Accurate potential energy curve for helium dimer retrieved from viscosity coefficient data at very low temperatures

TL;DR

This paper develops a novel method to derive the helium-helium interaction potential directly from low-temperature viscosity data, achieving high accuracy comparable to ab initio calculations.

Contribution

It introduces a robust procedure using sensitivity analysis and quantum theory to extract the long-range potential from experimental viscosity data at very low temperatures.

Findings

Potential describes viscosity with 1.68% average error

Method retrieves potential consistent with ab initio results

Effective at temperatures below 5K for helium dimer

Abstract

The long range potential of helium-helium interaction, which requires accurate 'ab initio' calculation, due to the small value of the potential depth, approximately 11 K (0.091 kJ/mol) at 2.96 angstrom, will be obtained in this study by an alternative technique. This work presents a robust and consistent procedure that provides the long range potential directly from experimental data. However, it is difficult to obtain experimental data containing information regarding such a small potential depth. Thereby, sensitivity analysis will be used to circumvent this difficulty, from which viscosity data at lower temperatures (<5K) were chosen as appropriate data to be used to retrieve the potential function between 3 and 4 angstrom. The linear relationship between the potential energy function and the viscosity coefficient will be established under quantum assumptions and the Bose-Einstein statistic. The use of quantum theory is essential, since the temperatures are below 5K. The potential obtained in this study describes the viscosity with an average error of 1.68% that is less than the experimental error (5%), with the results being similar to those obtained for recent 'ab initio' potentials.