  New scheme of definition of g-factors as ground as excited optical states of
a paramagnetic ion in zero external constant magnetic field has been proposed
and experimentally realized in optical systems in which Zeeman Effect is
manifested. A pulse of a weak magnetic field leads to occurrence of relative
phase shifts of the excited dipoles and, as consequence, to modulation of a
photon echo waveform if magnetic pulse (MP) overlaps in time with echo-pulse.
The modulation periods of the waveform depend on polarization of the laser
light, which excites the photon echo. The values of these periods for {\sigma}-
and {\pi}- laser light polarization have been measured and then the g-factors
of the ground 4I15/2 and excited 4F9/2 states of the Er3+ ion in the LuLiF4 and
the YLiF4 matrices have been determined. Values of the g-factors have been
compared with the known literary data.
