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The Journal of Chemical Physics

An accurate potential model for the a3Σu+ state of the alkali dimers Na2, K2, Rb2, and Cs2

Jascha A. Lau, Jan Peter Toennies, Kwong Tin Tang

Published Nov 21, 2016• 13 citations
Publisher

Abstract

A modified semi-empirical Tang-Toennies potential model is used to describe the a3Σu+ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth De, well location Re, and the harmonic vibrational frequency ωe of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na2, K2, Rb2, and Cs2, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li2 and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li2 less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.

DOI
10.1063/1.4967333

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The Journal of Chemical Physics•Sep 12, 2017•18 citations
A modified semi-empirical Tang-Toennies potential model is used to describe the a3Σu+ potentials of the alkali dimers. These potentials are currently of interest in connection with the laser manipulation of the ultracold alkali gases. The fully analytical model is based on three experimental parameters, the well depth De, well location Re, and the harmonic vibrational frequency ωe of which the latter is only slightly optimized within the range of the literature values. Comparison with the latest spectroscopic data shows good agreement for Na2, K2, Rb2, and Cs2, comparable to that found with published potential models with up to 55 parameters. The differences between the reduced potential of Li2 and the conformal reduced potentials of the heavier dimers are analyzed together with why the model describes Li2 less accurately. The new model potential provides a test of the principle of corresponding states and an excellent first order approximation for further optimization to improve the fits to the spectroscopic data and describe the scattering lengths and Feshbach resonances at ultra-low temperatures.
A new four parameter Tang-Toennies type potential model is described for the a 3Σu+ triplet state of the alkali dimers Na2, K2, Rb2, and Cs2. Compared to an earlier three parameter semi-empirical model based on the experimental well depth, De, well location, Re, and the harmonic vibrational frequency, ωe [Lau et al., J. Chem. Phys. 145, 194308 (2016)], the new model is also adjusted to be consistent with the scattering length. The results are shown to have a similar good agreement with the spectroscopic term values as the earlier model with the advantage that the scattering length is properly described. The deviations from recent potentials for Cs2 are discussed.
Abstract Heteronuclear lithium-containing alkali dimers in their ground triplet state offer both electric and magnetic dipole moments, which arise from their unpaired electron distributions and make them suitable for exploring many-body quantum phenomena. Currently, no simple yet accurate analytical form exists to model the triplet interaction potentials of heavier Li-alkali pairs such as LiK, LiRb and LiCs. The Sheng-Tang–Toennies(STT) potential, containing merely two fitting parameters, has earlier successfully reproduced the lowest triplet potential curve of Li 2 and LiNa. In this work, we extend its application to predict the a 3 Σ + state interactions for the three dimers LiK, LiRb, and LiCs. The derived analytical potentials agree closely with high-level a b i n i t i o benchmarks and existing spectroscopic measurements over the complete range of internuclear separations. Our findings verify the robustness and portability of the STT model for representing triplet state potentials across heteronuclear alkali dimers that include lithium.
The Morse/Long Range (MLR) potential has become one of the most reliable and highly \nused potential energy functions for diatomic molecules. It includes the theoretical long range \nbehaviour that diatomic molecules are known to exhibit as they approach the dissociation \nlimit. Heavy alkali metals with adjacent electronic states often exhibit strong coupling \nbetween the spin and orbital angular momentum. The ground state X¹Σg⁺ and the lowest \nlying triplet state aᶟΣᵤ⁺ of Cs₂ exhibit such coupling effects and as a result, modeling the \nhighest vibrational states of these states is a non-trivial problem. Utilizing scattering length \nvalues obtained from published analysis of 60 Feshbach resonances, the correct form of the \npotential energy function was determined. Moreover, the scattering length values were used \nto determine the correct leading dispersion coefficient that describes the true form of the \nlong-range potential energy functions. All previous attempts to determine global potential \nenergy functions for these states have considered only the optical spectroscopic data. This is \nthe first ever effort attempting to use scattering lengths determined from cold atom collision \nexperiments in a combined analysis with conventional spectroscopic data.
A semiempirical potential energy curve for the a3Σ+-state of the KRb molecule with only five parameters is reported. The potential is continuous over the entire range of internuclear distances and has the correct long-range attractive dispersion potential from established theory. The potential provides an equally good fit of the laser induced fluorescence Fourier transform spectroscopic data of Pashov et al. [Phys. Rev. A 76, 022511 (2007)] as their multi-parameter potential. The new potential is supported by the good agreement of the well parameters De, Re and the harmonic vibrational constant ωe with combining-rule estimates. The scattering lengths for all six isotopologues are also in excellent agreement with experiment with a 0.2% adjustment within theoretical uncertainty of the leading dispersion coefficient C6. An analysis of the harmonic vibrational constant ωe and the constant ωexe of the potential of Pashov et al. reveals a significant difference to the present potential which turned out to be due to an oscillatory deviation in their potential in the vicinity of the potential minimum. The new potential is, thus, the best available because its simplicity is ideal for further applications.
This paper clarifies the disagreement in the depth of the potential energy curve of the cesium dimer singlet ground state which has lasted for nearly a decade. We point out that the origin of this disagreement must be a technical misprint in the values of the three binding energies reported by Danzl et al. [Science 321, 1062 (2008)], while the X1Σg+ state potential reported by Coxon and Hajigeorgiou [J. Chem. Phys. 132, 094105 (2010)], based on experimental data by Amiot and Dulieu [J. Chem. Phys. 117, 5155 (2002)], is quite correct. We have recalculated the potential energy function of the triplet ground state a3Σu+ by using the available experimental data spanning both the attractive and the repulsive branches so that the potential energy function complies asymptotically with the singlet ground state X1Σg+ potential energy function by Coxon and Hajigeorgiou. This is important for the simulation of the near dissociation properties such as Feshbach resonances, which are typically observed in modern experiments with ultracold atoms and molecules.