Motivated by recent V.A. Nikitin's reports on observation of 9-MeV$/c^2$
charged particles with a 2 meter JINR propane bubble chamber we perform an
experiment at the LPI electron synchrotron "Pakhra" with the aim to detect
such particles in the Bethe--Heitler process. Theoretical limits for masses
of new light charged particles of spin 0, 1/2 and 1 arising from precise
data on the muon anomalous magnetic moment are recalculated and updated. A
geometry of the photoproduction experiment is proposed that optimizes
sigma-to-noise ratio. Preliminary results of the experiment are exposed.