Calculation of Intensity Distribution in the Vibrational Structure of Electronic Transitions: The B 3Π+u—X 1Σ+g Resonance Series of Molecular Iodine

Abstract

Franck—Condon overlap integrals have been calculated which predict within experimental error the intensity distribution of the sixty measured lines in the visible fluorescence spectrum of molecular iodine, B ³Π_0⁺u(v′ = 15, 16, or 26)→X ¹Σ_0⁺g(v″ = 0 to 69). Rydberg—Klein—Rees potentials were used for both electronic states, and exact vibrational eigenfunctions were obtained by direct numerical solution of the radial Schrödinger equation, including vibration—rotation interaction. The electronic transition moment was assumed to be independent of internuclear distance. Overlap integrals derived in the same way for Morse potentials fail to give even qualitative agreement with experiment for lines with v″≳10. Because of the rapid oscillation of the vibrational wavefunctions for high v′ and v″, a shift in the potential of only 0.002 Å is found to alter appreciably the calculated intensity distribution; thus the agreement obtained provides a very severe test of the RKR potentials and the Franck—Condon principle. The radiative lifetime of the B state has also been calculated from the absolute intensity of a single line and the integrated intensity of the band system, and the results compare favorably with direct lifetime measurements.