Deeply boundπ−states in207Pbformed in the208Pb(d,3He)reaction. II. Deduced binding energies and widths and the pion-nucleus interaction

We find a remarkable agreement of the excitation energy spectrum of the ${}^{208}\mathrm{Pb}{(d,}^3\mathrm{He})$ reaction measured at $T_d=600\mathrm{}\mathrm{MeV}$ near the ${\pi }^{-}$ production threshold with its theoretical prediction. Their comparison leads us to assign the distinct narrow peak observed at about 5 MeV below the threshold to the formation of bound pionic states ${\pi }^{-}{\otimes }^{207}\mathrm{Pb}$ of the quasisubstitutional configurations ${\mathrm{}\left(2p\right)\mathrm{}}_{{\pi }^{-}}{(3p}_{3/2}{,3p}_{1/2}{)}_n^{-1}.$ A small bump observed on the tail of the peak is assigned to the pionic $1s$ state. The binding energies ${(B}_{\mathrm{nl}})$ and the widths $\left({\Gamma }_{\mathrm{nl}}\right)$ of the pionic orbitals are deduced to be $B_{2p}=5.13\mathrm{}\pm 0.02\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.12\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\mathrm{}\mathrm{MeV}$ and ${\Gamma }_{2p}=0.43\mathrm{}\pm 0.06\mathrm{}\left(\mathrm{stat}\right)\mathrm{}\pm 0.06\mathrm{}\left(\mathrm{syst}\right)\mathrm{}\mathrm{}\mathrm{MeV}$ by decomposing the experimental spectrum into the pionic $1s$ and $2p$ components. While $B_{2p}$ and ${\Gamma }_{2p}$ are determined with small ambiguity, $B_{1s}$ and ${\Gamma }_{1s}$ are strongly correlated with each other, and are affected by the relative $1s/2p$ cross section ratio assumed, since the $1s$ component is observed only as an unresolved bump. Thus, we have to allow large uncertainties $6.6\mathrm{MeV}<B_{1s}<6.9\mathrm{}\mathrm{MeV}$ and $0.4\mathrm{MeV}<{\Gamma }_{1s}<1.2\mathrm{}\mathrm{MeV}.$ The experimental binding energies and widths are compared with theoretically calculated values based on various optical potential parameter sets, and are jointly used to deduce the effective ${\pi }^{-}$ mass in the nuclear medium.