Relaxation time and effective mass of ions in liquid helium

Abstract

A measurement of momentum relaxation times for charged particles in liquid helium is reported. The method is to measure the change in the reflection coefficient of a microwave cavity caused by the admission of ions. The measured relaxation times can be combined with the known dc mobilities of the ions to yield values for the effective masses. Most extensive measurements were performed using positive ions in He II. A temperature-dependent effective mass, increasing from approximately 40 helium masses at 1.3 K to over twice this value near the lambda point is found. The data are shown to be consistent with the electrostriction model of the ion, including contributions to the mass from both normal and superfluid components. A core radius of approximately 6 Å is shown to account both for the mass and for the mobility in the viscous flow region. Data on the negative carrier near 1.8 K yield an effective mass of 100 to 200 helium masses, and are consistent with the bubble model. The radius implied both by the mass and an analysis of mobility data in the viscous flow regime is 14±3 Å, quite consistent with the value deduced from other measurements. A measurement on the positive carrier in saturated (NBP) helium vapor indicates a mass of 75±20 helium masses. Both the mass and the mobility of this carrier are consistent with a droplet of radius 11±2 Å forming on the ion. The theoretical droplet radius is 12.6 Å.