Measurement of the 229 Th isomer energy with a magnetic micro-calorimeter
Tomas Sikorsky, Jeschua Geist, Daniel Hengstler, Sebastian Kempf, Loredana Gastaldo, Christian Enss, Christoph Mokry, Jörg Runke, Christoph E. Düllmann, Peter Wobrauschek, Kjeld Beeks, Veronika Rosecker, Johannes H. Sterba, Georgy Kazakov, Thorsten Schumm, Andreas Fleischmann
MMeasurement of the
Th isomer energy with a magnetic micro-calorimeter
Tomas Sikorsky,
1, 2, ∗ Jeschua Geist, ∗ Daniel Hengstler, Sebastian Kempf, Loredana Gastaldo, ChristianEnss, Christoph Mokry,
3, 4
J¨org Runke,
3, 5
Christoph E. D¨ullmann,
3, 4, 5
Peter Wobrauschek, Kjeld Beeks, Veronika Rosecker, Johannes H. Sterba, Georgy Kazakov, Thorsten Schumm, and Andreas Fleischmann Kirchhoff-Institute for Physics, Heidelberg University, INF 227, 69120 Heidelberg, Germany Institute for Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020, Vienna, Austria Johannes Gutenberg University, 55099 Mainz, Germany. Helmholtz Institute Mainz, 55099 Mainz, Germany. GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany (Dated: May 28, 2020)We present a measurement of the low-energy (0–60 keV) γ ray spectrum produced in the α -decay of U using a dedicated cryogenic magnetic micro-calorimeter. The energy resolution of ∼
10 eV, together with exceptional gain linearity, allow us to measure the energy of the low-lyingisomeric state in
Th using four complementary evaluation schemes. The most accurate schemedetermines the
Th isomer energy to be 8 . . γ spectroscopy, and agreeing with a recent measurement basedon internal conversion electrons. We also measure branching ratios of the relevant excited states tobe b = 9 . b = 0 . The low-energy metastable isomeric state in
Th( m Th) has fascinated researchers over the past 40years [1]. It is expected to have an excitation energyof ∼ Th nucleus would allow to transfer the precisionof laser spectroscopy to nuclear structure analysis [2]. Avast plethora of applications and investigations have beenproposed for the m Th state, ranging from a nucleargamma laser [3], highly accurate and stable ion nuclearclock [4, 5] to compact solid-state nuclear clocks [6]. Suchclocks would allow to attain a new level of precision forprobes of fundamental physics, e.g., a variation of funda-mental constants [7, 8], search for dark matter [9, 10] oras a gravitational wave detector [11]. They can be usedin different applications, such as geodesy [12] or satellite-based navigation [13].Despite considerable efforts, neither the resonant op-tical excitation of m Th from the nuclear ground statenor the emission of fluorescence photons in radiative de-cay has been observed [14]. Several recent attempts toexcite the nucleus using broadband synchrotron radiationfailed to detect a signal [15–17]. All currently availableinformation about the existence [18], the energy [19–22],or lifetime [23] of the isomer is derived from experimentswhere the
Th isomer is produced in α -decay of U, orthrough the x ray pumping of the second excited nuclearstate [24].The existence of a low-lying isomeric state in
Th wasdeduced in 1976 from analysis of a γ ray spectrum associ-ated with α -decay of U [25]. Refined measurements ofthe same spectrum performed in the early nineties withdifferent Ge and Si(Li) detectors, whose energy resolutionwas about several hundreds of eV, determined the isomerenergy to be 3 . . ∼
30 eV measured an isomer en-ergy of 7 . ∼
40 eV energy resolution reported theisomer energy to be 8 . m Th state was also studied by direct spec-troscopy of recoil ions emerging from a
U source. The U → Th decay populates the m Th state with a2% probability [28]. Thorium ions were slowed down ina buffer gas and selectively extracted in a quadrupolemass separator [18]. Nuclear magnetic dipole and elec-tric quadrupole momenta of the m Th isomer have beendeduced from laser spectroscopy data [28]. The life-time of the m Th state for atoms deposited onto theMCP detector surface has been measured [23]. Finally,an isomer energy of 8 . m Th ions, neutralized by agraphene foil [19]. This value was deduced by combin-ing spectroscopy data of conversion electrons with calcu-lated distributions of initial/final electronic states. Thecalculated uncertainty of the initial/final electronic statedistribution significantly contributes to the uncertaintyof the reported isomer energy (0 .
