Generalization of the Formalism of Pearson Curves in the Problems of Approximation of Profiles of Continuous Bands in Electronic Spectra of Molecules

摘要

A solution of the differential equation d ln (x) / dx = Pk(x) / Qn(x), where Pk(x) and Qn(x) are poly-nomials of orders k and n, respectively, whose coefficients are expressed in terms of the function (x) as a solution of the system of linear algebraic equations is proposed to be used for the approximation of the profiles of continuous bands of optical electronic transitions of molecules considered as a particular case of the general concept of the probability density function (x). The approach proposed is a generalization of a well-known formalism of the Pearson curves and differs from it in the possibility for successive refinement of the result by way of involving the entire series of moments accessible, as well as the possibility for its application to profiles with a clearly defined structure. The potentials of the new method are studied by using numerical examples.