Photon-Induced Reactions

Abstract

A detailed derivation is given of the Breit-Wigner formula for the case where one particle is a photon. The half-width ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ is found to have all the qualitative properties of a heavy particle half-width: It is proportional to the level spacing $D$ and to $X{P}_{l}(X)$ where $X=\ensuremath{\kappa}R$ and ${P}_{l}$ is the penetration probability for an uncharged particle. ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ also depends explicitly on the details of the many-particle structure of the compound state, so that single-particle estimates of ${\ensuremath{\Gamma}}_{\ensuremath{\gamma}}$ appear to be of limited applicability.The formulas are applied to recent $\ensuremath{\gamma}\ensuremath{-}n$ measurements on ${\mathrm{O}}^{16}$, ${\mathrm{N}}^{14}$, and ${\mathrm{F}}^{19}$. The breaks in the ${\mathrm{O}}^{16}$ excitation curve are due to resonances in ${\mathrm{O}}^{16}$, except for the threshold, which presumably does not represent a resonance. At higher energies the giant $\ensuremath{\gamma}\ensuremath{-}n$ electric dipole resonances are interpreted as indicating a certain "coherence" in the motion of the compound state, classically represented as countercurrent neutrons and protons. It is suggested that a flat shoulder in the excitation curves below the giant resonance may represent incoherent electric dipole excitation rather than coherent magnetic dipole and electric quadrupole excitation. The matrix elements necessary to fit the measured magnitudes are surprisingly large, which suggests that the one-particle wave functions have quite similar shapes in the ground state and in highly excited states.