Gamma-Ray Spectroscopy for 237\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{237}$$\end{document}Np Using a Transition-Edge Sensor with a Thick-Trilayer Membrane

Gamma-ray transition edge sensors (TESs) are intensively studied not only to measure isotopic composition of nuclear materials but to monitor transuranic radionuclides inside the human body. We have recently proposed a thick-trilayer membrane as an alternative to silicon-nitride (Six\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{x}$$\end{document}Ny\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{y}$$\end{document}) single-layer ones. It consists of silicon dioxide (SiO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document}), Six\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{x}$$\end{document}Ny\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{y}$$\end{document}, and SiO2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_2$$\end{document} layers. Their total thickness is 6.9 μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu $$\end{document}m and exhibits almost the same thermal conductance as conventional Six\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{x}$$\end{document}Ny\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{y}$$\end{document} ones with 1-μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upmu $$\end{document}m thickness. The thick-trilayer membrane is expected to have better mechanical strength against implementing heavy-bulk absorbers. In this paper, the gamma-ray TES with the thick-trilayer membrane is used to carry out the spectroscopy for the nuclear radiation source. Neptunium-237 and its decay product Protactinium-233 emit 86.5 and 86.6-keV lines, respectively, and they are clearly resolved by four pixels with the full-width-half-maximum (FWHM) resolution of (43.7±0.9\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$43.7\pm 0.9$$\end{document}) eV. Furthermore, their intensity ratio agrees with the radioactive equilibrium between the two nuclides. Our experimental results predict that a vast array of pixel formats will reduce the statistical uncertainty in less measuring time.


Introduction
Gamma-ray transition-edge sensors (TESs) are employed for assays of nuclear materials for safeguards and fuel-cycle applications [1]. TESs can nondestructively identify their composition and isotopic ratios. Decommissioning of nuclearpower plants requires the retrieval of fuel debris that remains inside reactor-containment vessels. In addition, simple and regular medical diagnostics are desired for checking whether organs of workers in such a plant are not contaminated by transuranic radionuclides (TRUs), e.g. neptunium (Np), plutonium (Pu), and americium (Am). Bioassays and lung-counters have been adopted to assess the radiological dose for nuclear workers and the publics [2]. Though the turnaround time for the diagnosis should be as short as possible, a bioassay typically requires several days because of chemically-based separations. In contrast, spectrometers based on radiation detectors which measure low-energy gamma rays and x rays from TRUs can decrease the overall time and costs of the analysis. High purity germanium (HPGe) detectors adopted by lung counters, whose energy resolution is limited to about 0.4 keV at 100 keV due to the statistics of charge creation and collection [3], cannot provide enough concentration analysis for several elements. TESs with much better energy resolution generally produce lower measurement uncertainty [1]. A large effective area which can reduce the measuring time will be accomplished by a vast arrays of pixels.
National Institute of Standards and Technology (NIST) developed gamma-ray TESs with 50-mm 2 detection area composed of 236 working pixels that achieved the excellent full width at half maximum (FWHM) resolution in the range of 40eV to 60eV at 97 keV [3,4]. Microwave superconducting quantum interference devices (SQUIDs) have been developed for simultaneous readout of several hundreds of pixels with a cable [5]. Los Alamos National Laboratory has analyzed samples which contain isotopic 239 Pu [6]. They currently combine the gammaray TESs and microwave SQUIDs provided by NIST for the future 512 pixels. The TES adopts conventional low-tensile silicon nitride (Si x N y ) monolayer membrane. An alternative way we have recently developed is a TES based on the thick-trilayer membrane consisting of silicon dioxide (SiO 2 ), Si x N y , and SiO 2 . The advantage and characterization of the thick-trilayer one are described in [7].
In this paper, we carry out gamma-ray spectroscopy of a neptunium ( 237 Np) sample in radioactive equilibrium with protactinium ( 233 Pa ) to demonstrate the resolving power of gamma-ray TESs based on the thick-trilayer membrane. Our TES with 4 pixles deposited on a thick-trilayer membrane exhibits the 44-eV FWHM and clearly resolves the 86.5-keV and 86.6-keV gamma-ray peaks originating from the two actinides 237 Np and 233 Pa , respectively. Furthermore, the intensity ratio agrees with an expectation based on the radioactive equilibrium. It will play a key role not merely in the non-destructive analysis of nuclear materials but in the next-generation bioassay and lung-counter systems.
Throughout this paper, we quote standard uncertainty unless otherwise specified. The datasets analyzed during the current study are available from the corresponding author on reasonable requests.

