Spectroscopy of Pionic Atoms in Sn122(d,He3)<

Abstract

We observed the atomic 1s and 2p states of π^{-} bound to ^{121}Sn nuclei as distinct peak structures in the missing mass spectra of the ^{122}Sn(d,^{3}He) nuclear reaction. A very intense deuteron beam and a spectrometer with a large angular acceptance let us achieve a potential of discovery, which includes the capability of determining the angle-dependent cross sections with high statistics. The 2p state in a Sn nucleus was observed for the first time. The binding energies and widths of the pionic states are determined and found to be consistent with previous experimental results of other Sn isotopes. The spectrum is measured at finite reaction angles for the first time. The formation cross sections at the reaction angles between 0° and 2° are determined. The observed reaction-angle dependence of each state is reproduced by theoretical calculations. However, the quantitative comparison with our high-precision data reveals a significant discrepancy between the measured and calculated formation cross sections of the pionic 1s state.

Recent progress in QCD condensate evaluations and sum rules

“…The difference between the two approaches gives an approximate estimate of the systematic uncertainties related to the non-linear terms in chiral perturbation theory. In this context, it is worth mentioning past [156,157] and ongoing [158] experimental efforts to measure deeply bound pionic atom spectra, which, if precise enough, can strongly constrain the chiral condensate value at finite density. For related theoretical work, see also Refs.…”

Search for $η'$ bound nuclei in the $^{12}{\rm C}(γ,p)$ reaction with simultaneous detection of decay products

“…For this purpose, we calculated the expected excitation energy of the η ′ + 11 B system E ex , relative to the production threshold E 0 , in the framework of a distorted wave impulse approximation (DWIA) [17,28]. The DWIA is the standard technique used for describing bound states such as in hypernuclei and pionic atoms [29][30][31][32][33][34]. In general, DWIA calculations nicely represent spectral shapes of bound states but hardly reproduce their absolute cross sections [29][30][31][32][33][34].…”

“…The DWIA is the standard technique used for describing bound states such as in hypernuclei and pionic atoms [29][30][31][32][33][34]. In general, DWIA calculations nicely represent spectral shapes of bound states but hardly reproduce their absolute cross sections [29][30][31][32][33][34]. We decomposed our DWIA calculation into the η ′ absorption and escape processes, and obtained a normalization factor F of the DWIA cross section by measuring η ′ escaping from a nucleus:…”