16 eV).In the work presented here, we perform γ spectroscopyusing the magnetic micro-calorimeter maXs-30. It is spe-cially designed for optimal performance around 30 keV,corresponding to the γ rays produced in the U → Th α -decay. This experiment complements the conversionelectron experiment in that the isomer energy is ex-tracted directly from the experimental data, without re-sorting to calculations. The only significant uncertaintyin our experiment is the statistical error.In magnetic micro-calorimeters (MMC), the energy of a r X i v : . [ nu c l - e x ] M a y U + + + + + +
10 20 30 40 50 60
Energy (keV) . e V FWHM=10.2 eV ab c
Absorber
Sensor
Heat bath . e V L S L m L m Heat bathL i I p + 𝛿 I AbsorberEnergy input
Magne�c fieldThermal link Read-out
SQUIDSensor . e V . e V E is Th FIG. 1. (a) Partial nuclear level scheme of the
Th nucleuswith relevant decay paths and energies. The total spectrumin the energy range up to 60 keV is shown in the bottom. (b)Schematic of a magnetic micro-calorimeter. A γ ray is ab-sorbed in a gold absorber. The heat is then transferred andmeasured by a Ag:Er paramagnetic sensor. A weak thermallink to the heat bath enables thermalization. (c) A persis-tent current ( I p ) circulates in the superconducting meander-shaped pick-up coil polarizing the magnetic moment in thesensor. As the flux in a superconducting loop is conserved,a change of flux ∆Φ driven by a temperature-induced changeof magnetization induces an additional screening current ( δI ),which is readout as a voltage drop over the dc-SQUID. a γ ray is converted into heat in a thin absorber plate(see Fig. 1b). The absorbers used in this experimentare made of 20 µ m thick gold layers, realizing 65 % stop-ping efficiency at 30 keV while having 10 eV resolution.For a precise determination of the small temperature riseon the order of some hundred µ K, MMC’s make use ofa paramagnetic temperature sensor operated in a weakmagnetic field [29, 30]. As a paramagnetic sensor, we usesilver doped with a few hundred ppm of erbium.The detector is composed of 8 × temperature sensor. Twoparallel meander-shaped pick-up coils made of niobiumare connected to the input coil of a dc-SQUID currentsensor. The pick-up coils of the two sensors generateopposing currents for an equivalent magnetization change in the two sensors. The resulting screening current ( δI )in the input coil of the dc-SQUID is directly proportionalto the temperature difference of the two sensors. We readout the screening current as a linearized voltage drop overthe dc-SQUID (see Fig. 1c) [31].The γ radiation is emitted from a solution contain-ing U. Uranium is dissolved in an aqueous solutionas uranyl nitrate UO (NO ) and is contained inside aPEEK-capsule. The wall thickness of 2 mm shields α and β radiation but is transparent for photons above few keV.The activity of the source was 74 MBq, it was chemicallypurified at the Institute for Nuclear Chemistry, JohannesGutenberg University Mainz, to remove daughter prod-ucts of the uranium chain (Th, Ra, Ac) which increasethe activity and hence background in the measurement. α and γ spectroscopy (using Ge detectors) performed onthe source indicate a 2 % U and a < U con-tamination. Additionally, traces of , , Pu,
Am,
Np where identified (see supplementary material).The γ spectrum in the energy range 0–60 keV wasrecorded over about 640 pixel × days, which correspondsto about 8 million events. For each absorption event, werecorded the full pulse shape, which shows a 9 . µ s fastvoltage increase, followed by a τ = 2 . U is extracted for each event by fitting ageneric, amplitude-scaled pulse shape [32].The raw amplitude data obtained from each pixelare corrected for temperature, which is extracted fromthe simultaneously triggered asymmetric pixel-pairs lo-cated in each of the four corners of the detector (seesupplementary material). The data from individualpixels ( p ) are corrected