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, η, 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 ξ₁ ²), 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_fP², and the breakup rate of the molecules, k_bP, where P is the noble-gas pressure. Fitting the model to the ⁸⁵Rb/Xe and ⁸⁷Rb/Xe experimental data of McGuyer and co-workers (and taking previously measured values for k_f and B_vdW), we find that η = 9 × 10^-3, ξ₁ ² = 5 × 10^-3, and k_b = 2.9×10⁷ s^-1/Torr.