Beta decays of Ne 18 and Ne 19 and their relation to parity mixing in F 18 and F 19

We have studied transitions weakly fed in the ${\ensuremath{\beta}}^{+}$ decays of $^{18}\mathrm{Ne}$ and $^{19}\mathrm{Ne}$. The $^{18}\mathrm{Ne}$ activity was produced by bombarding natural ${\mathrm{O}}_{2}$ gas with 12.0 MeV $^{3}\mathrm{He}$ ions. $\ensuremath{\gamma}$-ray groups with energies of 659, 1042, 1081, and 1700 keV were observed with relative intensities of 1.72\ifmmode\pm\else\textpm\fi{}0.05, 100.0, (2.89\ifmmode\pm\else\textpm\fi{}0.26)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}2}$, and 0.687\ifmmode\pm\else\textpm\fi{}0.013, respectively. These intensities correspond to relative branching ratios of 100.0, (2.70\ifmmode\pm\else\textpm\fi{}0.36)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}2}$, and 2.45\ifmmode\pm\else\textpm\fi{}0.05 for ${\ensuremath{\beta}}^{+}$ transitions to the 1042, 1081, and 1700 keV levels, respectively. Normalizing to previous data we obtain $\mathrm{ft}$ values of 1247\ifmmode\pm\else\textpm\fi{}11, 2971\ifmmode\pm\else\textpm\fi{}87, (1.03\ifmmode\pm\else\textpm\fi{}0.14)\ifmmode\times\else\texttimes\fi{}${10}^{7}$, and (3.00\ifmmode\pm\else\textpm\fi{}0.10)\ifmmode\times\else\texttimes\fi{}${10}^{4}$ see for the transitions to the ground state, 1042, 1081, and 1700 keV levels, respectively. The difference in excitation energies of the ${0}^{\ensuremath{-}}$ and ${0}^{+}$ states is found to be 39.20\ifmmode\pm\else\textpm\fi{}0.11 keV. The $^{19}\mathrm{Ne}$ activity was produced by bombarding S${\mathrm{F}}_{6}$ gas by 6.4 MeV protons. A branching ratio of (1.20\ifmmode\pm\else\textpm\fi{}0.20)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ was obtained for the transition to the 110 keV level which corresponds to an $\mathrm{ft}$ value of (1.15\ifmmode\pm\else\textpm\fi{}0.19)\ifmmode\times\else\texttimes\fi{}${10}^{7}$ sec. Transitions to the 1554 keV level were observed in a 9.2% Ge(Li) detector operated in the singles mode. A branching ratio of (2.34\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}5}$ was obtained which corresponds to an $\mathrm{ft}$ value of (5.01\ifmmode\pm\else\textpm\fi{}0.47)\ifmmode\times\else\texttimes\fi{}${10}^{5}$ sec. The $^{18}\mathrm{Ne}$(${0}^{+}$; 1)\ensuremath{\rightarrow}$^{18}\mathrm{F}$(1081 keV ${0}^{\ensuremath{-}}$; 0) and $^{19}\mathrm{Ne}$(${\mathrm{\textonehalf{}}}^{+}$; \textonehalf{})\ensuremath{\rightarrow}$^{19}\mathrm{F}$ (110 keV ${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$; \textonehalf{}) first-forbidden ${\ensuremath{\beta}}^{+}$ branches are analogs of the previously measured parity mixing of the 1042 keV (${0}^{+}$; 1) and 1081 (${0}^{\ensuremath{-}}$; 1) keV levels of $^{18}\mathrm{F}$ and of the ground (${\mathrm{\textonehalf{}}}^{+}$; \textonehalf{}) and 110 keV (${\mathrm{\textonehalf{}}}^{\ensuremath{-}}$; \textonehalf{}) levels of $^{19}\mathrm{F}$, respectively. We show that the strong exchange-current corrections to the axial charge operator dominating these $\ensuremath{\beta}$ transitions involve an operator identical, apart from an isospin rotation, to that mediating the pion-exchange contribution to the parity nonconserving $\mathrm{NN}$ force. These exchange current contributions can be extracted from the $\ensuremath{\beta}$-decay rates in a manner nearly independent of nuclear structure assumptions. Thus, in these cases, the usual structure uncertainties that obscure the connection between the $\ensuremath{\Delta}S=0$ weak hadronic interaction and nuclear observables can largely be circumvented. The $\mathrm{ft}$ values we obtain for the transitions to the 1081 keV and 110 keV levels of $^{18}\mathrm{F}$ and $^{19}\mathrm{F}$ suggest that the strengths of the $I=1$ and $I=0$ components of the parity nonconserving $\mathrm{NN}$ force are close to the "best values" of Desplanques, Donoghue, and Holstein. Except for a recent structure calculation employing complete $2h\ensuremath{\omega}$ and $1h\ensuremath{\omega}$ bases for the positive and negative parity states in $^{18}\mathrm{F}$, the $\ensuremath{\beta}$ decay and parity nonconserving matrix elements predicted in typical shell model studies are approximately three times larger than experiment. This and other evidence suggests that the softening of the nuclear Fermi surface by $2h\ensuremath{\omega}$ configurations is an essential, but missing, feature of most nuclear structure calculations of parity nonconserving matrix elements. We conclude by presenting shell model studies of the electromagnetic properties of low-lying states in $^{18}\mathrm{F}$, $^{19}\mathrm{F}$/$^{19}\mathrm{Ne}$, and $^{21}\mathrm{Ne}$/$^{21}\mathrm{Na}$ as well as the matrix elements for the operators that arise in a general meson-exchange parity nonconserving potential.RADIOACTIVITY $^{18}\mathrm{Ne}$, $^{19}\mathrm{Ne}$; measured $I\ensuremath{\gamma}$; deduced $\mathrm{ft}$. Compared to shell model calculations. Discussed connection of forbidden decays to parity mixing in $^{18}\mathrm{F}$ and $^{19}\mathrm{F}$.