[en] The physical process responsible for near UV photoabsorption by the Kr*₂ excimer are examined and the energy dependence of the photoabsorption cross sections is calculated. Near UV photoabsorption by the Kr*₂ is a multiprocess phenomenon involving direct photoionization and concurrent photoexcitation to a repulsive resonance state, which subsequently autoionizes or dissociates. An adiabatic nuclei theory is developed, based on the use of Feshbach projection operators, to separate the ionization and dissociation channels, and to device photoionization and photodissociation cross sections. These cross sections are expressed in terms of parameters obtained from fixed nuclei electronic calculations and in terms wavefunctions describing nuclear motion. Stieltjes Tchebycheff Moment Theory (STMT) techniques are used to extract information concerning the ionization continuum from localized L² electronic wavefunctions obtained from molecular electronic structure codes. Problems in the application of STMT techniques to narrow spectral features are examined. The cause of these problems is determined to be the use of the histogram midpoint approximation in low order STMT quadratures. Techniques are then developed which significantly improve the accuracy of STMT calculations for an isolated, narrow, resonance in a single continuum. Improved treatment of resonance profiles is demonstrated for pure Fano profiles, a shape resonance in a model barrier-and-well potential, and a shape resonance in the K-shell photoionization spectrum of N₂. The improved STMT techniques are then used to obtain the fixed nuclei resonance profiles in the spectrum of Kr₂