beta - gamma angular correlations in 20Na and 20F beta decay.

The \ensuremath{\beta}-\ensuremath{\gamma} angular correlations for the decay of $^{20}\mathrm{Na}$ and $^{20}\mathrm{F}$ to the 1.633 MeV state of $^{20}\mathrm{Ne}$ have been measured using a twenty-detector system of cylindrical symmetry. $^{20}\mathrm{Na}$ was produced by the $^{20}\mathrm{Ne}$(p,n${)}^{20}$Na reaction using a 19 MeV proton beam, and $^{20}\mathrm{F}$ was produced by the reaction $^{19}\mathrm{F}$(d,p${)}^{20}$F using ${\mathrm{SF}}_{6}$ gas and 4 MeV deuterons. The activated gasses were continuously transferred, through a thin capillary, from the target cell into the source cell in the center of the correlation apparatus. Two \ensuremath{\gamma} detectors and 16 \ensuremath{\beta} detector telescopes allowed for the simultaneous measurements of \ensuremath{\beta}-\ensuremath{\gamma} coincidences at 0\ifmmode^\circ\else\textdegree\fi{}, 25\ifmmode^\circ\else\textdegree\fi{}, 45\ifmmode^\circ\else\textdegree\fi{}, 65\ifmmode^\circ\else\textdegree\fi{}, 90\ifmmode^\circ\else\textdegree\fi{}, 115\ifmmode^\circ\else\textdegree\fi{}, 135\ifmmode^\circ\else\textdegree\fi{}, 155\ifmmode^\circ\else\textdegree\fi{}, and 180\ifmmode^\circ\else\textdegree\fi{}, and at their symmetric counterparts with respect to the 0\ifmmode^\circ\else\textdegree\fi{}--180\ifmmode^\circ\else\textdegree\fi{} direction. The \ensuremath{\beta}-\ensuremath{\gamma} correlation was also measured for the first-forbidden ${\ensuremath{\beta}}^{\mathrm{\ensuremath{-}}}$ decay of $^{124}\mathrm{Sb}$, in order to confirm the computed attenuation in measured anisotropy caused by the finite geometry of the detectors and the source cell. The correlation function is denoted by ${\mathit{W}}_{\ifmmode\pm\else\textpm\fi{}}$(${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\beta}}\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$)=1+${\mathrm{\ensuremath{\alpha}}}_{\ifmmode\pm\else\textpm\fi{}}$(E)(pE${)}^{2}$${\mathrm{cos}}^{2}$${\mathrm{\ensuremath{\theta}}}_{\mathrm{\ensuremath{\beta}}\mathrm{\ensuremath{-}}\ensuremath{\gamma}}$. The \ifmmode^\circ\else\textdegree\fi{} subscripts refer to electron or positron decay, p is the beta momentum, and E is the beta total energy in MeV. The present result for $^{20}\mathrm{Na}$(\ensuremath{\beta}-\ensuremath{\gamma}) correlation is ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{\ensuremath{-}}}$(E)=(-4.45\ifmmode\pm\else\textpm\fi{}0.31)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$E+(1.87\ifmmode\pm\else\textpm\fi{}0.42)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}4}$${\mathit{E}}^{2}$. The least squares fit to the energy dependence for $^{20}\mathrm{F}$ was performed by assuming the quadratic energy dependence measured for $^{20}\mathrm{Na}$, and the linear term in ${\ensuremath{\alpha}}_{+}$(E) yielded ${\mathrm{\ensuremath{\alpha}}}_{+}$(E)=(0.08\ifmmode\pm\else\textpm\fi{}0.16)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$E.First and second class induced pseudotensor form factors (${d}_{\mathrm{I}}$ and ${d}_{\mathrm{II}}$) were evaluated by combining the linear energy dependences and yielded ${d}_{\mathrm{II}/\mathrm{Ac}=\mathrm{\ensuremath{-}}1.1\ifmmode\pm\else\textpm\fi{}0.7}$ and ${d}_{\mathrm{I}/\mathrm{Ac}=11.3\ifmmode\pm\else\textpm\fi{}0.7}$. The 1977 Calaprice calculations for the value of the second-forbidden axial vector form factor ${j}_{2}$ were used. Assuming the Calaprice prediction for ${j}_{2}$, ${j}_{3}$ could be deduced from the quadratic term of the energy dependence of the asymmetry. We obtained ${j}_{3}$=-(19.5\ifmmode\pm\else\textpm\fi{}3.0)\ifmmode\times\else\texttimes\fi{}${10}^{4}$. We conclude that the angular correlations in mass 20 are close to and may be in agreement with expectations based on conserved vector current theory. Our best value for second class axial currents, ${d}_{\mathrm{II}/\mathrm{Ac}=\mathrm{\ensuremath{-}}1.1\ifmmode\pm\else\textpm\fi{}0.7}$, is at the level of 10% of the weak magnetism term; however, the statistical error given and the large uncertainty in ${j}_{2}$, derived from shell model wave functions, preclude a more definite statement regarding the existence of second class currents.