Spinning "Snowballs" in SuperfluidHe4

Abstract

We propose a simple mechanism that generates nonparabolicity in the dispersion of the positive charge carrier (snowball) in superfluid 4 He. Specifically, we pursue the consequences of a model where (1) the snowball behaves as a rigid rotator and (2) the hydrodynamic contribution to its mass (with rotator axes fixed) is anisotropic. The nonparabolicity that we calculate leads to a linear temperature variation of the snowball effective mass. The model is consistent with recent measurements if we assume a mass anisotropy of (9-13)%. An additional T 3 mass enhancement by long-wavelength phonons is negligible for the snowball but may be observable for the negative charge carrier.PACS numbers: 67.40.Yv Recent measurements at millikelvin temperatures ' indicate a substantial linear variation in the effective mass of the positve charge carrier (ion) in superfluid 4 He. As in the earlier experiment at somewhat higher temperatures by Ott-Rowland et al., 3 the effective ion mass is inferred from resonant modes of pools of ions trapped below the liquid surface. In this Letter we consider a source of nonparabolicity in the dispersion of the positive ion. In close analogy to the case of elastic constants in anharmonic solids, nonparabolicity in the dispersion then leads to a temperature-dependent mass. Putterman, Roberts, and Fiszdon 4 have evaluated the strength of the nonparabolicity arising from compression of the liquid surrounding the ion and find that it is too small by about a factor of 350 to explain the observations. We propose a much stronger source of nonparabolicity that results from the rotational degree of freedom and associated mass anisotropy of the positive ion. When compared with experiment our results provide interesting information about the structure of this ion. We also suggest new experiments to spectroscopically probe its rotational modes.The ion-pool experiments have utilized two independent probes of the positive-ion effective mass: (1) the absolute value of the plasma frequency 1,2 and (2) the cyclotron shift of the plasma frequency. * Consistency in the temperature variation of the ion effective mass as inferred from (1) and (2) suggests that an intrinsic property of the ion is being measured rather than a collective phenomenon. Indeed, the strong nonlinear response observed by (backbending of the resonance curve) is attributed by Putterman, Roberts, and Fiszdon 4 to the same nonparabolicity responsible for the mass variation rather than the much weaker pondermotive nonlinearity in the plasma equations. Finally, the cyclotron frequency shifts were shown to be independent of trapping depth 1 so that surface effects (e.g., ripplons) evidently also play no significant role.The structure of the positive ion in 4 He has been qualitatively described by the "snowball" model. 5 " 7 The helium atoms in the core of the ion are believed to form a solid by virtue of the strong electrostrictive attraction to the positive charge. The size of the solid core can be estimated by the location of the distance from t...