quadratically E ( p ) = a ( p ) × (cid:0) U ( p ) + b ( p ) U ( p ) (cid:1) to account for small differences in theindividual pixel’s gain characteristics and combined intoa single dataset E [33]. The maXs-30 shows an excellentgain linearity with a nonlinearity of only about 0 . b ( p ) are ex-tracted directly from the experimental data. From en-ergy conservation within the nuclear level structure, weidentified two decay loops: 54 . . . . . . . b ( p ) are adjusted to self-consistentlyfulfill the two conditions above (see supplementary ma-terial).To convert from the amplitude U to energy E , we usethe reference lines listed in Table I. Experimentally, thelinear correction terms for every pixel a ( p ) are deter-mined by minimizing the squares of the residuals, withthe calibration points weighted by the fit and the liter-ature uncertainties (see Fig. 2). For the calibration, wehave chosen only well-resolved gamma lines. We excludedthe Th lines that are used in further data analysis andx ray lines because their energy and lineshape might beinfluenced by the chemical environment [34]. Three outof four energy calculations schemes used below are in-sensitive to the energy calibration (see Eqs. (1) to (4)).Either the difference of energy levels (Eqs. (2) and (3))is used to extract the isomer energy, or their lineshape isanalyzed Eq. (1). However, the absolute energy schemeusing Eq. (4) is sensitive to the energy calibration, and adifferent choice of calibration lines can lead to a differentresult.Experimental imperfections, i.e., nonlinearities in theanalog-to-digital conversion or detector chip inhomogene-ity, can lead to small oscillations of the residuals of theenergy calibration curve. These are too small to be quan-tified experimentally (see Fig. 2). We use the standarddeviation of calibration lines from their literature valuesto estimate the uncertainty due to the local calibrations.The calibration uncertainty of every peak is (0 .
76 eV).
Decay path Measured [eV] Reference [eV] resid. [ σ ] ref. Th(9 / + (cid:1) / + ) 25314.4(8) 25314.6(8) 0.2 [26] Np(5 / − (cid:1) / + ) 26345.3(8) 26344.6(2) 3.4 [35] Np(7 / + (cid:1) / + ) 33195.8(8) 33196.3(2) 2.2 [36] U (2 + → + ) 43496.8(8) 43498.1(10) 1.3 [37] Th(9 / + (cid:1) / + ) 53609.3(8) 53610.7(11) 1.2 [26] Th(9 / + (cid:1) / + ) 54703.0(8) 54704.0(11) 0.9 [38]TABLE I. Reference lines used in the calibration. The un-certainty for measured values is dominated by the calibrationuncertainity (0 .
76 eV). The contribution of the statistical un-certainty of the fit is negligible. The deviation from the liter-ature values is reported as the number of standard deviationsfrom the reference values [ σ ]. While higher-order nonlinearities contribute to the un-certainty of each peak’s absolute energy, there is one moreartefact affecting the lineshapes that we have to considerduring data analysis. The electronic signal after the pho-ton absorption decays faster than the temperature of thepixel. This is caused by a differential readout of the pixel-pairs and design details of the pair-wise heat-sinking ofpixels [30, 39]. If a new event occurs in the pixel-pairbefore it cooled down to idle state, the signal responseto energy input is reduced, leading to a reduced signalheight, and low energy tails in the spectrum. We miti-gated this effect during the experiment by applying thehold-off mentioned above, but small distortions from aGaussian lineshape are still present.To adequately describe the data, we use a generic line-shape based on an asymmetric Voigt profile (see supple-mentary material) that can fit all the gamma lines in thespectrum. The Gaussian function, characterized by vari-
Energy [keV] Q u a d r a � c c o rr e c � o n [ e V ]
20 30 40 50 60 -2-1012 C a li b r a � o n e rr o r [ e V ] Energy [keV]
