Electromagnetic Decays of Baryon Resonances in the Harmonic-Oscillator Model

Abstract

The harmonic-oscillator model for baryons is used to estimate the radiative widths of the observed $N^{*}$ resonances. In the "second resonance region" of pion photoproduction, both the $S_{11}\mathrm{}\left(1550\right)\mathrm{}$ and $D_{13}\mathrm{}\left(1525\right)\mathrm{}$ resonances [and possibly the $P_{11}\mathrm{}\left(1470\right)\mathrm{}$, depending on what should be taken as its $N\pi$ width] are expected to be important, while in the "third resonance region" $F_{15}\mathrm{}\left(1690\right)\mathrm{}$, $S_{11}\mathrm{}\left(1710\right)\mathrm{}$, and $D_{13}\mathrm{}\left(1690\right)\mathrm{}$ are expected to have comparable contributions. The mixing angle between the two $S_{11}$ resonances is determined to be about 35°. In inelastic electron scattering $\mathrm{ep}\to e{N}^{*}$, the $S_{11}\mathrm{}\left(1550\right)\mathrm{}$ and $D_{13}\mathrm{}\left(1525\right)\mathrm{}$ resonances are expected to dominate over the $P_{11}\mathrm{}\left(1470\right)\mathrm{}$. The neutral $P_{11}\mathrm{}\left(1470\right)\mathrm{}$ radiative width is found to be smaller than the charged width, in contrast to an $\mathrm{SU}\left(3\right)\mathrm{}$ $\overline{1}\overline{0}$ assignment for this resonance.