A theoretical analysis of the collisional broadening and shift of Rydberg levels:with angular momenta J 1 taking into account the anisotropy of the Rydberg-perlurber potential is presented. The symmetry of the problem is used far the calculation of the collision S matrix in a semiclassical approximation with rectilinear trajenories. The obtained expressions for the broadening and shift cross sections allow an explanation of the observed differences between the broadening and shift of the anisotropic np, nd and IIP,,~ levels in comparison with those for the spherical ns and "PI,, states
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