Analytic potentials and vibrational energies for Li$_{2}$ states dissociating to $\mbox{Li}\left(2S\right)+\mbox{Li}\left(3P\right)$. Part 1: The $^{2S+1}Π_{u/g}$ states

Abstract

Analytic potentials are built for all four 2S+1 Π u/g states of Li2 dissociating to Li(2S) + Li(3P ): 3b(3 3 Πu), 3B(3 1 Πu), 3C(3 1 Πg), and 3d(3 3 Πg). These potentials include the effect of spin-orbit coupling for large internuclear distances, and include state of the art long-range constants. This is the first successful demonstration of fully analytic diatomic potentials that capture features that are usually considered too difficult to capture without a point-wise potential, such as multiple minima, and shelves. Vibrational energies for each potential are presented for the isotopologues 6,6 Li2, 6,7 Li2, 7,7 Li2, and the elusive 'halo nucleonic molecule' 11,11 Li2. These energies are claimed to be accurate enough for new high-precision experimental setups such as the one presented in [Sebastian et al. Phys. Rev. A, 90, 033417 (2014)] to measure and assign energy levels of these electronic states, all of which have not yet been explored in the long-range region. Measuring energies in the longrange region of these electronic states may be significant for studying the ab initio vs experiment discrepancy discussed in [Tang et al. Phys. Rev. A, 84, 052502 (2014)] for the C3 long-range constant of Lithium, which has significance for improving the SI definition of the second.

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“…The point-wise potential is then subjected to spline interpolation. Nowadays many extremely accurate potentials are available in analytic form, − due to meticulous fitting to high-precision spectroscopic experiments, that represent a better alternative to the spline interpolation. One has to also be extremely careful with splines, particularly with spacing between the points that are provided for interpolation, because it is very easy to obtain spurious extrema or wiggles when doing spline interpolation.…”