Continuum resonance Raman scattering of light by diatomic molecules. II. Theoretical study of the Q branches of Δn=1 profiles of molecular bromine

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Abstract
The methods developed in Part I for the calculation of continuum resonance Raman scattering amplitudes are applied to the calculation of the Q branches of the Δn=1 profiles of Br2 which have been measured by Baierl and Kiefer [J. Raman Spectrosc. 3, 353 (1975)]. The experimental conditions being such as to imply many initial and final rovibrational states, we first of all study the effect of rotation on the scattering amplitudes. It is observed that while the amplitudes may vary substantially with the rotational number of the initial state, almost no effect is introduced by taking into account the changes in rotational quantum numbers which accompany transitions between different electronic states. This is useful to derive an efficient formula for the scattering cross section. The profiles are then calculated with the potentials available for the 1Π1u and B (3Π+0u) excited states which, as shown by previous workers, interfere strongly in producing the spectra. These calculations make it possible to examine the effect of (1) using semiclassical scattering amplitudes rather than the more accurate coupled channel results, (2) using R‐dependent electronic transition moments instead of constant ones, (3) introducing the effect of the angular momentum quantum number J instead of using the amplitudes calculated for J=0, (4) choosing the potentials among those derived from absorption data. The conclusions which emerge from these calculations are that: (a) The semiclassical procedure is fairly accurate. This success indicates that a Raman profile for a giving exciting wavelength represents in fact a very local test (over a range of ∼0.03 Å) of the excited states potentials. Changing the wavelength from 5017 to 4579 Å (two of the lines available from an argon ion laser) amounts to scanning each of the potentials over a region of no more than 0.1 Å; (b) The changes in the scattering amplitudes brought about by the introduction of varying electronic transition moments can be correlated with the values taken by the moments at the radiative crossing points. This is supported both by a detailed analysis of the coupled channel amplitudes and by the form taken by the semiclassical amplitudes; (c) The effect of J on the amplitudes is masked in the profiles as a result of superposition effects; (d) None of the published potentials was able to fit all five profiles. A local downward displacement of the potentials for the 1Π1u and B (3Π+0u) states removes the main unsatisfactory features of the spectra.