We observed three $\gamma$-ray bursts related to thunderclouds in winter
using the prototype of anti-neutrino detector PANDA made of 360-kg plastic
scintillator deployed at Ohi Power Station at the coastal area of the Japan
Sea. The maximum rate of the events which deposited the energy higher than
$3\,$MeV was $(5.5 \pm 0.1) \times 10^2 {\rm /s}$.
Monte Carlo simulation showed that electrons with approximately monochromatic
energy falling downwards from altitudes of order $100\,$m roughly produced the
observed total energy spectra of the bursts. It is supposed that secondary
cosmic-ray electrons, which act as seed, were accelerated in electric field of
thunderclouds and multiplied by relativistic runaway electron avalanche. We
actually found that the $\gamma$-rays of the bursts entered into the detector
from the direction close to the zenith. The direction stayed constant during
the burst within the detector resolution.
In addition, taking advantage of the delayed coincidence detection of the
detector, we found neutron events in one of the bursts at the maximum rate of
$\sim 14\pm5\,{\rm /s}$.Comment: 16 pages, 7 figures; Accepted for publication in Physics Letters B;
Figure 5 added, some minor changes in the tex