An inversion procedure for oscillatory continuum spectra: Method and application to NaK

An inversion procedure is developed for determining an attractive potential energy well from the structure of an oscillatory absorption or emission continuum originating in a single vibrational level of that well. It is successfully applied to synthetic data for the 1Π1u←X(1Σ+g) absorption continuum of Br2, and to experimental data for d(3Π1)→a(3Σ+) emission of NaK. The latter application succeeds in spite of the facts that (i) the repulsive wall of the final-state potential is also not known, and (ii) this final-state curve has an attractive well whose location causes the structured emission continuum to be truncated, making the vibrational assignment uncertain. This analysis yields potentials for the well of the d(3Π1) state and the repulsive wall of the a(3Σ+) state of NaK, together with the slope of the transition dipole function coupling these two states.