FIG. 2. Residual uncertainty of the calibration lines with re-spect to the literature values (see Table I) before the quadraticcorrection. The residuals follow the quadratic polynomial, in-dicating that quadratic correction is sufficient. Inset: residualenergy differences after the quadratic correction. ance ( σ ), is convolved with a wider Lorentzian profileon the low energy side ( γ ) and a narrower Lorentzianprofile on the high energy side ( γ ). All three parame-ters follow a weak quadratic dependence on the energyof the line σ = σ (cid:0) cE (cid:1) and γ = γ (cid:0) cE (cid:1) .These four parameters ( σ, γ , γ , c ) were extracted froma simultaneous fit of all γ lines; they are common to allthe γ lines in the spectrum. For each individual line fit,only two free parameters are varied, the amplitude ( A )and the energy ( E ). Energy [eV] C o un t s p e r e V E is b branching ra�o [%] E n e r g y [ e V ] FIG. 3. Lineshape of the 29 . b and the isomer energy ( E is ) can be extracted directly fromthis fit. The inset shows a 2-D plot of χ as a function ofbranching ratio and the isomer energy. The white dashedlines point to the fitted E is and b values. The energy resolution of ∼
10 eV (see Fig. 1a) to-gether with the outstanding linearity (see Fig. 2) of themaXs-30 micro-calorimeter allows us to perform four dif-ferent types of data analysis to extract the
Th isomerenergy. With high resolution, we can partly resolve the29 . E is ) and the branch-ing ratio ( b ). To analyze the line doublets, we use apair of generic lineshapes from Fig. 4 and let the doubletsplitting and their relative amplitudes as free parame-ters. From their relative amplitudes, we measure thatthe 5 / + state has a significant inter-band decay proba-bility of b = 9 . . E is , lineshape = 7 . . (1)The 42 . b (cid:0) . → .
08 keV42 . → (cid:1) = b < . b = 9 . b lies in the range of theoreti-cal predictions 0 . < b <
2% [40]. There is a strongcorrelation between the E is , lineshape and b . A more ac-curate independent measurement of b combined withour experiment would further decrease the uncertaintyof the isomer energy.The second analysis makes use of the two pairs ofclosely spaced lines at 29 keV and 42 keV. Measuring thedistances of these two pairs yields the isomeric state en-ergy ( E is ) (see Fig. 4). A previous experiment performedwith a silicon semiconductor micro-calorimeter extracted E is using this scheme, however, with a much higher un-certainty due to the limited resolution and higher non-linearities [20, 21].The absolute energy scheme uncertainty of each peak isdominated by the calibration uncertainty (0 .
76 eV). Be-cause the calibration uncertainty is a slowly varying func-tion of the energy, it is significantly compensated whensubtracting energies of closely spaced lines ∆E and∆E (see Fig. 4). The lines 29 .
18 keV and 42 .
43 keV, dueto their doublet nature, are fitted with two generic line-shapes each. The relative amplitudes of these functionsare set according to known inter-band branching ratiosand the spacing is E is (see supplementary material). Theinter-band branching ratios are b = 9 . . and b = 0 . [21, 24].We obtain the isomer energy as, E is , = 206 . − . . . (2)The uncertainty emerges from the statistics of the weak29 . .
12 eV), from the uncertainty of thebranching ratio (0 .
03 eV), and from the uncertainty of
Energy [keV] C o un t s p e r e V Energy [keV] C o un t s p e r e V Np E is FIG. 4. MMC spectra of the 29 keV and 42 keV doublets. The
Np contamination leads to a weak signal (29 378 . . the Np contamination (0 .
12 eV), see supplementarymaterial.Alternatively we can extract the isomer energy as, E is , = 42 433 . −
13 242 . −
29 182 . . . (3)This method has the advantage of avoiding the weakinter-band 29 . Th to the (5/2 + ) state(inter-band transition), the excitation energy was mea-sured as 29 189 . + ) state to the isomer state: 29 182 . is , E is , abs = 29 189 . −
29 182 . . . (4)The estimated uncertainty is dominated by the cali-bration uncertainty (0 .
