Pionic modes of excitation in nuclei: Inelastic electron and proton scattering to the (1 +, T=1; 15.1 MeV) state in 12C

Abstract

The M1 form factor for the transition into the 15.1 MeV state in 12C is calculated with inclusion of large-space pionic polarisation involving both nucleon- and Δ-hole excitations. The corresponding particle-hole interaction incorporates one- and two-pion-exchange, the latter represented by the relevant ππ → N N helicity amplitude squared, plus additional short range correlations. We find that the non-resonant Born part of two-pion exchange, in addition to ϱ exchange, plays a crucial role to obtain the proper enhancement of the M1 form factor at large q. We conclude that a reduction of the repulsive correlations accompanying OPE to unreasonably small amounts is not required, hence the “critical opalescence” situation is unlikely to be encountered in this process. The excitation of the same state with 800 MeV protons is also investigated, with the aim of obtaining further independent information on a possible amplification of the nuclear pion field at q ∼ 2−3 m π. Measurable enhancement effects are suggested, but a more precise knowledge of the spin-isospin dependent NN amplitudes is required to draw further conclusions.