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.