  For solar conditions, we numerically integrate the density matrix equation
for a thermal electron in the field of a Be-7 ion and other plasma ions and
smeared-out electrons. Our results are in agreement with previous calculations
that are based on a different physical picture, a picture which 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 a 1% accuracy, the
effects of screening can be described at high temperatures by a Salpeter-like
factor which can be derived from the density matrix equation. The total
theoretical uncertainty in the electron capture rate is about 2%.
