The pion-nucleon bremsstrahlung $\pi+N\Longrightarrow\gamma'+\pi'+N'$ is studied in a new form of current conservation. According to this condition, the internal and external particle radiation parts of the $\pi N$ radiation amplitude have opposite signs, i.e., they contain terms which must cancel each other. Therefore, one has a screening of the internal and external particle radiation in the $\pi N$ bremsstrahlung. In particular, it is shown that the double $\Delta$ exchange diagram with the $\Delta-\gamma' \Delta'$ vertex cancel against the appropriate longitudinal part of the external particle radiation diagrams. Consequently, a model independent relation between the magnetic dipole moments of the $\Delta^+$ and $\Delta^{ ++}$ resonances and the anomalous magnetic moment of the proton $\mu_p$ is obtained, where $\mu_{ \Delta}$ is expressed by $\mu_p$ as $\mu_{ \Delta^+}={ { M_{ \Delta}}\over { m_p}} \mu_p$ and $\mu_{ \Delta^{ ++}}={ 3\over 2}\mu_{ \Delta^+}$ in agreement with the values extracted from the fit for the experimental cross section of the $\pi^+ p\to\gamma'\pi^+ p$ reaction.
Categories: nucl-th hep-ph