Electromagnetic Decays of Baryon Resonances in the Symmetric Quark Model

We study the radiative decays of the $D_{13}\mathrm{}\left(1515\right)\mathrm{}$, $S_{11}\mathrm{}\left(1525\right)\mathrm{}$, $F_{15}\mathrm{}\left(1690\right)\mathrm{}$, and ${Y_0}^{*}\mathrm{}\left(1520\right)\mathrm{}$ resonances within the framework of the symmetric quark model with harmonic-oscillator wave functions. We point out that if it is assumed that the quarks have large anomalous magnetic moments, then it becomes necessary to consider the so-called "spin-orbit" term in the nonrelativistic electromagnetic interaction Hamiltonian. Including the effect of this term, we show that it is possible to understand the vanishing contribution of the $D_{13}\mathrm{}\left(1515\right)\mathrm{}$ resonance to backward or forward pion photoproduction in terms of a cancellation between electric and magnetic multipoles. Requiring such a cancellation gives a value of the oscillator range parameter, $\alpha =105\mathrm{}$ MeV. Using this value and assuming that the quark scale magnetic moment $\mu$ is equal to the proton moment, we calculate the multipole amplitudes involved in the decays of interest, and compare the results for the $D_{15}\mathrm{}\left(1515\right)\mathrm{}$ and $S_{11}\mathrm{}\left(1525\right)\mathrm{}$ resonances with the recent phenomenological multipole analysis by Chau, Dombey, and Moorhouse of pion photoproduction in the second resonance region. Agreement is reasonably good. For the ${Y_0}^{*}\mathrm{}\left(1520\right)\mathrm{}$ we obtain a radiative width ${\Gamma }_{\gamma }=0.051\mathrm{}$ MeV to be compared with a recent experimental result ${\Gamma }_{\gamma }=0.15\mathrm{}\pm 0.03$ MeV, and an angular distribution compatible with experimen t. We comment on the contribution of the $F_{15}\mathrm{}\left(1690\right)\mathrm{}$ resonance to pion photoproduction.