Analytic potentials and vibrational energies for Li₂ states dissociating to mbox{Li}left\(2Sright\)+mbox{Li}left\(3Pright\). Part 1: The ^2S+1Π_u/g states

Analytic potentials are built for all four ^2S+1Π_u/g states of Li₂ dissociating to Li(2S) + Li(3P): 3b\(3³Π_u\), 3B\(3¹Π_u\), 3C\(3¹Π_g\), and 3d\(3³Π_g\). 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 ^6,6Li₂, ^6,7Li₂, ^7,7Li₂, and the elusive `halo nucleonic molecule' ^11,11Li₂. 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 long-range 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.