Quantum Second Virial Coefficient Calculation for the4He Dimer on a Recent Potential

Éderson D'Martin Costa,Nelson H T Lemes,Márcio O Alves,João P Braga,Rita C O Sebastião

doi:10.5935/0103-5053.20130046

Abstract

This paper focuses on the calculation of the quantum second virial coefficient, under a recently developed potential. This coefficient was determined to within 4-5 significant figures in the temperature range from 3 to 100 K. Our results are within experimental error. The three contributions to the overall value of the coefficient are the quantum scattering (continuum state contribution), the bound state (discrete state contribution) and the quantum ideal gas; we discuss these contributions separately. The most significant contribution is from the scattering states, whereas the smaller contributions are from the discrete states. A sensitivity analysis was performed as a function of temperature for one parameter in the short-range region of the potential and for three parameters in the long-range regions of the potential. For both temperatures considered, 10 and 100 K, the C6 dispersion coefficient was the most significant, and the C10 dispersion term was the least significant to the overall result. In general, the precision required to describe the potential decays as the temperature increases. The overall accuracy and the relationship of the parameters to the experimental errors are discussed.

Highlights

A quantum second virial coefficient calculation provides important information that is necessary for analyzing model potentials, for this calculation involves low temperature data.[1]
A study of this recent potential was conducted using second virial coefficient data at low temperature.The quantum virial coefficient can be determined by evaluating the quantum ideal gas term, the scattering phase shift dependence on angular momentum[22,23,24,25,26,27,28,29] and the bound states by Levinson’s theorem.[25,26]
Guided by the experimental error of 0.6 cm[3] mol–1 for lower temperatures, one may conclude that the potential used in the present calculation is appropriate in this temperature range.[8,38]

Summary

Introduction

A quantum second virial coefficient calculation provides important information that is necessary for analyzing model potentials, for this calculation involves low temperature data.[1]. A quantum second virial coefficient calculation provides important information that is necessary for analyzing model potentials, for this calculation involves low temperature data.[1] These potential energy function can be obtained by a direct procedure, such as fitting parameters to experimental data, or, by

Results

Conclusion