The 7Be Electron Capture Rate in the Sun

For solar conditions, we numerically integrate the density matrix equation for a thermal electron in the field of a ⁷Be ion and other plasma ions and smeared-out electrons. With this technique, we can calculate the capture rate without either assuming the existence of bound states or requiring fluctuations to be spherical. Our results are in agreement with previous calculations that are based on a different physical picture, a picture that postulates the existence of distinct continuum and bound-state orbits for electrons. The density matrix calculation of the electron capture rate is independent of the nature of electron states in the solar plasma. To within 1% accuracy, the effects of screening can be described at high temperatures by a Salpeter-like factor of exp (-Ze²/kTR_D), which can be derived from the density matrix equation. We show that nonspherical fluctuations change the reaction rate by less than 1%. The total theoretical uncertainty in the electron capture rate is about +/-2%.