High resolution differential cross sections of LiF in the J=1 rotational state in both a polarized condition and an unpolarized condition were experimentally studied with an Ar target for a range of LiF energies from 0.3 to 1.9 eV. The technique for performing such experiments is described in detail, including a description of the high resolution state selector and the seeded supersonic source. High frequency and rainbow features are observed in the differential cross sections. Manifestations of these oscillations are also observed in the significant difference in cross section due to polarization. The infinite order sudden approximation was used in a preliminary way to interpret the data. A model potential was used that had an inverse radial power series and appropriate angular dependent Legendere polynomials. The differential cross section is sensitive to the anisotropy parameters chosen. The cross section is generally larger for the (J, M)=(1, 1) polarization along the relative velocity for the energies and the small angles observed here. © 1979 American Institute of Physics.