Radiative capture estimates via analytic continuation of elastic-scattering data, and the solar-neutrino problem
Abstract
Measurements of ${\ensuremath{\sigma}}_{\ensuremath{\gamma}}$ for $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$, central to the solar $\ensuremath{\nu}$ 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 $^{3}\mathrm{He}\ensuremath{-}\ensuremath{\alpha}$ separations determine ${\ensuremath{\sigma}}_{\ensuremath{\gamma}}$. ${N}_{\frac{3}{2}}$ and ${N}_{\frac{1}{2}}$ are given by (simpler) measurements of ${\ensuremath{\sigma}}_{\ensuremath{\gamma}}$ at a higher energy $E$, or, as here, by analytic continuation of the $^{3}\mathrm{He}\ensuremath{-}\ensuremath{\alpha} {p}_{\frac{3}{2}}$ and ${p}_{\frac{1}{2}}$ phase shifts, $\ensuremath{\delta}(E)$. The method has been successfully tested on calculations of Tang et al. Better measurements of $\ensuremath{\delta}(E)$ are called for.[NUCLEAR REACTIONS $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\gamma})^{7}\mathrm{Be}$, $E<300$ keV, $^{3}\mathrm{He}(\ensuremath{\alpha},\ensuremath{\alpha})^{3}\mathrm{He}$, $E<4$ MeV, effective range function, analytic continuation technique, bound state energies, and normalization.]