DIRECT POTENTIAL FITTING FOR THE $A\,^3\Pi_{1u}$ and $X\,^1\Sigma^+_g$ STATES OF ${\rm Br_2}$

Abstract

Bromine dimer has been studied by many researchers in various wavelength regions. The $A\,^3\Pi_{1u}$ and $X\,^1\Sigma^+_g$ states have been well observed using magnetic rotation spectroscopy, by laser-induced fluorescence,, J.~Mol.~Spectrosc.\ 200, 104 (2000).}$^,$, to be published.} by laser absorption,, Columbus Meeting, paper WH02 (2005).} by Fourier transform absorption,, J.\ Physique, 48, 1685 (1987).} and by UV emission., J.~Mol.~Spectrosc.\ 96, 247 (1982).}~ This yields a data set consisting of 16916 transitions in which the observed vibrational levels for the $X\,^1\Sigma^+_g$ and $A\,^3\Pi_{1u}$ states span 83\% and 99\% of the potential well depths, respectively, with the highest observed vibrational level of the $A\,^3\Pi_{1u}$ state lying only 2 cm$^{-1}$ below the dissociation limit.$^a$ In order to provide the most compact and comprehensive description of these data, and the ability to make reliable predictions outside their range, we have chosen to perform a "direct potential fit'' (DPF), rather than a conventional Dunham-expansion analysis. In particular, accurate analytic potential energy functions for the $A\,^3\Pi_{1u}$ and $X\,^1\Sigma^+_g$ states are determined from a combined-isotopologue DPF analysis that also yields the electronic isotope shift, the $\Omega$-doubling radial strength function, and an experimental value for the long-range inverse-power $C_5$ constant of the $A\,^3\Pi_{1u}$ state, as well as centrifugal Born-Oppenheimer Breakdown (BOB) functions for both states. To reveal characteristics of the $A\,^3\Pi_{1u}$ state, band constants calculated from these potentials are compared with those determined from a conventional parameter-fitting analysis reported by Coxon.