Spectroscopy of Pionic Atoms in ${}^{122}\mathrm{Sn}(d,{}^3\mathrm{He})$ Reaction and Angular Dependence of the Formation Cross Sections

We observed the atomic $1s$ and $2p$ states of ${\pi }^{-}$ bound to ${}^{121}\mathrm{Sn}$ nuclei as distinct peak structures in the missing mass spectra of the ${}^{122}\text{Sn}(d,{}^3\text{He})$ 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.

Figure 1

A schematic view of the experimental facility, BigRIPS [22], and the detector setup. A deuteron beam impinged on a target located at the nominal target position $F0$. The emitted ${}^3\mathrm{He}$ particles were momentum analyzed at the dispersive focal plane at $F5$ and the tracks were measured by the MWDCs. The scintillation counters at $F5$ and $F7$ were used for particle identification.

Figure 2

(Top panel) Measured excitation spectrum of the ${}^{122}\text{Sn}(d,{}^3\text{He})$ reaction at the angular range of $0<\theta <2°$. Three distinct peaks are observed in the region $E_{\mathrm{ex}}=[134,139]\mathrm{MeV}$. The left and middle peaks are mainly originating from formation of pionic $1s$ and $2p$ states, respectively. The right peak is partly contributed from the other pionic states ($2s$, $3p$, and $3s$). The spectrum is fitted in the region indicated. The fitting curve and contributions from the $1s$ and the $2p$ states are presented by solid, dashed, and dotted lines, respectively. (Bottom panel) Decomposition of the pionic $1s$ and $2p$ strengths into contributions from each neutron hole state of ${}^{121}\mathrm{Sn}$ as indicated. Note that fragmentation is taken into consideration for $(2d_{5/2}{)}_n^{-1}$.

Figure 3

The measured excitation spectrum in Fig. 2 is decomposed into spectra with different $\theta$ ranges as indicated. The overall fitting curves and the $1s$ and $2p$ components are shown by the solid, dashed, and dotted lines, respectively.

Figure 4

(Top panel) Determined pionic-$nl$-state formation cross sections $I_{nl}(\theta )$ for different $\theta$ ranges. Statistical errors are shown by the boxes and systematic errors in addition by the bars. The deduced cross sections are compared with the theoretical calculations [19, 28]. (Bottom panel) $I_{2p}(\theta )/I_{1s}(\theta )$. Systematic errors are canceled by taking the ratios.