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Bosonic cluster effect with helium

PTB measurements with the dielectric-constant gas thermometer as preparation for the Boltzmann Project have confirmed ab-initio theories for the interaction between two helium atoms for the range from 3.7 K to 26 K. At lower temperatures, however, deviations from this are exhibited, which could be explained by a novel bosonic cluster effect.

Cryostatic insert with a dielectric-constant gas thermometer, the core piece of the low temperature experiment for the determination of the gas properties of helium

The principle of dielectric-constant gas thermometry (DCGT) used for the redetermination of the Boltzmann constant is based on the in-situ density determination of helium gas. For that purpose, the relative capacity change of a capacitor filled with helium gas is measured. With a constant temperature and different pressures in the measuring capacitor, the temperature can be determined by means of fundamental relations. A key role in this method is exhibited by the atomic dipole polarizability of the measuring gas helium. For some years now, its value has been known with the necessary relative uncertainty of less than 1 ppm, which makes the DCGT one of the most precise primary thermometers. With it, the Boltzmann constant is to be determined at the triple point of water, in order to enable linking the future definition of the temperature unit to the previous one. In addition to this, the measuring gas is of interest to fundamental research, which concerns the particle interactions, above all, at lower temperatures. Below a certain temperature, helium exhibits particular properties, as, for example, superfluidity (vanishing viscosity, among other things), which cannot be described by the laws of classical physics.

The latest PTB measurements in the range between 3.7 K and 26 K display a nearly perfect agreement of the experimentally determined two-particle interaction with the latest quantum mechanical calculations. In the range from 2.4 K – the lowest temperature open to the experiment – to 3.7 K, the DCGT measurements with the helium-4 isotope show, however, a clear deviation from the temperature and interaction values. This unexpected result can be explained by the formation of bosonic helium-4 clusters in the gas phase, which leads to an increase in the molar polarizability and a change in the particle interaction. In cooperation with theorists of the University of Rostock, an attempt is now being made to obtain a founded theoretical description of the cluster effect and to confirm the assumption that the driving force of this effect is the same as that of superfluidity in the liquid phase.

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