Many-Body Approach to the Hyperfine Pressure Shift in Optical-Pumping Experiments

Abstract

The formulation of the van der Waals (VDW) interaction between atoms in terms of frequency-dependent polarizabilities is extended to the problem of the long-range contribution to the hyperfine pressure shift in optical-pumping experiments. The requisite perturbed-energy expression for the present problem involves two orders of VDW interaction and one order of magnetic hyperfine interaction. This expression is recast in terms of integrals involving requisite frequency-dependent response functions which are evaluated using the Brueckner-Goldstone many-body technique applied earlier to VDW energy calculations. Specific applications are made to H-He and H-Ne systems. The fractional shift $\frac{\ensuremath{\Delta}\mathcal{A}}{{\mathcal{A}}_{0}}$ of the hyperfine constant is expressed in the form of $\frac{{D}_{\mathrm{H}X}}{{R}^{6}}$, where $R$ (a.u.) is the separation between H and $X$ atoms. The values we obtain for ${D}_{\mathrm{H}X}$ are 13.34 and 26.13 for $X=\mathrm{He} \mathrm{and} \mathrm{Ne}$, respectively. This analysis removes one of the important uncertainties in hyperfine-pressure-shift calculations, namely, the influence of correlation effects on the long-range part of $\frac{\ensuremath{\Delta}\mathcal{A}}{{\mathcal{A}}_{0}}$.