76 eV). This scheme was recentlyused in another experiment, reporting an isomer energyof ( E is = 8 . Th isomerstate was measured by recording a high resolution(FWHM ≈
10 eV) high bandwidth ( ∼
60 keV) γ spectrumusing a cryogenic magnetic micro-calorimeter. We ex-tracted the isomer energy using four different schemes. Acomparison of all four results with previous experimentsis summarized in Fig. 5. Weighting these results with E n e r g y ( e V ) W a v e l e n g t h ( n m ) FIG. 5. Isomer energies E is measured in this study com-pared to previous experiments using γ spectroscopy. Thegreen and red faded areas represent the isomer energy re-ported in [19, 21], respectively, with their corresponding un-certainties. Error bars for our E is represent the root sumsquare of statistical and systematic uncertainty. their statistical and systematic uncertainty and combin-ing them, we constrain the one-sigma interval for theisomer energy to be 7 .
88 eV < E is < .
16 eV. We alsomeasured the branching ratio of the second excited state b = 9 . U liquid-source container,J. Schwestka for sample preparation at TU Wien and S.Stellmer and P. Thirolf for helpful discussions. ∗ T.S. and J.G. contributed equally to this work.[1] P. G. Thirolf, B. Seiferle, and L. von der Wense, Journalof Physics B: Atomic, Molecular and Optical Physics ,203001 (2019).[2] E. Peik and M. Okhapkin, “Nuclear clocks basedon resonant excitation of γ -transitions,” (2015),arXiv:1502.07322v1.[3] E. V. Tkalya, Phys. Rev. Lett. , 162501 (2011).[4] E. Peik and C. Tamm, Europhysics Letters , 181 (2003).[5] C. J. Campbell, A. G. Radnaev, A. Kuzmich, V. A.Dzuba, V. V. Flambaum, and A. Derevianko, Phys. Rev.Lett. , 120802 (2012).[6] G. A. Kazakov, A. N. Litvinov, V. I. Romanenko,L. P. Yatsenko, A. V. Romanenko, M. Schreitl, G. Win-kler, and T. Schumm, New Journal of Physics (2012),10.1088/1367-2630/14/8/083019.[7] V. V. Flambaum, Phys. Rev. Lett. , 092502 (2006).[8] P. Thirolf, B. Seiferle, and L. Von der Wense, Annalender Physik (2019), 10.1002/andp.201970022.[9] P. Wcislo, P. Morzynski, M. Bober, A. Cygan, D. Lisak,R. Ciurylo, and M. Zawada, Nature Astronomy , 0009(2016).[10] A. Arvanitaki, J. Huang, and K. Van Tilburg, Phys.Rev. D , 015015 (2015).[11] A. Derevianko and M. Pospelov, Nature Physics (2014),10.1038/nphys3137.[12] Bondarescu, Mihai, Bondarescu, Ruxandra, Jetzer,Philippe, and Lundgren, Andrew, EPJ Web of Confer-ences , 04009 (2015).[13] Proc. 30th Intern. Tech. Meeting of the Satellite Divisionof the Institute of Navigation (Portland, OR, 2017).[14] L. von der Wense, B. Seiferle, and P. G. Thirolf, Mea-surement Techniques , 1178 (2018).[15] J. Jeet, C. Schneider, S. T. Sullivan, W. G. Rellergert,S. Mirzadeh, A. Cassanho, H. P. Jenssen, E. V. Tkalya,and E. R. Hudson, Phys. Rev. Lett. , 253001 (2015).[16] A. Yamaguchi, H. Muramatsu, T. Hayashi, N. Yuasa,K. Nakamura, M. Takimoto, H. Haba, K. Konashi,M. Watanabe, H. Kikunaga, K. Maehata, N. Y. Ya-masaki, and K. Mitsuda, Phys. Rev. Lett. , 222501(2019).