  A pair of atoms interacts with non-resonant light via its anisotropic
polarizability. This effect can be used to tune the scattering properties of
the atoms. Although the light-atom interaction varies with interatomic
separation 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 determined
without any formal difficulty. The scattering dynamics are essentially governed
by the long-range part of the interatomic interaction and can thus be
accurately described by an asymptotic model [Crubellier et al., New J. Phys.
17, 045020 (2015)]. Here we use the asymptotic model to determine the
field-dressed scattering length from the s-wave radial component of a
particular threshold wave function. Applying our theory to the scattering of
two strontium isotopes, we calculate the variation of the scattering length
with the intensity of the non-resonant light. Moreover, we predict the
intensities at which the scattering length becomes infinite for any pair of
atoms.
