Semiclassical analysis of measurements of the total cross section Q and the small-angle differential cross section for Csf Ar: An accurate method for absolute Q values

Abstract

The semiclassical analysis of small-angle scattering shows that the shape and the magnitude of the small-angle differential cross section σ a(θ) and the total cross section Q a are fully determined by the attractive branch V a ( r) - C s / r s of the intermolecular potential. We measure the beam attenuation S 1 = ζ Q a in an in-Iine crossed-beam experiment and the differentially scattered intensity S 2 = ζω 0σ a(θ), with ζ = ( g/υ 1 ( nl) and g υ 1 the relative velocity and the primary-beam velocity, respectively, ( nl) the product of number density scattering length of the secondary beam and the center-of-mass solid angle acceptance of the beam machine. The ratio S 2 / S 1 is in first order independent of ( nl) and determines the absolute value of Q a, if we assume an effective power s of the attractive branch. For CsFAr this method results in Q a = 515 × (1000/ g) 0.36 (A 2 in the range 913 < g(ms −1) 1043, where ε has been fixed at s = 6.6 by relative measurements of the velocity dependence of the total cross section in the range 650 < g (m s −1 < 1050. The result for ζ = S 1 Q a is consistent with the value of ( nl) derived from accurate information on the center-line intensity of the cryopumped, supersonic secondary beam.