Knowledge Bank

Integrals necessary for the determination of transition moment matrix elements have been evaluated numerically by use of vibrational wave functions derived from RKR potentials and a power series expansion of the electronic transition moment in terms of a reduced internuclear distance. The significant quantities, which can be related to arbitrary center of expansion, are overlap integrals [Franck-Condon factors] and quantities of the form $\int \psi 1r""dr\int \psi rn-1\psi ""dr$. Experimental band intensities are needed to determine the expansion coefficients. Calculations have been made for ionization from the ground electronic state of CO and for electronic transitions in $CO+$. Some limitations on the use of the r-centroid approximation are examined.