[17] S. Stellmer, G. Kazakov, M. Schreitl, H. Kaser, M. Kolbe,and T. Schumm, Phys. Rev. A , 062506 (2018).[18] L. von der Wense, B. Seiferle, M. Laatiaoui, J. B. Neu-mayr, H.-J. Maier, H.-F. Wirth, C. Mokry, J. Runke,K. Eberhardt, C. E. D¨ullmann, N. G. Trautmann, andP. G. Thirolf, Nature , 47 (2016).[19] B. Seiferle, L. von der Wense, P. V. Bilous, I. Amersdorf-fer, C. Lemell, F. Libisch, S. Stellmer, T. Schumm, C. E.D¨ullmann, A. P´alffy, and P. G. Thirolf, Nature , 243(2019).[20] B. R. Beck, J. A. Becker, P. Beiersdorfer, G. V. Brown,K. J. Moody, J. B. Wilhelmy, F. S. Porter, C. A. Kil-bourne, and R. L. Kelley, Phys. Rev. Lett. , 142501(2007).[21] B. Beck, C. Wu, P. Beiersdorfer, G. Brown, J. Becker,K. Moody, J. Wilhelmy, F. Porter, C. Kilbourne, andR. Kelley, , (2009), lLNL-PROC-415170.[22] A. Yamaguchi, H. Muramatsu, T. Hayashi, N. Yuasa,K. Nakamura, M. Takimoto, H. Haba, K. Konashi,M. Watanabe, H. Kikunaga, K. Maehata, N. Y.Yamasaki, and K. Mitsuda, Physical ReviewLetters (2019), 10.1103/PhysRevLett.123.222501,arXiv:1912.05395.[23] B. Seiferle, L. von der Wense, and P. G. Thirolf, Phys.Rev. Lett. , 042501 (2017).[24] T. Masuda, A. Yoshimi, A. Fujieda, H. Fujimoto,H. Haba, H. Hara, T. Hiraki, H. Kaino, Y. Kasamatsu,S. Kitao, K. Konashi, Y. Miyamoto, K. Okai, S. Okubo,N. Sasao, M. Seto, T. Schumm, Y. Shigekawa, K. Suzuki,S. Stellmer, K. Tamasaku, S. Uetake, M. Watanabe, T. Watanabe, Y. Yasuda, A. Yamaguchi, Y. Yoda,T. Yokokita, M. Yoshimura, and K. Yoshimura, Nature , 238 (2019).[25] L. Kroger and C. Reich, Nuclear Physics A , 29(1976).[26] R. G. Helmer and C. W. Reich, Physical Review C ,1845 (1994).[27] Z. O. Guimar˜aes Filho and O. Helene, Phys. Rev. C ,044303 (2005).[28] J. Thielking, M. V. Okhapkin, P. Glowacki, D. M. Meier,L. von der Wense, B. Seiferle, C. E. D¨ullmann, P. G.Thirolf, and E. Peik, Nature , 321 (2018).[29] A. Fleischmann, C. Enss, and G. M. Seidel, “Metal-lic Magnetic Calorimeters,” in Cryogenic Particle De-tection , edited by C. Enss (Springer Berlin Heidelberg,Berlin, Heidelberg, 2005) pp. 151–216.[30] A. Fleischmann, L. Gastaldo, S. Kempf, A. Kirsch,A. Pabinger, C. Pies, J. P. Porsf, P. Ranitzsch, S. Sch¨afer,F. V. Seggern, T. Wolf, C. Enss, and G. M. Seidel, in
AIP Conference Proceedings , Vol. 1185 (American Insti-tute of Physics, 2009) pp. 571–578.[31] S. Kempf, M. Wegner, L. Deeg, A. Fleischmann,L. Gastaldo, F. Herrmann, D. Richter, and C. Enss, Su-perconductor Science and Technology , 065002 (2017).[32] C. Enss, A. Fleischmann, K. Horst, J. Sch¨onefeld, J. Soll- ner, J. S. Adams, Y. H. Huang, Y. H. Kim, and G. M.Seidel, Journal of Low Temperature Physics , 137(2000).[33] C. R. Bates, C. Pies, S. Kempf, D. Hengstler, A. Fleis-chmann, L. Gastaldo, C. Enss, and S. Friedrich, AppliedPhysics Letters , 023513 (2016).