Optical-model analysis of twoρ0-photoproduction experiments

Abstract

An optical-model analysis of two important experiments measuring ${\ensuremath{\rho}}^{0}$ photoproduction on complex nuclei is presented. In an effort to determine ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$, the ${\ensuremath{\rho}}^{0}$-nucleon total cross section, and ${\ensuremath{\alpha}}_{\ensuremath{\rho}}$, the ratio of the real to the imaginary part of the ${\ensuremath{\rho}}^{0}$-nucleon forward elastic scattering amplitude, the best normalization of the theory to the experimental data is determined for many pairs of values of these parameters. It is concluded that uncertainties in the theory make it impossible to determine ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ and ${\ensuremath{\alpha}}_{\ensuremath{\rho}}$ uniquely, but that if one is taken as known, the other can be determined well; and the two experiments give approximately the same relationship between ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ and ${\ensuremath{\alpha}}_{\ensuremath{\rho}}$. If ${\ensuremath{\alpha}}_{\ensuremath{\rho}}$ is taken to be \ensuremath{\sim} -0.2, ${\ensuremath{\sigma}}_{\ensuremath{\rho}}\ensuremath{\approx}27$ mb is obtained, consistent with older analyses. Some attention is also focused on ${|{f}_{0}|}^{2}$, the forward differential cross section for ${\ensuremath{\rho}}^{0}$ photoproduction on one nucleon, and the closely related parameter $\frac{{{\ensuremath{\gamma}}_{\ensuremath{\rho}}}^{2}}{4\ensuremath{\pi}}$. These quantities are somewhat uncertain, however, because of theoretical ambiguities in determining the normalization of the experimental cross sections. Various uncertainties in the optical model are discussed, and it is concluded that they may make small numerical changes in the results but do not affect the qualitative picture.