  We present a reanalysis of the experimental data of electron capture in
$^7$Be embedded in Ta which have been published by other authors. Our goal is
to set upper limits on a mixture of electron neutrino with a possible
right-handed heavy neutrino in the 150--800 keV mass range. In the published
experiment a $^7$Li recoil energy spectrum in the 20--200 eV range was
measured. In case of electron capture with emission of a heavy neutrino, the
recoil spectrum should be shifted to the lower energies. We search for an
additional Gauss-shaped structure with the same energy width as the main
K-shell transition peak. For this we digitize the published spectrum curve,
find the energy resolution, calculate the moving sum of the events along the
spectrum in the energy interval of about 3 sigma of energy resolution. Then we
use the statistical error of this sum to exclude at some level the appearance
of an additional peak. Finally, we present the upper limits at a 95\%
confidence level on electron neutrino -- heavy neutrino mixing element, $U^2$,
in the mass matrix. New upper limits are at least one order of magnitude lower
than the existing data in 300--800 keV mass range.