[34] J. Campbell, Nuclear Instruments and Methods inPhysics Research Section B: Beam Interactions with Ma-terials and Atoms , 115 (1990).[35] R. G. Helmer and C. Van Der Leun, Nuclear Instrumentsand Methods in Physics Research, Section A: Acceler-ators, Spectrometers, Detectors and Associated Equip-ment (2000), 10.1016/S0168-9002(00)00252-7.[36] M. Basunia, Nuclear Data Sheets , 2323 (2006).[37] E. Browne and J. Tuli, Nuclear Data Sheets , 681(2007).[38] V. Barci, G. Ardisson, G. Barci-Funel, B. Weiss,O. El Samad, and R. K. Sheline, Phys. Rev. C , 034329(2003).[39] A. G. Kozorezov, C. J. Lambert, S. R. Bandler, M. A.Balvin, S. E. Busch, P. N. Nagler, J.-P. Porst, S. J. Smith,T. R. Stevenson, and J. E. Sadleir, Phys. Rev. B ,104504 (2013).[40] E. V. Tkalya, C. Schneider, J. Jeet, and E. R. Hudson,Phys. Rev. C , 054324 (2015). easurement of the Th isomer energy with a magnetic micro-calorimeter
Tomas Sikorsky,
1, 2, ∗ Jeschua Geist, ∗ Daniel Hengstler, Sebastian Kempf, Loredana Gastaldo, ChristianEnss, Christoph Mokry,
3, 4
J¨org Runke,
3, 5
Christoph E. D¨ullmann,
3, 4, 5
Peter Wobrauschek, Kjeld Beeks, Veronika Rosecker, Johannes H. Sterba, Georgy Kazakov, Thorsten Schumm, and Andreas Fleischmann Kirchhoff-Institute for Physics, Heidelberg University, INF 227, 69120 Heidelberg, Germany Institute for Atomic and Subatomic Physics, TU Wien, Stadionallee 2, 1020, Vienna, Austria Johannes Gutenberg University, 55099 Mainz, Germany. Helmholtz Institute Mainz, 55099 Mainz, Germany. GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany (Dated: May 28, 2020)
Sample contamination
The
U source was chemically purified to removedaughter products of
Am and
U. After purification,we detected molar ratios U / U = 2 × − , U / U =1 × − , Pu / U = 7 × − , Pu / U = 1 × − , Am / U = 7 × − and Np / U =8 . × − .The Np contamination is important because it pro-duces a line at 29 378 . . U decay.
80 85 90 95
Energy (keV) c o un t s
85 86 87 88 89
Energy (keV) c o un t s data fit w/o Np Np FIG. 1. A γ spectrum of the sample recorded using an HPGedetector. After subtracting , , U and their daughterelements, a signal at 86 . This appears in the spectrum as an anomalous lowenergy tail of the 29 . Np background, we need to measure its concen-tration. To get the concentration we fit the 29 . Np / U =8 . × − .To confirm the Np concentration we recorded an-other γ spectrum in the energy range 0–100 keV us- ing a liquid nitrogen-cooled High Purity Ge detector(HPGe) Intertechnique (see Fig. 1). In the spectrum weidentify the Pa(5 / + → / − ) 86 . Np / U =8 . × − . Combining these two mea-surements we obtained the Np / U =8 . × − molar concentration, which was used in the data anal-ysis. Signal processing
The signal rise after the γ photon absorption event isdetermined by the thermal conductivity of the region be-tween the absorber and the sensor, resulting in an ex-pected signal rise time of about τ = 9 . µ s. The ACsignal decay is 0 .
