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Physical Chemistry Chemical Physics

Full-range analytical potential for the a 3 Σ + state of LiNa: robust prediction of vibrational levels and scattering length

Dongying Li, Xiaowei Sheng

Published Jan 1, 2026• 1 citation
Publisher

Abstract

-wave scattering length was calculated as -71.28 a.u., consistent with experimental bounds (-76 ± 5 a.u.). This work demonstrates that the STT model is effective for modeling the PEC of heteronuclear alkali dimers involving a Li atom.
DOI
10.1039/d5cp04966k

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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.
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.
The scattering lengths that characterize the low-energy elastic scattering of 23 Na atoms by 39 K, 40 K and 41 K atoms, when they interact via the X 1 Σ + and a 3 Σ + states of the NaK dimer, are calculated. The systematic variation of the short- and long-range parts of the interaction potentials reveals that the calculated scattering lengths are sensitive to uncertainties in the potentials. It is concluded that precise spectroscopic measurements of the least-bound ro-vibrational levels supported by the ground electronic state, which would reduce the uncertainties in both the molecular potentials, are needed for an accurate determination of the scattering lengths.
Ultracold collisional interactions are crucial to both the dynamical evolution and the steady-state behavior of systems designed to observe Bose-Einstein condensation, and are relevant to the advances in high precision measurements, and the creation of more highly accurate atomic clocks based on laser-cooled neutral atoms. An important parameter for understanding these collisions is the s-wave scattering length {alpha}, which can be determined from accurate knowledge of the two-body interaction potential. Photoassociation of ultracold lithium atoms into bound vibrational levels of the A{sup 1}{Sigma}{sub u}{sup +} excited state is used to probe the X{sup 1}{Sigma}{sub g}{sup +} ground state interaction potential of {sup 6}Li{sub 2} and {sup 7}Li{sub 2}. It had been predicted that the s-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive scattering length. The authors present the observation of this novel effect, and use the location of the minimum to precisely determine the singlet s-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the scattering lengths for collisions involving {sup 7}Li atoms in different hyperfine states.
Photoassociation of ultracold lithium atoms into bound vibrational levels of the $A^{1}\ensuremath{\Sigma}_{u}^{+}$ excited state is used to probe the $X^{1}\ensuremath{\Sigma}_{g}^{+}$ ground-state interaction potential of 6Li2^{6}\mathrm{Li}_{2}6Li2​ and 7Li2^{7}\mathrm{Li}_{2}7Li2​. It had been predicted that the sss-wave photoassociation signal strength would pass through a minimum as a function of vibrational level for positive sss-wave scattering length. We report the observation of this novel effect, and use the location of the minimum to precisely determine the singlet sss-wave scattering length for both isotopes. The sensitivity of this technique is demonstrated by distinguishing the minima for collisions involving 7Li^{7}\mathrm{Li}7Li atoms in different hyperfine states.
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.