The inverse processes of photoionization and electron-ion recombination for hv + N v <-> N VI + e, hv + N VI <-> N VII + e, hv + F VII <-> F + e, and hv + F VIII <-> F IX + e are studied in detail using a self-consistent unified method for the total electron-ion recombination. The method enables calculation of the total and level-specific recombination rate coefficients alpha(R) and alpha(R)(i), subsuming both radiative and dielectronic recombination (RR and DR). The photoionization and recombination cross sections sigma(PI) and sigma(RC) are computed using an identical wave function expansion for both processes in the close coupling approximation using the R-matrix method. The results include total and partial photoionization cross sections and recombination rate coefficients for all fine-structure levels up to n <= 10, about 100 for Li-like N V and F VII with 1/2 <= J <= 17/2, and over 170 for He-like N VI and F VIII with 0 <= J <= 10. Level-specific sigma(PI)(nSLJ) and alpha(R)(T; nSLJ) are calculated for the first time for these ions. The coupled-channel wave function expansions for N V and F VII consist of 17 levels of cores N VI and F VIII, respectively, and for N vi and F VIII consist of 16 levels of cores N VII and F IX, respectively. Relativistic fine structure is considered through the Breit-Pauli R-matrix method. The single-valued total alpha(R)(T) is presented over an extended temperature range for astrophysical and laboratory plasma applications. Although the total unified alpha R(T) for all ions agree well with the available published RR+DR rates, significant differences are noted at the DR peak for N v. Total sigma(RC)(E) and alpha(R)(E) as functions of photoelectron energy are presented for comparison with experiments. Total rates for H-like N VIIi and F IX are also given for completeness. The cross sections sigma(PI) and alpha(RC) include important atomic effects such as radiation damping, channel couplings, and interference of DR and RR, and should be accurate to within 10% - 15%. The comprehensive data sets are applicable for ionization balance and recombination-cascade models for UV and X-ray lines.
