Results are presented for the inverse processes of photoionization and electron-ion recombination of (h nu + Ne VIII <-> Ne IX + e) and (h nu + Ne IX <-> Ne x + e) using the self-consistent unified method. The method employs an identical wave function expansion for both photoionization and recombination, and it includes both radiative and dielectronic recombination. Total, as well as level-specific, photoionization cross sections, sigma(PI)(E; nSLJ), and recombination rate coefficients, alpha(R)(T; nSLJ), are presented for all fine-structure levels up to n <= 10. These correspond to a total of 98 bound fine-structure levels of Ne VIII with 1/ 2 <= J <= 17/2, and 178 bound levels of Ne IX with 0 <= J <= 10. Total recombination cross sections and rates as functions of electron energy are also presented. The coupled channel wave function expansions for the core ions include 17 levels of Ne IX and 16 levels of Ne x. Relativistic fine structure is considered through the Breit-Pauli R-matrix (BPRM) method. The photoionization and recombination cross sections include important atomic effects such as radiation damping, channel coupling, and interference and should be of definitive accuracy. Level-specific sigma(PI)(nSLJ) and alpha(R)(T; nSLJ) are calculated for the first time. In addition, we describe the applicability of these comprehensive data sets to not only ionization balance and recombination-cascade models for astrophysical and laboratory plasmas, but also to (1) models of UV and X-ray lines in He-like ions from C v to Ne IX involving the 2 P-3(0,1,2)o -> 2 S-3(1) allowed triplet transitions in the UV, and 2(P-1(1)o; P-3(1,2)o, S-3(1)) -> 1 S-1(0) allowed, inter-combination, and forbidden transitions in the X-ray, and (2) calculation of dielectronic satellite intensities from the highly resolved resonances in the unified recombination cross sections of He-like and Li-like ions through straightforward integration over a Maxwellian or other electron distribution functions.
