AN EMPIRICAL DIPOLE POLARIZABILITY FOR He FROM A FIT TO SPECTROSCOPIC DATA YIELDING ANALYTIC EMPIRICAL POTENTIALS FOR ALL ISOTOPOLOGUES OF HeH+

Cho, Young-Sang

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https://hdl.handle.net/2142/79340 Copy

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Title

AN EMPIRICAL DIPOLE POLARIZABILITY FOR He FROM A FIT TO SPECTROSCOPIC DATA YIELDING ANALYTIC EMPIRICAL POTENTIALS FOR ALL ISOTOPOLOGUES OF HeH+

Author(s)

Cho, Young-Sang

Contributor(s)

• Dattani, Nikesh S.
• Le Roy, Robert J.

Issue Date

22-Jun-15

Keyword(s)

Mini-symposium: High-Precision Spectroscopy

Abstract

All available spectroscopic data for all stable isotopologues of HeH$^+$ are analyzed with a direct-potential-fit (DPF) procedure that uses least-squares fits to experimental data in order to optimize the parameters defining an analytic potential. Since the coefficient of the leading ($1/r^4$) inverse-power term is $C_4 = alpha^{rm He}/2$, when treated as a free parameter in the fit, it provides an independent empirical estimate of the polarizability of the He atom. The fact that the present model for the long-range behaviour includes accurate theoretical $C_6$, $C_7$ and $C_8$ coefficients (which are held fixed in the fits) should make it possible to obtain a good estimate of this quantity. The Boltzmann constant $k_B$, a fundamental constant that can define temperature, is directly related to the dipole polarizability $alpha$ of a gas by the expression $~{textstyle %%begin{equation} k_B =frac{alpha}{3epsilon_0}left(frac{epsilon_r+2}{epsilon_r-1}right)frac{p}{T} %%end{equation} }~$, %% in which $epsilon_0$ is the permitivity of free space, and $epsilon_r$ is the relative dielectric permitivity at pressure $p$ and temperature $T$. If $k_B$ can be determined with greater precision, it can be used to define temperature based on a fundamental constant, rather than based on the rather arbitrary triple point of water, which is only known to 5 digits of precision. $alpha$ for He is known theoretically to 8 digits of precision, but an empirical value lags behind. This work, examines the question of how precisely $alpha^{rm He}$ can be determined from a DPF to spectroscopic HeH$^+$ data, where the limiting long-range tail of the analytic potential has the correct form implied by Rydberg theory: $alpha^{rm He}/2r^4$. Although the highest observed vibrational level is bound by over 1000 cm$^{-1}$, our current fits determine an empirical $C_4 = alpha^{{rm He}}/2$ with an uncertainty of only 0.6%. It has been shown that with more precise spectroscopic data near the dissociation, $alpha^{{rm He}}$ can be determined with high enough precision to determine a more precise $k_B$ and hence redefine temperature more accuratelyfootnote{Dattani N S. & Puchalski M. (2015) textit{Physical Review Letters} (in press)}.

Publisher

International Symposium on Molecular Spectroscopy

Type of Resource

text

Language

English

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http://hdl.handle.net/2142/79340

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