75 ms and DC signal decays in 2 . time [μs] time [ms] P u l s e a m p l i t u d e [ V ] P u l s e a m p l i t u d e [ V ] FIG. 2. Left: Closeup of the first 50 µ s of a single pulse afterthe absorption of a γ photon. The red line shows the exponen-tial fit τ = 9 . µ s. Right: The first 30 ms of the signal decay.The red line shows the exponential fit of the DC-coupled sig-nal, and the green line shows the AC-coupled signal. Detector anatomy
The maXs-30 detector was fabricated at Kirchhoff Insti-tute for Physics, Heidelberg [1]. It is cooled to an operat-ing temperature of 12 mK by a dry dilution refrigerator.The
U source is placed outside the cryostat behind apolyimide window, yielding a count rate of ≈ a r X i v : . [ nu c l - e x ] M a y in-house [2]. The two-stage SQUID channels are readout at room temperature by SQUID-electronics of typeXXF-1 and a 16-channel digitizer card SIS3316 with abandwidth of up to 125 MHz and a resolution of 16 bit.It is composed of 8 × FIG. 3. Layout of the maXs-30 detector chip with a closeupshowing one quadrant of the chip: (1) absorber; (2) temper-ature sensor; (3) read-out lines; (4) connecting lines for thepersistent current; (5) contacts for the individual lines. providing a total active area of 4 mm × µ m, result-ing in a 65 % stopping power at 30 keV to reach a goodcompromise between energy resolution and detection ef-ficiency. In each of the four corners, a pixel-pair allowsto detect and correct for temperature fluctuations of thedetector chip.Since the U source cannot be installed inside thecryostat, the outer shield has been equipped with an xray window made of 150- µ m thick polyimide, enablinghigh-energy photons to enter the cryostat. The innerradiation shields have holes with x ray windows made of6- µ m thin mylar foil coated with about 40 nm aluminum.A 1-mm thick aluminum container encloses the detectorplatform and acts as a superconducting shield againstexternal electromagnetic perturbations. Additionally, itreduces the count rate for photons below the γ , lineat 29.19 keV where the spectrum is dominated by x raysfrom electron shell transitions. Energy calibration
The energy calibration was constrained to maintain theenergy conservation in the
Th nuclear level structure.The five transitions that were used are shown in Fig. 4.
Self-consistent isomer energy calculation
The absolute, the 3-lines, and the 4-lines schemes requirean isomer energy as an input. For each scheme, we em- ploy the self-consistent iterative approach to calculatethe energy. This method is very robust, as the sensitiv-ity of the output energy on the input energy is quite low(0 .
02 eV eV − ) (see Fig. 5). Th . e V + + + + + + . e V . e V FIG. 4. Partial nuclear level scheme of the
Th with relevantdecay paths and energies. The levels that were used for thecalibration of the quadratic term ( b ) are highlighted. Input energy [eV] O u t pu t e n e r g y [ e V ] FIG. 5. The sensitivity of the output isomer energy ( E is ) onthe input isomer energy. The blue line represents the 4-linesscheme, the red line represents the 3-lines scheme, and thegreen line represents the absolute energy calculation scheme. Generic lineshape
The asymmetric Voigt profile is constructed by asym-metrically convoluting a Lorentz with a Gaussian distri-bution (see Fig. 7). The Gaussian distribution ( σ =4 .
06 eV) is convoluted with a Lorentz profile (Γ =0 .
72 eV) on the low energy side and (Γ = 0 .
52 eV) on thehigh energy side. These terms scale quadratically withenergy as c = 1 . × − eV − (see Fig. 6). Energy [keV] F W H M [ e V ] FIG. 6. Full width at half maximum (FWHM) of the genericlineshape as a function of energy. The linewidth scales withenergy as FWHM=9 .
87 eV+ c · E . At the 29 . . C o un t s p e r e V C o un t s p e r e V FWHM=10.4 eV
Energy [eV]
FIG. 7. Asymmetric Voigt fits of the calibration lines. The inset shows the comparison of the Gaussian (red) and asymmetricVoigt fit (black). The spacing between minor ticks is 5 eV.
Error calculation summary
Value Total error Statistical Branching ratio Np concentration Fluctuation4-lines subtraction 8.10 0.17 0.12 0.03 n/a3-lines subtraction 8.08 1.34 0.25 0.02 n/a
Absolute energy 7.79 0.76 0.02 0.02 n/a
Lineshape 7.84 0.29 0.20 n/a n/aTABLE I. Summary of the various contributions to the uncertainty for each scheme to derive the isomer energy. The mostdominant contribution for each scheme is marked in bold. ∗ T.S. and J.G. contributed equally to this work.[1] D. Hengstler,