This paper studies full vibrational spectra {Ev} and molecular dissociation energies De by using conventional least-squares （LS） fitting and an algebraic method （AM） proposed recently for 10 diatomic electronic states of ^7Li2, Na2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset [Ev^expt] respectively. Studies show that： （1） although both the full AM spectrum {Ev^AM} and the LS spectrum {Ev^LS} can reproduce the known experimental energies in [Ev^expt], the {EAM} is superior to the {Ev^LS} in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in {Ev^LS}, and so is the AM dissociation energy De^AM; （2） the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.
This paper introduces a correlation-polarization potential with high order terms for vibrational excitation in electron-molecule scattering. The new polarization potential generalizes the two-term approximation so that it can better reflect the dependence of correlation and polarization effects on the position coordinate of the scattering electron. It applies the new potential on the vibrational excitation scattering from N2 in an energy range which includes the ^2Ⅱg shape resonance. The good agreement of theoretical resonant peaks with experiments shows that polarization potentials with high order terms are important and should be included in vibrational excitation scattering.
