Zero-energy π−–D scattering: precise determination of the πN scattering lengths and of the charged coupling constant

Abstract

The recent progress in the study of the pion–nucleus s-wave interaction by the discovery of discrete excited states below the pion threshold in heavy nuclei is reviewed. These states are populated by ( d, 3He ) reactions at bombarding energies of 500–600 MeV, with the 3He observed at forward direction under kinematic conditions, where a large energy (in the order of a pion mass), but only a small momentum is transferred (recoil-free). The resulting distinct pattern of states can be uniquely assigned to deeply bound π− states coupled to well known neutron–hole states with the configurations (nl)π(n′l′j)n−1. With sufficient energy resolution in the ( d, 3He ) spectroscopy it was for the first time possible to determine the excitation energy of each configuration with respect to the ground state of the residual nucleus with A−1 and from this also the binding energy, Bnl, and even the natural width, Γnl, of the pionic state.A summary of the results on binding energies and widths of pionic 1s and 2p states in nuclei with large neutron excesses, such as 207Pb, 205Pb, 123Sn, 119Sn and 115Sn is given. The structure of these states is determined by a superposition of a large repulsive s-wave π−–nucleus interaction and an attractive Coulomb interaction, such that the pions are bound in a potential pocket at the surface of the nuclei, which leads to a halo-like pion distribution around the nucleus. The repulsive s-wave interaction reduces the binding energies of the 1s states in the Pb nuclei by roughly a factor of two and the widths to about 760 keV, which makes them discrete with no overlap to other states. The pion–nucleus interaction has its maximum contribution from an effective density ρe≈0.6ρ0. So it is a sensitive tool to test in-medium effects by comparison with the known s-wave pion–nucleon interaction. An empirical procedure is developed to derive the s-wave pion nucleus potential parameters unambiguously by using only 1s-state binding energies and widths of pionic atoms of light N=Z nuclei as well as of deeply bound pionic 1s states of heavy nuclei with large neutron excesses. The isovector s-wave parameter was deduced as b1=−0.115±0.007mπ−1, which is found to be enhanced over the free πN scattering length (−0.090mπ−1). This result indicates that the order parameter of chiral symmetry breaking, fπ∗(ρ0)2, is reduced by a factor of ∼0.64 in a nucleus with density ρ0=0.17 fm. We also obtained the scaling parameter for the density dependence of the isovector pion–nucleus interaction strength to αρ0∼0.36 in good agreement with theoretical expectations. Thus we find clear evidence for partial chiral symmetry restoration in a nuclear medium.