Calculation of Nuclear Reactions inO16in the Random-Phase Approximation

We present a practical formalism of low-energy nuclear reactions in which the ground-state correlations are treated in the random-phase approximation. The building blocks of the method are the matrix elements of two weakly energy-dependent effective interactions describing particle-hole pair scattering and pair creation or annnihilation in a correlated system. The corresponding transition operators, which give complete information on any nuclear reaction, are then introduced. We apply the method to a study of nucleon scattering, photonuclear, muonuclear reactions proceeding through the $1^{-}$ states of ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$. The single-particle basis states are generated by a local, real Woods-Saxon potential, while the residual interaction has a zero range. In the relatively high excitation energy being studied, the correlations retained in the random-phase approximation affect very little nucleon scattering but reduce transition rates in photonuclear reactions and muon capture by about 8%.