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

Frequency Light Shifts Caused by the Effects of Quantization of Atomic Motion in an Optical Lattice