Asymptotic normalization coefficients and radiative widths

Abstract

The asymptotic normalization coefficient (ANC) is an important quantity in the calculation of radiative width amplitudes, providing limits on the radiative width. Here we present some examples showing the connection between the ANC and radiative width. In particular, the radiative width of the $E1$ transition $^{17}\text{F}(1/{2}^{\ensuremath{-}},\phantom{\rule{0.16em}{0ex}}{E}_{x}=3.104\phantom{\rule{4pt}{0ex}}\mathrm{MeV})$ to $^{17}\mathrm{F}(1/{2}^{+},{E}_{x}=0.495\phantom{\rule{4pt}{0ex}}\mathrm{MeV})$ reported by Rolfs [Nucl. Phys. A 217, 29 (1973)] is $(1.2\ifmmode\pm\else\textpm\fi{}0.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ eV. Meanwhile the ANC for the first excited state in $^{17}\text{F}$ puts a lower limit on the radiative width, which is $(3.4\ifmmode\pm\else\textpm\fi{}0.50)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ eV. Such a strong disagreement between the measured radiative width and the lower limit imposed by the ANC calls for a new measurement of this radiative width. Other examples are also considered.