  The circular polarized laser beam of the ``magic'' wavelength may be used for
mixing the $^3P_1$ state into the long-living metastable state $^3P_0$, thus
enabling the strictly forbidden $^1S_0$$-$$^3P_0$ ''clock'' transition in even
isotopes of alkaline-earth-like atoms, without change of the transition
frequency. In odd isotopes the laser beam may adjust to an optimum value the
line width of the "clock" transition, originally enabled by the hyperfine
mixing. We present a detailed analysis of various factors influencing
resolution and uncertainty for an optical frequency standard based on atoms
exposed simultaneously to the lattice standing wave and an additional
"state-mixing" wave, including estimations of the "magic" wavelengths, Rabi
frequencies for the ''clock'' and state-mixing transitions, ac Stark shifts for
the ground and metastable states of divalent atoms.
