In a kinematically complete experiment at the Mainz microtron MAMI, pion angular distributions of the $^3$He(e,e'$\pi^+)^3$H reaction have been measured in the excitation region of the $\Delta$ resonance to determine the longitudinal ($L$), transverse ($T$), and the $LT$ interference part of the differential cross section. The data are described only after introducing self-energy modifications of the pion and $\Delta$-isobar propagators. Using Chiral Perturbation Theory (ChPT) to extrapolate the pion self energy as inferred from the measurement on the mass shell, we deduce a reduction of the $\pi^+$ mass of $\Delta m_{ \pi^+} = (-1.7^{ + 1.7}_{ - 2.1})$ MeV/c$^2$ in the neutron-rich nuclear medium at a density of $\rho = (0.057^{ + 0.085}_{ - 0.057})$ fm$^{ -3}$. Our data are consistent with the $\Delta$ self energy determined from measurements of $\pi^0$ photoproduction from $^4$He and heavier nuclei.
Categories: nucl-ex