Differential cross sections for pion-proton bremsstrahlung at 269, 298, and 324 MeV

We present the results of new measurements of pion-proton bremsstrahlung (${\pi }^{+}p\to {\pi }^{+}p\gamma$ and ${\pi }^{-}p\to {\pi }^{-}p\gamma$) at incident kinetic energies of 269 and 324 MeV, together with the final version of our earlier published results at 298 MeV. We have obtained differential cross sections over a wide range of photon angles, at photon energies between 15 and 150 MeV. The differential cross section in all 108 spectra decreases monotonically with increasing photon energy and its gross features agree with the external-emission-dominance calculation. Application of the model of Pascual and Tarrach to our data yields for the magnetic dipole moment of the ${\Delta }^{++}\mathrm{}\left(1232\right)\mathrm{}$ resonance the result $+4.7\mathrm{}{\mu }_N<{{\mu }_{\Delta }}^{++}<6.7\mathrm{} {\mu }_N$, where ${\mu }_N=\frac{e\hslash }{2m_{p}c}$. This agrees with the SU(6) prediction of $+5.6\mathrm{}{\mu }_N$.