3
Journal of Low Temperature Physics (2023) 211:207-213 2 Detector Design Figure 1 displays the TES chip consisting of five pixels. The titanium-gold (Ti/Au) bilayer with 30-nm and 100-nm thickness, respectively, is deposited on the trilayer membrane. It has exhibited transition temperature T c ≃130 mK and normal resistance R n ≃ 80 mΩ . All of the TES sizes are kept 0.25 mm square. A tin (Sn) absorber is supported by four gold bumps [8]. Our membrane consists of the SiO 2 /Si x N y /SiO 2 trilayer. We have adjusted stress of the trilayer membrane low tensile (∼ +20 MPa) to prevent wrinkles on it. It has 6.9 μ m thickness in total. The middle Si x N y layer has 5.7 μ m thickness to make TESs sturdier than conventional ones. In our calculation with a load-deflection equation valid for Si x N y membranes [9][10][11], a thicker membrane provides less deflection and a wider ideal elastic region where linear loaddeflection relation is valid. We believe that the former and the latter contribute to high strength and uniform heat conductance among pixels, respectively, in future large-format TES arrays. Thermal conductance (G) of conventional Si x N y membranes with 1-μ m thickness is known for G≃ 3 nW/K [4]. Moreover, their G is known to be proportional to their thickness [12]. Our trilayer membrane shows G≃1.5nW/K in spite of the 6.9-μ m thickness [7]. Fall time of the output pulse is 1.4 msec at 130 mK [7], which is almost the same as those of 1-μ m thick Si x N y membranes [4]. Conventional membranes exhibit a ballistic phonon transport in the membrane [13], on the other hand, our trilayer one shows an intermediate state between ballistic and diffusive transports [7,14].

Measurement
In the current setup shown in Fig. 1, the gamma-ray source with 0.22 kBq is located 8 mm away from the detector array in order that the solid angle covers the whole array. Thin aluminum films in front of the 237 Np source shield alpha rays and the beta continuum. An interface chip includes shunt resistors for the TES-bias circuit R sh = 10 mΩ . The five pixels A1, A2, B1, B2, and C2 are biased in series and they are simultaneously read out by a microwave SQUID multiplexer [15]. TES dominates the system noise as reported in [7]. A HPGe is adopted to obtain the spectrum in advance. Energy calibration is important for spectroscopy aimed for high resolving power. Our target in this experiment is discrimination of 233 Pa line at 86.6 keV from 237 Np one at 86.5 keV. Since the former provides roughly 1 count per hour per pixel, statistical data-analysis needs signal integration of about 100 h for single-pixel detection. During such long operation, our adiabatic demagnetization refrigerator (ADR) with short-term stability of 6 μ K rms at 100 mK provides long-term time drift of TES output shown in Fig. 2a. Figure 2b and c indicate that the drift correction based on a so-called spline interpolation compensates the time drift of both the pulse area and the baseline which affect the estimation of photon energy. Other tall lines are corrected in the same way with different parameters of the spline function. We pick some of them to build a calibration curve between the pulse area and energy E. Figure 3 is a spectroscopic result measured by HPGe and our single-pixel TES based on trilayer membrane for 60-hours detection. Here, lines of Uranium and TRUs are discriminated with TES, while some of them are overlapped with HPGe. Combined spectrum with 4 pixels A2, B1, B2, and C2 summed over. Energy shift for each pixel, B1's example is shown in (Left), is corrected so that all pixels exhibit the same peak energy of 237 Np line as the literature. The fitting results give FWHM energy resolutions of (43.7 ± 0.9) eV and (44.9 ± 2.5) eV for the 86.5-keV and 86.6-keV peaks, respectively (color figure online) spectrum over the 4 pixels. We decided not to sum the A1 spectrum, because the FWHM resolution was worse than the others. The TES clearly resolves the two complex lines with the FWHM resolution (43.7±0.9) eV for 86.5 keV and (44.9±2.5) eV for 86.6 keV.
The 237 Np source is in the radioactive equilibrium with 233 Pa . According to the International Bureau of Weights and Measures (BIPM), the intensity ratio of the 86.5-keV to 86.6-keV lines is 6.16±0.31 . As shown in Fig. 4 (Right), the 237 Np intensity is (344.1±11.4) counts per 11-eV bin and the 233 Pa intensity is (54.4±4.6) counts per 11-eV bin for the 4-pixels TES operating for 60 h. The 86.6-keV line can be fitted with the Gaussian function. The intensity ratio 6.32±0.58 is in good agreement with the expected value of 6.16±0.31. To study the effect of further signal integration on the intensity ratio, we increase the total detection time from 60 to 240 h, without remarkable degradation of the energy resolution, due to four-times ADR recycle. As a result, their intensity ratio becomes 6.22±0.30 , which is closer to the expected value of 6.16±0.31 than 6.32±0.58 obtained for the 60-hours measurement with single recycle of ADR. This result predicts that a larger-scale array with uniform characteristics will reduce the statistical uncertainty in less measuring time in the future.

Conclusions
A four-pixels TES based on a thick-trilayer membrane exhibited 44-eV FWHM energy resolution and clearly resolved the 86.5-keV and 86.6-keV lines of 237 Np and 233 Pa , respectively. We demonstrated that the degree of Gaussian fit of their lines improved with increasing of the pulse count. As a result, their peak ratio well agreed with an expectation based on the radioactive equilibrium between the two nuclides. This predicts that the larger-scale TES array with uniform characteristics will reduce the statistical uncertainty in less measuring time.