  Context. In stellar interiors, rotation is able to drive turbulent motions,
and the related transport processes have a significant influence on the
evolution of stars. Turbulent mixing in the radiative zones is currently taken
into account in stellar evolution models through a set of diffusion
coefficients that are generally poorly constrained.
  Aims. We want to constrain the form of one of them, the radial diffusion
coefficient of chemical elements due to the turbulence driven by radial
differential rotation, derived by Zahn (1974, 1992) on phenomenological grounds
and largely used since.
  Methods. We performed local, direct numerical simulations of stably
stratified homogeneous sheared turbulence using the Boussinesq approximation.
The domain of low P\'eclet numbers found in stellar interiors is currently
inaccessible to numerical simulations without approximation. It is explored
here thanks to a suitable asymptotic form of the Boussinesq equations. The
turbulent transport of a passive scalar is determined in statistical steady
states.
  Results. We provide a first quantitative determination of the turbulent
diffusion coefficient and find that the form proposed by Zahn is in good
agreement with the results of the numerical simulations.
