Measurements of Strong-Interaction Effects in Kaonic-Helium Isotopes at Sub-eV Precision with X-Ray Microcalorimeters

We have measured the $3d\to 2p$ transition x rays of kaonic ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ atoms using superconducting transition-edge-sensor microcalorimeters with an energy resolution better than 6 eV (FWHM). We determined the energies to be $6224.5\pm 0.4(\mathrm{stat})\pm 0.2(\mathrm{syst})\mathrm{eV}$ and $6463.7\pm 0.3(\mathrm{stat})\pm 0.1(\mathrm{syst})\mathrm{eV}$, and widths to be $2.5\pm 1.0(\mathrm{stat})\pm 0.4(\mathrm{syst})\mathrm{eV}$ and $1.0\pm 0.6(\mathrm{stat})\pm 0.3(\mathrm{stat})\mathrm{eV}$, for kaonic ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$, respectively. These values are nearly 10 times more precise than in previous measurements. Our results exclude the large strong-interaction shifts and widths that are suggested by a coupled-channel approach and agree with calculations based on optical-potential models.

Figure 1

TES-measured x-ray spectrum summed across all the ${}^3\mathrm{He}$ data. The characteristic lines used for the energy calibration are labeled. The expected $3d\to 2p$ x-ray energies from the kaonic ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ are indicated as dotted lines. The small feature near 6500 eV, just above the $K^{-}{}^4\mathrm{He}$ $L\alpha$ energy, is the Bi $M\beta$ escape peak of the Cu $K\beta$ line.

Figure 2

(a) Correlation between the energy deposited ($dE$) in the last beam counter and the TES pulse timing. (b) Timing histogram of the TES pulses with $dE>16\mathrm{MeV}$. The hatches show the timing ranges of kaonic-atom formation events and asynchronous-background events. These plots include events in the x-ray energy range of $6100<E<6600\mathrm{eV}$.

Figure 3

Final x-ray spectra after all event selections. The asynchronous background was estimated via the timing ranges defined in Fig. 2. The peak fitting lines, including decomposition into the main peak and the low-energy tail components, are shown.

Figure 4

Strong-interaction shifts and widths in the $2p$ state of kaonic-helium atoms. Results in this Letter (J-PARC E62) are compared to the past measurements of the SIDDHARTA [16] and the KEK E570 experiments [14]. The KEK E570 result is shown as a band because no width value is reported. The errors quoted here are the quadratic sum of the statistical and systematical errors. The uncertainty in the electromagnetic calculation is not considered.