SIMPLE METHOD FOR NONPARAMETRIC ESTIMATION OF THE PROBABILITY DISTRIBUTION FUNCTION OF DIATOMIC-MOLECULES BY ELECTRON-DIFFRACTION

Treating the Debye intensity relationship as a linear Fredholm integral equation of the first kind, a method is developed for a non-parametric estimation of the probability distribution function P/r) for diatomic molecules from electron-diffraction data. Since the problem is an ill-posed one, Tikhonov's regularization procedure was used for the solution. The method was applied to iodine for which the non-parametric P/r) function is obtained. Based on this function the electron-diffraction parameters rg, ra and la are estimated by the linear least-squares method without a priori assumptions about the form of the vibrational potential. Approximating the potential by the Dunham expansion, the parameters re, ωe, K3 and K4 are also estimated. The results are compared with those obtained from conventional analytical representation of an intensity function. Comparison is also made with spectroscopic data for iodine. © 1979.