Altenative expressions for photoionization cross-sections and dielectric influence functions are suggested to study the photoionization cross-sectlons of atoms in solid system. The basic picture is that the photoionization cross-section of atoms in a real system can be described as the coupling between quantum quantity (QQ) and classical quantity (CQ) parts The QQ pail represents the photoionization cross sections of an i solaled particle, while the CQ part may represent most of the important influence of the macroscopic effects (e.g.. the interactions of all surrounding polarized particles, and the dielectric property. etc.) on the photoionization cross-sections. The applications to the barium system show that tbe number-density-dependent new photoionization formula not only obtains the same cross-sections as those from the first order approximation for ideal gas. but also can generate the cross-sections for solid barium by transforming those of ideal gas of the same species using the dielectric influence function.

The energy-consistent method for calculating accurate potential energy curves of diatomic states is proposed based on a modified Murrel-Sorbie (MS) potential. The accurate vibrational eigenvahues and eigenfunctions for the physical potentials of stable diatomic moleculegs are obtained using this method. The artefact of the MS potential shown in the Huxley-Murrell formulation dissappearss in the present method.

An analytical five-term expansion potential is suggested to improve the recently proposed energy consistent method (ECM) potential based on a three-term expansion [Weiguo Sun, Mol. Phys. 92, 105 (1997) and Weiguo Sun and Hao Feng, J. Phys. B: At., Mol. Opt. Phys. 32, 5109 (1999)]. Applications of the new ECM to the electronic excited state 31Ⅱ of NaK, the excited state 23Σ+g of Na2, and the excited states 31Σ+u 1 and 31Ⅱu of K2 molecules show that the new ECM potential not only agrees excellently with the known Rydberg-Klein-Rees (RKR) data or accurate configuration interaction (CI) studies but also gives the potential data at the molecular asymptote and the dissociation region where experimental and quantum mechanical studies may have difficulties. The new ECM can correct the artifact which appeared in the three-term expansion potentials of both the previous ECM and the Huxley-Murrell-Sorbie (HMS) potential and can describe some states to which both the previous ECM and the HMS fail.

The vibrational excitation differntial coross sections (DCS) of low-energy eleeltron-N2 soattering are studied using vibrational elm-coupling (VCC) scattering method and quantum scattering potentials which include starie, exchange, and polarizatinn contributions hased on ab initio calculation. By including the contributions of 11 partial waves (up to l=21), 15 vibrational states, and 16 molecular symmetries (up to A=7), the converged vibrational excitation (0→2, 0→3, 0→4) DCSs. the scattering resonance, and the vibrational multi-peak structtore agree well with experimenial results.

The calculation of electron-molecule cross sections at scattering energies well below 0.1 eV using conventional algorithms for solving the Schr