Continuum Shell-Model Calculation forO16

Abstract

The resonance states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ have been calculated within a particle-hole basis using the unified-shell-model approach to reaction theory with a finite Saxon-Woods potential and a zero-range effective interaction. Coulomb wave functions are used for both scattering and bound proton orbitals, so the analog spin quantum number is needed. The resonance states for $J^{\pi }=0^{-},1^{-},2^{-},\mathrm{and} 3^{-}$ are presented together with their analog spin impurity and their neutron and proton widths. Coupling to the single-nucleon continuum states produces a downward energy shift and several instances of analog spin mixing. Two $J^{\pi }=1^{-}$ states at 16.23 and 17.26 MeV exhibit a complete breakdown of analog spin and isospin. The ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma ,p_0){}_{}{}^{15}{}_{}{}^{}\mathrm{N}$ and ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}(\gamma ,n_0){}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ cross sections are calculated using the $K$ matrix of MacDonald and Mekjian. The effects of isospin impurity in resonance states are drastically suppressed in an illustration of the "dynamic criterion" for isospin mixing in resonant amplitudes.