First application of superconducting transition-edge-sensor microcalorimeters to hadronic-atom x-ray spectroscopy

High-resolution pionic-atom x-ray spectroscopy was performed with an x-ray spectrometer based on a 240-pixel array of superconducting transition-edge-sensor (TES) microcalorimeters at the piM1 beam line of the Paul Scherrer Institute. X-rays emitted by pionic carbon via the 4f->3d transition and the parallel 4d->3p transition were observed with a full-width-at-half-maximum energy resolution of 6.8 eV at 6.4 keV. Measured x-ray energies are consistent with calculated electromagnetic values which considered the strong-interaction effect assessed via the Seki-Masutani potential for the 3p energy level, and favor the electronic population of two filled 1s electrons in the K-shell. Absolute energy calibration with an uncertainty of 0.1 eV was demonstrated under a high-rate hadron beam condition of 1.45 MHz. This is the first application of a TES spectrometer to hadronic-atom x-ray spectroscopy and is an important milestone towards next-generation high-resolution kaonic-atom x-ray spectroscopy.

1. Introduction A hadronic atom consists of a negatively-charged hadron (e.g., π − , K − , p, Σ − , Ξ − ) and electrons that are bound by a Coulomb field to an atomic nucleus. Such a system can be used to probe the strong interaction between hadrons and atomic nuclei in the low-energy limit. The mass of the hadron, significantly larger than the mass of the electron it replaces, shifts the atomic transition energies in the hadronic atom to significantly higher energies than those of the standard atom. In addition, effects of the strong interaction appear in the most tightly bound energy level. These perturbations include an energy shift from that given only by the electromagnetic interaction, and a lifetime broadening due to absorption of the hadron by the nucleus. The shift and width can be experimentally extracted via x-ray-emission spectroscopy of characteristic transitions into this lowest orbital.
In kaonic atoms, the understanding of the low-energy KN interaction has been substantially deepened by the most recent kaonic-hydrogen-atom measurement [1] and theoretical studies (e.g., [2]). However, the depth of the K-nucleus potential remains unknown because of insufficient precision in the kaonic-atom data for Z ≥ 2; this is one of the greatest present concerns in strangeness nuclear physics [3].
In recent years, Balmer-series x-rays of the K − -He atom (∼ 6 keV) were measured at the K5 beamline of KEK-PS [4] and the DAΦNE electron-positron collider of the Laboratori Nazionali di Frascati [5,6]. These measurements followed discussions of the importance of the measurement of the strong-interaction shift and width of the 2p level in kaonic-helium atoms (K − -He) over 30 years ago [7,8]. Both experiments employed Silicon Drift Detectors (SDDs) whose FWHM energy resolution is typically ∼ 200 eV at 6 keV [4][5][6]. To observe spectral effects as predicted by theoretical calculations [9][10][11], e.g., a 0.2 eV shift and 2 eV line width, a new approach with a significantly improved resolution is essential.
We are preparing a high-resolution x-ray measurement of kaonic atoms at a kaon beamline of J-PARC [12] using a novel superconducting transition-edge-sensor (TES) microcalorimeter (J-PARC E62 [13]). The FWHM energy resolution of this type of detector can be as good as about 2 eV at 6 keV [14,15] which is about two orders of magnitude better than that of SDDs. The spectrometer is a highly sensitive thermal sensor that measures energy deposition via the increase in the resistance of a superconducting thin film that is biased within the sharp phase transition between the normal and superconducting phases. The detailed working principles and the recent progress of the TES system are described in Refs. [15][16][17].
An alternate high-resolution x-ray spectroscopy technology is based on diffraction from Bragg crystals. However, they have not been used to study the strong interaction in most hadronic atoms due to their low efficiency. Only pion beams and the resulting x-ray emission are intense enough to enable the study of pionic atom x-rays [18][19][20]   multi-pixel TES arrays (more than 100 pixels; each having ∼0.1 mm 2 effective area) allow the performance of a precision kaonic-atom measurement in a realistic data acquisition time.
Until this experiment, a TES x-ray spectrometer has never been utilized in a hadronbeam environment. To study the in-beam performance of the TES spectrometer at a hadron beamline and demonstrate the feasibility of TES-based hadronic-atom x-ray spectroscopy, we performed a pioneering experiment at a pion beamline by measuring the x-rays from the 4f → 3d transition of pionic carbon (π-12 C). This x-ray transition was chosen because the energy (∼ 6.5 keV) is similar to the K − -He 3 → 2 x-ray energy, while the strong-interaction effects are negligibly small.

