A DPF analysis yields accurate analytic potentials for Li${}_2(a{}^3{\Sigma }_u^{+})$ and Li${}_2(1{}^3{\Sigma }_g^{+})$ that incorporate 3-state mixing near the $1{}^3{\Sigma }_g^{+}$-state asymptote

Abstract

A combined-isotopologue direct-potential-fit (DPF) analysis of optical and photoassociation spectroscopy data for the $a{}^3{\Sigma }_u^{+}$ and $1{}^3{\Sigma }_g^{+}$ states of Li${}_2$ has yielded accurate analytic potential energy functions for both states. The recommended M3LR${}_{5,3}^{8.0}(3)$ potential for the $a{}^3{\Sigma }_u^{+}$ of ${}^{7,7}$Li${}_2$ has a well depth of ${\mathfrak{D}}_e=333.758(7)\mathrm{c}{\mathrm{m}}^{-1}$ and equilibrium distance of $r_e=4.17005(3)$Å, and the associated scattering lengths are $a_{\mathrm{SL}}=-14.759(9)$Å for ${}^{7,7}$Li${}_2$ and $-1906(50)$Å for ${}^{6,6}$Li${}_2$. For the $1{}^3{\Sigma }_g^{+}$ state, in spite of a gap of $\sim 5200{\mathrm{cm}}^{-1}$ (from $v(1{}^3{\Sigma }_g^{+})=8-61$) for which there are no data, the DPF procedure has no difficulty determining an accurate overall potential. The $1{}^3{\Sigma }_g^{+}$ state of the ${}^{7,7}$Li${}_2$ isotopologue has a well depth of ${\mathfrak{D}}_e=7092.417(33)\mathrm{c}{\mathrm{m}}^{-1}$ and equilibrium distance of $r_e=3.06524(9)$Å. The long-range tail of the recommended M3LR${}_{6,3}^{3.6}(9)$ potential energy function for the $1{}^3{\Sigma }_g^{+}$ state is defined by the lowest eigenvalue of a $3\times 3$ long-range interstate coupling matrix to take into account the 3-state mixing near its asymptote.

18 pages, 7 figures

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