Precision spectroscopy of pionic 1s states of Sn nuclei and evidence for partial restoration of chiral symmetry in the nuclear medium

Abstract

Deeply bound 1s states of $π^-$ in $^{115,119,123}$Sn were preferentially observed using the Sn($d$,$^3$He) 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 $b_1 =-0.115\pm 0.007 ~m_π^{-1}$. The observed enhancement of $|b_1|$ over the free $πN$ value ($b_1^{\rm free}/b_1 = 0.78 \pm 0.05$) indicates a reduction of the chiral order parameter, $f^{*}_π (ρ)^2/f_π^2 \approx 0.64$, at the normal nuclear density, $ρ= ρ_0$.