Experiment
The experiment was carried out at the πM1 beamline [21] of the Paul Scherrer Institute (PSI) in October 2014. Pions were created by a proton beam of energy 590 MeV at a current of up to 2.3 mA passing through a graphite target located in the main beamline of the PSI synchro-cyclotron, and were transported through the πM1 beamline.
A schematic view of the experimental setup is shown in Fig. 1. With a 2.2 mA primary proton beam, the π − beam rate with momentum 173 MeV/c was 1.45 × 10 6 /sec at BC1 (10×10 cm 2 plastic scintillation counter) located at a distance 30 cm upstream from the focal point. The π − /e − ratio was ∼0.7 due to a missing electrostatic separator in the beamline.
The incident π − 's were degraded in moderators, counted with beamline counters (BCs), and stopped in a carbon graphite target where π-12 C atoms were generated. X-rays were emitted by the highly excited atoms and detected by a TES x-ray spectrometer through a 150µm-thick beryllium vacuum window and three layers of 5-µm-thick aluminum IR-blocking filters (one at each of the three temperature stages: 50K, 3K, 50 mK).
A 240-pixel TES array [22] was the x-ray spectrometer. Each pixel had a 4-µm-thick bismuth absorber (80% absorption efficiency for 6.4 keV x-rays) which converted the incident x-ray energy to heat; the absorber was coupled to a sensitive thermal sensor, the TES, composed of a superconducting Mo/Cu proximity bilayer film. Each absorber had a collimated effective area of 320 µm × 305 µm, thus the total collecting area of the array was 3/10 about 23 mm 2 . Each TES pixel was electrically biased to the superconducting critical temperature (T C ∼ 107 mK) and to about 20 -30% of their normal resistance of ∼10 mΩ. A pulse-tube-backed adiabatic demagnetization refrigerator (ADR) [23] cooled the system to a regulated bath temperature of 75 mK ± 7 µK (rms). The regulated hold time was about 36 hours, after which the ADR cycle (magnetic field increased isothermally and decreased adiabatically) took 2 hours before another 36 hours of operation at 75 mK.
SQUID current amplifiers were used to read out the current signal from the low-resistance TESs. For the 240-pixel readout, a time division SQUID multiplexing (TDM) scheme [24] was employed to reduce the number of wires running to the low temperature stages of the cryocooler. The signal from each TES channel was coupled to a SQUID amplifier, and the outputs from 30 individual channels were switched sequentially and read out by a single amplifier. The multiplexing frame time was 9.6 µs (0.32 µs/channel). The sampling rate was therefore 104 kHz for each pixel. The 240 pixel readout was realized by use of eight TDM columns in parallel.
TES data were continuously streamed into a PC server, and were recorded to disk only when a current "pulse" due to an x-ray event was triggered. The system recorded 1024 samples (9.83 ms) for each event, where the first 256 samples corresponded to a pre-triggered timing region. The typical exponential rise and decay time constants of an x-ray pulse were ∼200 µsec and ∼500 µsec respectively. The x-ray energy corresponding to each pulse height was calculated with an optimal-filter technique [25]. The data-acquisition system recorded also a stopped-π trigger timing defined by beamline counters as BC1 ⊗ BC2 ⊗ BC3 ⊗ BC4, where the pulse-height threshold of BC2 was carefully set in order to select only stoppedpion events which deposited more energy than an electron, a muon or an in-flight pion event. The relative timing of this triggering system to the TES events was reconstructed during the offline analysis.
Precise absolute energy calibration was crucial for this measurement. Because independent energy calibration was necessary for each of the 240 pixels, it was essential to supply intense calibration x-rays to achieve sufficient statistics for in-situ calibration. An x-ray tube source was installed as shown in Fig. 1. Characteristic x-rays were produced by shining a controllable flux of x-rays, which was generated by an electron gun with a Rh target, on 99.999% pure chromium and cobalt pieces. These calibration x-rays traveled through the hollow, conical carbon target to the TES spectrometers. Figure 2 shows a summed x-ray energy spectrum of 209 working TES pixels obtained with the x-ray generator without a pion beam. The achieved energy resolution was 4.6 eV (FWHM) at 6.4 keV with a count rate of 4.4 Hz/pixel. The energy calibration was performed with the four calibration x-ray lines, Cr K α , Cr K β , Co K α , and Co K β , with natural cubicspline interpolation. Energies and natural widths of the calibration x-rays were fixed with the reference values [26] in the spectral fitting. Lower-yield x-rays, Fe K α (6.4 keV) and Cu K α (8.0 keV), originated respectively from stainless steel vacuum fittings in the tube source and Cu inside of the detector package. These were not used for calibration.

