The Resolution of Laser-Induced Europium(III) Ion Excitation Spectra through the Use of the Marquardt Nonlinear Regression Method

Abstract

The ability to resolve a7F0→5D0spectrum into individual peaks is important in the study of Eu(III) complexes where the wavelength of the transition is sensitive to the environment of the ion. This paper describes a computer program, based upon the Marquardt nonlinear regression algorithm, developed to resolve such spectra. Several different line shapes were examined, with the Lorentzian function providing the most accurate description for solid complexes and the Lorentzian-Gaussian product function being the most acceptable for species in solution. The program can resolve a spectrum into as many as five peaks with the option to hold any of the parameters constant. The best fit is determined by evaluation of the sum of the squares of the differences between the calculated and the experimental values.