Radiative capture estimates via analytic continuation of elastic-scattering data, and the solar-neutrino problem

Measurements of ${\sigma }_{\gamma }$ for ${}_{}{}^3{}_{}{}^{}\mathrm{He}(\alpha ,\gamma ){}_{}{}^7{}_{}{}^{}\mathrm{Be}$, central to the solar $\nu$ problem, disagree. In a direct capture model, the normalization constants $N_{\frac{3}{2}}$ and $N_{\frac{1}{2}}$ of the $P_{\frac{3}{2}}$ and $P_{\frac{1}{2}}$ bound state wave functions of ${}_{}{}^7{}_{}{}^{}\mathrm{Be}$ at large ${}_{}{}^3{}_{}{}^{}\mathrm{He}-\alpha$ separations determine ${\sigma }_{\gamma }$. $N_{\frac{3}{2}}$ and $N_{\frac{1}{2}}$ are given by (simpler) measurements of ${\sigma }_{\gamma }$ at a higher energy $E$, or, as here, by analytic continuation of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}-\alpha p_{\frac{3}{2}}$ and $p_{\frac{1}{2}}$ phase shifts, $\delta \mathrm{}\left(E\right)\mathrm{}$. The method has been successfully tested on calculations of Tang et al. Better measurements of $\delta \mathrm{}\left(E\right)\mathrm{}$ are called for.