  Frequency light shifts resulting from the localization effects and effects of
the quantization of translational atomic motion in an optical lattice is
studied for a forbidden optical transition $J$=0$\to$$J$=0. In the Lamb-Dicke
regime this shift is proportional to the square root from the lattice field
intensity. With allowance made for magneto-dipole and quadrupole transitions,
the shift does not vanish at the magic wavelength, at which the linear in
intensity shift is absent. Preliminary estimates show that this shift can have
a principal significance for the lattice-based atomic clocks with accuracy of
order of 10$^{-16}-10^{-18}$. Apart from this, we find that the numerical value
of the magic frequency depends on the concrete configuration of the lattice
field and it can vary within the limits 1-100 MHz (depending on element) as one
passes from one field configuration to another. Thus, theoretical and
experimental investigations of contributions originated from magneto-dipole and
quadrupole transitions are of principal self-dependent interest.
