Quantum second virial coefficient calculation for the 4He dimer on a recent potential

Abstract

Este trabalho concentra-se no cálculo do segundo coeficiente virial quântico, a partir de um potencial desenvolvido recentemente. Este coeficiente foi determinado com 4-5 algarismos significativos na faixa de temperatura de 3 a 100 K. Nossos resultados estão dentro do erro experimental. Três contribuições para o valor total deste coeficiente são o espalhamento quântico (contribuição de estados no contínuo), o estado ligado (contribuição de estados discretos) e o gás ideal quântico; discutimos estas contribuições separadamente. A contribuição mais importante é do espalhamento quântico, enquanto que as contribuições menores são dos estados discretos. Uma análise da sensibilidade foi realizada em função da temperatura para um parâmetro na região de curto alcance do potencial e para três parâmetros na região de longo alcance do potencial. Para ambas as temperaturas consideradas, 10 e 100 K, o coeficiente de dispersão C 6 foi o mais significativo, e o termo dispersão C 10 foi o menos significativo para o resultado total. Em geral, a precisão exigida para descrever os potenciais diminui com o aumento da temperatura. A precisão total e a relação dos parâmetros com os erros experimentais são discutidas. 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 C 6 dispersion coefficient was the most significant, and the C 10 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.

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

“…The average difference between both is less than 2.6 % between 3 and 4Å, with an even smaller difference in the potential depth, -11.1 K against -11.0 K. The potential depth is important result, which shows that there is excellent agreement with a bound state prediction of the 4 He dimer. [7] The refined potential describes the viscosity coefficient with an average error of 1.6823 % that is less than the experimental error (5 %), a result similar to that found for the ab initio potential (1.1173 %).…”

“…[7] When this potential is compared with the most accurate potential describing the system, [9] the difference is less than 22.4 µeV, between 2.4 and 4.5Å. Nevertheless, both curves, Varandas [8] and Przybytek et al [9], describe the viscosity coefficient with an error less than 5 % for temperatures between 1 and 5 K.…”

“…[6] The theoretical interpretation of the results has been performed with the ab initio potential function. [7] The helium dimer has a very small potential well depth, measuring approximately 11 K, [8,9] consequently, highly accurate calculations are required to obtain the potential energy function. [8,9] The present paper presents an alternative way to refine the helium potential energy function from viscosity coefficient data at low temperatures.…”