Precision Spectroscopy of Pionic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>1</mml:mn><mml:mi>s</mml:mi></mml:math>States of Sn Nuclei and Evidence for Partial Restoration of Chiral Symmetry in the Nuclear Medium

Abstract

Deeply bound $1s$ states of ${\ensuremath{\pi}}^{\ensuremath{-}}$ in $^{115,119,123}\mathrm{S}\mathrm{n}$ were preferentially observed using the $\mathrm{S}\mathrm{n}(d,^{3}\mathrm{H}\mathrm{e})$ pion-transfer reaction under the recoil-free condition. The $1s$ binding energies and widths were precisely determined and were used to deduce the isovector parameter of the $s$-wave pion-nucleus potential to be ${b}_{1}=\ensuremath{-}(0.115\ifmmode\pm\else\textpm\fi{}0.007){m}_{\ensuremath{\pi}}^{\ensuremath{-}1}$. The observed enhancement of $|{b}_{1}|$ over the free $\ensuremath{\pi}N$ value (${b}_{1}^{\mathrm{f}\mathrm{r}\mathrm{e}\mathrm{e}}/{b}_{1}=0.78\ifmmode\pm\else\textpm\fi{}0.05$) indicates a reduction of the chiral order parameter, ${f}_{\ensuremath{\pi}}^{*}(\ensuremath{\rho}{)}^{2}/{f}_{\ensuremath{\pi}}^{2}\ensuremath{\approx}0.64$, at the normal nuclear density, $\ensuremath{\rho}={\ensuremath{\rho}}_{0}$.