  A neutron lifetime measurement conducted at the Japan Proton Accelerator
Research Complex (J-PARC) is counting the number of electrons from neutron
decays with a time projection chamber (TPC). The $\gamma$ rays produced in the
TPC cause irreducible background events. To achieve the precise measurement,
the inner walls of the TPC consist of $^6$Li-enriched lithium-fluoride
($^6$LiF) tiles to suppress the amount of $\gamma$ rays. In order to estimate
the amount of $\gamma$ rays from the $^{6}{\rm LiF}$ tile, prompt gamma ray
analysis (PGA) measurements were performed using germanium detectors. We
reconstructed the measured $\gamma$-ray energy spectrum using a Monte Carlo
simulation with the stripping method. Comparing the measured spectrum with a
simulated one, the number of $\gamma$ rays emitted from the$^{6}{\rm LiF}$ tile
was $(2.3^{+0.7}_{-0.3}) \times 10^{-4}$ per incident neutron. This is
$1.4^{+0.5}_{-0.2}$ times the value assumed for a mole fraction of the
$^{6}{\rm LiF}$ tile. We concluded that the amount of $\gamma$ rays produced
from the $^{6}{\rm LiF}$ tile is not more twice the originally assumed value.
