15min:

NIKESH S. DATTANI, Department of Chemistry, Oxford University, Oxford, OX1 3QZ, UK; XUAN LI, Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, 94720-8176, USA.

Recent high-resolution (\pm 0.00002 cm^-1) photo-association spectroscopy (PAS) data of seven previously unexplored vibrational levels of the 1³ _g⁺ state of Li₂ have allowed for the first ever experimental determination of the spin-spin ( _v) and spin-rotation ( _v) coupling constants in a diatomic lithium system. For triplet states of diatomic molecules such as the 1³ _g⁺ state of Li₂, the three spin-spin/spin-rotation resolved energies associated with a ro-vibrational state |v,N\rangle were expressed explicity in terms of B_v, _v, and _v in 1929 by Kramer's first-order formulas and then in 1937 by Schlapp's more refined formulas. Given spectroscopic data, while it has never been difficult to extract _v and _v from Schlapp's formulas, it has been a challenge to reliably predict how accurate these extracted values are. This is for two reasons: (1) the lack of a rigorous method to estimate the uncertainty in B_v, (2) the non-linearity of Schlapp's coupled equations has meant that traditionally they have had to be solved numerically by Newton iterations which makes error propagation difficult. The former challenge has been this year solved by Le Roy with a modification of Hutson's perturbation theory of, and the latter problem has now been solved by symbolic computing software that solves Schlapp's coupled non-linear equations analytically for the first time since their introduction in 1937.