Nonlinear collision shifts of the 0-0 hyperfine transition due to van der Waals molecule formation

We consider the origin of nonlinear collision shifts for the 0-0 hyperfine transition in alkali/noble-gas systems due to van der Waals molecule formation. Developing a semi-empirical model, we describe the shift as arising from three fundamental interactions: (1) a fractional change in the alkali's valence electron density at the alkali nucleus, eta, which affects the hyperfine contact term; (2) a mixing of p-wavefunction character into the alkali ground state (characterized by the probability for p-state character appearing in the perturbed wavefunction xi(2)(1)), which gives rise to an electric quadrupole term in the ground-state hyperfine splitting; and (3) an interaction of the alkali's valence electron with the magnetic field produced by molecular rotation, characterized by a magnetic field strength B-vdW. In addition to these molecular parameters, the model also depends on the formation rate of van der Waals molecules, k(f)P(2), and the breakup rate of the molecules, k(b)P, where P is the noble-gas pressure. Fitting the model to the Rb-85/Xe and Rb-87/Xe experimental data of McGuyer and co-workers (and taking previously measured values for k(f) and B-vdW), we find that eta = 9 x 10(-3), xi(2)(1) = 5 x 10(-3), and k(b) = 2.9x10(7) s(-1)/Torr.