Results
Time and energy distributions of π-12 C x-rays measured with the 209 working TES pixels are shown in Fig. 3. The data were accumulated for 13.5 hours with a pionbeam intensity of 1.45 MHz and a stopped-π trigger rate of 34.5 kHz. Figure 3  2 An x-ray energy spectrum obtained from a tube-source x-ray generator shining on Cr and Co calibration pieces without a pion beam. The Cr K α , Cr K β , Co K α , and Co K β lines are used for the energy calibration. Lower-yield x-rays, Fe K α (6.4 keV) and Cu K α (8.0 keV), originate respectively from the stainless steel vacuum fittings of the tube source and the metal structure of the 50 mK detector package.
array for stopped-π − trigger events. A clear peak was observed with a time resolution of 1.2 µsec FWHM. Figure 3 (a) shows a correlation plot of the time difference versus the x-ray energy measured by TESs. At around 6.43 keV, a clear time-energy correlation corresponding to π-12 C 4f → 3d x-ray was observed. Figure 3 (c) shows an x-ray energy spectrum of only those events recorded within the stopped-π − timing gate (±1.5 µsec) that is indicated in Fig.  3 (b). A sharp peak from the π-12 C 4f → 3d transition is observed. The TES spectrometer has sufficient energy resolution to observe the parallel transition 4d → 3p. Figure 3 (c) shows contributions from those 4f → 3d and 4d → 3p lines whose centroids are only 7.4 eV apart. The timing selection improved the peak-to-background ratio of the π-12 C line from 2 to 10. As a reference in this experiment, a SDD is installed just beneath the carbon target as shown in right panel of Fig. 1. The FWHM energy resolution of the SDD of ∼ 165 eV is not nearly enough to resolve any of the important features of the spectrum (Fig 3 (d)). The tube source produces Cr and Co calibration x-rays constantly during data acquisition with the pion beam. The energy calibration with Cr and Co x-rays is recalculated every 2 hours to mitigate gain drift. A fit of the energy spectrum with the in-beam condition of π − beam gives a FWHM energy resolution of 6.8 eV at 6.4 keV with a TES hit rate of 4.8 Hz/pixel, of which 0.4 Hz is due to the pion beam. The deterioration of the energy resolution and the size of low-energy and high-energy tail components in the non-Gaussian energy response of TESs both increase as a function of pion beam intensity. These beamcorrelated effects are explained by the production of thermal cross-talk pulses which are due to direct charged-particle hits in the silicon substrate of the TES array. The detail of the detector response and the absolute energy calibration was presented in a separate paper [27].
The x-ray generator fluoresces materials containing iron (e.g., the stainless steel vacuum fittings around the target cell); therefore characteristic x-rays of iron are observed that are 5  uncorrelated with the pion-beam timing. The Fe K α1 (6.404 keV) and Fe K α2 (6.391 keV) lines were used to evaluate the accuracy of energy calibration that was then used to determine π-12 C x-ray energy. A result of a spectral fit of Fe K α and π-12 C x-rays is shown in Fig. 3 (c). The energy-calibration accuracy is assessed by the fit to the measured Fe K α line. The measured energy of our Fe K α11 line is: 6404.07 ± 0.10(stat.) +0.06 −0.04 (syst.) eV where the first error is statistical and the second is systematic. The quoted systematic uncertainty is a quadratic summation of the contributions from continuum background parameter and asymmetry of the fit function. A comparison with the reference value of 6404.148(2) eV [26] for pure, metallic iron shows good agreement within the errors. To determine the energy of pionic carbon transition x-ray, the critical issue is the uncertainty precisely at the lines of interest, 6430 eV. It is difficult to assess the systematic uncertainty introduced by our choice for the calibration curves in its full generality. Fortunately, the Fe K α line at 6404 eV is very close to the line of interest, and this good agreement with the reference value validated the choice of the present energy calibration curves.
