  It is shown that a new light gauge boson $X$ which might be produced in the
decays of pseudoscalar mesons $\pi^{0}(\eta)\to\gamma + X$ could be effectively
searched for in neutrino experiments via the Primakoff effect, in the process
of $X + Z\to \pi^{0}(\eta) + Z$ conversion in the external Coulomb field of a
nucleus. An estimate of the $X\to \pi^{0}$ conversion rate for the NOMAD
neutrino detector at CERN is given.
