$ shell. The first-forbidden $\beta^-$ transition $^{50}$ K(0$^-$)$\,\to{}^{50}$Ca(0$^+$) g.s. has been evaluated for the first time by a direct measurement of $\beta$- and $\gamma$- activities. Its importance (61.0 $\pm$ 7.4$\%$) is interpreted as an effect of the meson-exchange current (MEC) l eading to an enhancement factor of 62(5)$\%$ in comparison with the value predicted by shell-model calculations using the impulse approximation. For the $^{38}$ Ca$\,\to{}^{38}$K decay, chemical selec tive production was obtained through separation of the molecular ion CaF$^+$ without contamination by isobars. In these conditions, the measurement of very weak $\beta$-branches, at a level of 10$^{-3}\%$ decays, could be made and a limit, at the 2$\sigma$-confidence level, has been obtained for the 0$^+\to$ 0$^-$ branch to the level at E$_x$ = 2993 keV (I$_\beta$ < 0.0046$\%$). Imp lications of these results on the general trend of meson-exchange enhancements of first-forbidden transitions within the framework of the spherical shell model are discussed.