Deeply bound<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>π</mml:mi></mml:mrow><mml:mrow><mml:mi>−</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>states in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>207</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi></mml:math>formed in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>208</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">Pb</mml:mi><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mi>d</mml:mi><mml:mo>,</mml:mo></mml:mrow><mml:mrow><mml:mn>3</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">He</mml:mi><mml:mo>)</mml:mo></mml:math>reaction. II. Deduced binding energies and widths and the pion-nucleus interaction

Abstract

We find a remarkable agreement of the excitation energy spectrum of the ${}^{208}\mathrm{Pb}{(d,}^{3}\mathrm{He})$ reaction measured at ${T}_{d}=600\mathrm{MeV}$ near the ${\ensuremath{\pi}}^{\ensuremath{-}}$ 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 ${\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\bigotimes}}^{207}\mathrm{Pb}$ of the quasisubstitutional configurations ${(2p)}_{{\ensuremath{\pi}}^{\ensuremath{-}}}{(3p}_{3/2}{,3p}_{1/2}{)}_{n}^{\ensuremath{-}1}.$ 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 $({\ensuremath{\Gamma}}_{\mathrm{nl}})$ of the pionic orbitals are deduced to be ${B}_{2p}=5.13\ifmmode\pm\else\textpm\fi{}0.02(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.12(\mathrm{syst})\mathrm{}\mathrm{MeV}$ and ${\ensuremath{\Gamma}}_{2p}=0.43\ifmmode\pm\else\textpm\fi{}0.06(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}0.06(\mathrm{syst})\mathrm{}\mathrm{MeV}$ by decomposing the experimental spectrum into the pionic $1s$ and $2p$ components. While ${B}_{2p}$ and ${\ensuremath{\Gamma}}_{2p}$ are determined with small ambiguity, ${B}_{1s}$ and ${\ensuremath{\Gamma}}_{1s}$ 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 $6.6\mathrm{MeV}&lt;{B}_{1s}&lt;6.9\mathrm{MeV}$ and $0.4\mathrm{MeV}&lt;{\ensuremath{\Gamma}}_{1s}&lt;1.2\mathrm{MeV}.$ 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 ${\ensuremath{\pi}}^{\ensuremath{-}}$ mass in the nuclear medium.