Circularly polarised laser (CPL) field causes a shift proportional to the beam intensity, in the nuclear magnetic resonance spectra of all substances. As opposite shifts are obtained for left- and right-CPL, switching between the two splits the resonance lines. We present quadratic response calculations of the splitting for atomic 21 Ne, 83 Kr and 129 Xe, both far away from and approaching optical resonance. Off-resonance shifts of the order 0.01, 0.1 and 1×10 −6 Hz for 21 Ne, 83 Kr and 129 Xe, respectively, are predicted for the beam intensity of 10 W/cm 2 . Large enhancement occurs when the frequency increases and/or systems of increasing polarisability are concerned.