Spectroscopy of pionic atoms in mathbf{{}¹²²{textbf Sn}({textit d},{}³{textbf He})} reaction and angular dependence of the formation cross sections

We observed the atomic $1s$ and $2p$ states of $\pi^-$ bound to ${}^{121}{\rm Sn}$ nuclei as distinct peak structures in the missing mass spectra of the ${}^{122}{\rm Sn}(d,{}^3{\rm He})$ nuclear reaction. A very intense deuteron beam and a spectrometer with a large angular acceptance let us achieve potential of discovery, which includes 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 $2^\circ$ 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.