Influence of Film-Mediated Interactions on the Microwave and Radio Frequency Spectrum of Spin-Polarized Hydrogen on Helium Films

We argue that helium film-mediated hydrogen-hydrogen interactions strongly reduce the magnitude of cold collision shifts in spin-polarized hydrogen adsorbed on a helium film. With plausible assumptions about experimental parameters this can explain (i) the 2 orders of magnitude discrepancy between previous theory and recent experiments and (ii) the anomalous dependence of the cold collision frequency shifts on the film’s ${}^3\mathrm{He}$ covering. The mediated interaction is attractive, suggesting that in current experiments the gas will become unstable before reaching the Kosterlitz-Thouless transition.

Figure 1

(a) Rescaled mediated potential as a function of interparticle separation divided by $\lambda$, as given by Eq. (8), with $\xi =1$, 4, 15 from top to bottom. (b) Scattering amplitudes $f$ as a function of mediated potential depth factor $V_d\equiv (2{\delta }^2)/({\pi }^3{\lambda }_0^{2}M{C}_3^2)=V_0(\lambda /{\lambda }_0{)}^2$ with ${\lambda }_0\equiv 50\AA$, for the triplet (dashed) and singlet (solid) scattering channels. Vertical lines indicate $V_d$ for the typical parameters given in the text (dashed line) and for $V_d=0$ (solid). The divergences near $V_d=0$ have been rounded off for display. (c) Contour plot of the factor by which $V_{\mathrm{med}}$ reduces the frequency shift as a function of $\lambda$ and $V_d$. Typical values of parameters are shown by the black dot, while factor of 2 variations comprise the interior of the black rectangle. The contour plot is hidden in the white “resonance” region (far away from the relevant regime), where the scattering amplitude diverges.