Pion electroproduction off 3He and self energies of the pion and the Δ isobar in the medium

The differential coincident pion electroproduction cross section of the 3He(e,e'π+)3H reaction in the excitation region of the Δ resonance has been measured with the high resolution three-spectrometer facility at the Mainz Microtron MAMI. It was the aim of the experiment to study the influence of the nuclear medium on the properties of the pion and the Δ(1232) resonance. Two experimental methods have been applied. For fixed four-momentum transfers Q2=0.045 [0.100] (GeV/c)2 with the pions detected in parallel kinematics, the incident energy was varied between 555 and 855 MeV in order to separate the longitudinal (L) and transverse (T) structure functions. In the second case the emitted pions with respect to the momentum transfer direction were detected over a large angular range at fixed incident energy E0=855 MeV and the two fixed four-momentum transfers. From the angular distributions the LT interference term has been extracted. The experimental data are compared to model calculations which are based on the elementary pion production amplitude that contains besides the Born terms also the excitation of the Δ and higher resonances. Moreover, three-body Faddeev wave functions are used and the final state interaction of the outgoing pion is taken into account. The experimental cross sections are reproduced only after additional medium modifications of the pion and the Δ isobar have been considered in terms of self energies. In the framework of Chiral Perturbation Theory the pion self energy is related to a reduction of the π+ mass of Δmπ+=(-1.7-2.1+1.7) MeV/c2 in the neutron-rich nuclear medium at a density of ρ=(0.057-0.057+0.085) fm-3. This result is fully consistent with the one obtained within a two-loop approximation of ChPT. It is also interesting to compare the determined negative mass shift Δmπ+ with a positive mass shift Δmπ- of 23 to 27 MeV/c2 derived recently from deeply bound pionic states in 207Pb and 205Pb. Both pion mass shifts observed in complementary approaches may be understood within the Tomozawa-Weinberg scheme of isovector dominance of the πN interaction, which provides a strong guidance for the understanding of the pion modifications in the nuclear medium. The Δ self energy as extracted from previous data of π0 photoproduction from 4He is compatible with the results of the present experiment. Subsequently, the mass and the decay width of the Δ resonance in the nuclear medium are increased by ΔMΔ=(40-50) MeV/c2 and ΔΓΔ=(60-70) MeV in the considered kinematical region. (author)