Fits to our energy spectra determined the energies of the π-12 C 4f → 3d and 4d → 3p transition x-rays and their yield ratios to be: where the first error is statistical and the second is systematic. The quoted systematic uncertainty is a quadratic summation of the contributions from uncertainties of the energy calibration, the non-Gaussian response function, and the timing window width. The tail component of Fe K α line affects the fit results. We assessed it by varying the relative strength of the Fe x-ray tail by changing the timing window. The Fe tail is the main source of systematic errors both for x-ray energies and yield ratio. The energy dependence of transmissions of these two π-12 C peaks is negligible to determine the yield ratio, since these energies are very close and no absorption edge structure exists around those peaks.
We have calculated the 3p, 3d, 4d and 4f energy levels of the pionic 12 C using only the electromagnetic (EM) interaction and tabulated the results in Table 1. These EM values are calculated from the Klein-Gordon equation including vacuum polarization with higher-order correction, the relativistic-recoil effect and the nuclear-finite-size effect. The latest charged pion mass, 139.57018(35) MeV/c 2 , given by the particle data group [28] is used.
Strong-interaction effects on these energy levels were assessed via the Seki-Masutani potential [29]. The strong-interaction shift of the 3p level from its EM value is calculated to be 0.78 eV, while the shifts of the 4f , 4d, 3d levels are below 10 −4 eV.
The effect of the electrons populating the K-and L-shells, the so-called electron-screening effect, is not negligible especially in the solid target. The electron-screening correction to the x-ray energy is largely determined by the number of 1s electrons in the atom, which depends on the balance between Auger-electron emission and the electron-refilling process from neighboring atoms. We have estimated the electron screening effect with the "Z − 1" approximation, namely the captured pion screens one unit of the nuclear charge seen by 7/10 Table 1 Calculated values of pionic 12 C electromagnetic energies and strong-interaction energy shifts via the Seki-Masutani potential [29]. For the 4f → 3d and 4d → 3p transitions, electron-screening effects are assessed with the cases of filling one 1s electron and two 1s electrons in the K-shell. The experimental results are shown as well. the electrons. Thus, the maximum electron-screening correction is given by the 1s 2 2s 2 2p 1 electronic configuration. In Table 1, the EM values of the 4f → 3d and 4d → 3p transitions are tabulated for the no electron, 1s 1 2s 2 2p 1 and 1s 2 2s 2 2p 1 electronic configurations. Here, the electron-density functions in each configuration are evaluated using the hydrogenic wave function with effective nuclear charge based on Hartree-Fock calculations. The experimental results are consistent with the 1s 2 2s 2 2p 1 configuration within the errors.

Conclusion
We observed the π-12 C 4f → 3d transition x-ray line with a novel 240pixel microcalorimetric x-ray detector based on transition edge sensors. The achieved averaged energy resolution is 6.8 eV FWHM at 6.4 keV under a high-rate pion beam intensity of 1.45 MHz. The timing resolution is 1.2 µsec FWHM. Absolute energy calibration is realized by an x-ray generator shining on calibration metals during the data acquisition. The resulting systematic uncertainty in the π-12 C 4f → 3d transition x-ray energy is less than 0.1 eV, which meets our goal for a future measurement of the kaonic-helium 3d → 2p x-ray energy.
The TES spectrometer had sufficient energy resolution to observe the parallel transition π-12 C 4d → 3p x-ray for the first time. The strong-interaction effect of the 3p level is not negligible because it has smaller angular momentum than the 3d level. The measured x-ray 8/10 energy of the parallel transition 4d → 3p was found to be consistent with the calculated strong-interaction effect assessed via the Seki-Masutani potential [29].
Our data allow the determination of the electron population status of the atoms. Both the 4f → 3d and 4d → 3p transition energies obtained favor two 1s electrons in the K-shell. Moreover we have determined the yield ratio between the 4f → 3d and 4d → 3p transitions. Whether the observed x-ray yields can be consistently explained by a cascade calculation with the electronic configuration of two filled 1s electrons in the K-shell remains to be solved in future theoretical work.
We successfully demonstrated the feasibility of hadronic-atom x-ray spectroscopy with an absolute energy uncertainty of 0.1 eV in the 6 keV energy region. This is an important milestone towards a more general use of high-resolution microcalorimeter spectrometers at charged-particle beamlines.