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A pair of atoms interacts with non-resonant light via its anisotropicpolarizability. This effect can be used to tune the scattering properties ofthe atoms. Although the light-atom interaction varies with interatomicseparation as $1/R^{3}$, the effective s-wave potential decreases more rapidly,as $1/R^{4}$ such that the field-dressed scattering length can be determinedwithout any formal difficulty. The scattering dynamics are essentially governedby the long-range part of the interatomic interaction and can thus beaccurately described by an asymptotic model [Crubellier et al., New J. Phys.17, 045020 (2015)]. Here we use the asymptotic model to determine thefield-dressed scattering length from the s-wave radial component of aparticular threshold wave function. Applying our theory to the scattering oftwo strontium isotopes, we calculate the variation of the scattering lengthwith the intensity of the non-resonant light. Moreover, we predict theintensities at which the scattering length becomes infinite for any pair ofatoms.

Controlling the s-wave scattering length with non-resonant light: Predictions of an asymptotic model