Skip to main content

The electron capture in 163Ho experiment – ECHo

Abstract

Neutrinos, and in particular their tiny but non-vanishing masses, can be considered one of the doors towards physics beyond the Standard Model. Precision measurements of the kinematics of weak interactions, in particular of the 3H β-decay and the 163Ho electron capture (EC), represent the only model independent approach to determine the absolute scale of neutrino masses. The electron capture in 163Ho experiment, ECHo, is designed to reach sub-eV sensitivity on the electron neutrino mass by means of the analysis of the calorimetrically measured electron capture spectrum of the nuclide 163Ho. The maximum energy available for this decay, about 2.8 keV, constrains the type of detectors that can be used. Arrays of low temperature metallic magnetic calorimeters (MMCs) are being developed to measure the 163Ho EC spectrum with energy resolution below 3 eV FWHM and with a time resolution below 1 μs. To achieve the sub-eV sensitivity on the electron neutrino mass, together with the detector optimization, the availability of large ultra-pure 163Ho samples, the identification and suppression of background sources as well as the precise parametrization of the 163Ho EC spectrum are of utmost importance. The high-energy resolution 163Ho spectra measured with the first MMC prototypes with ion-implanted 163Ho set the basis for the ECHo experiment. We describe the conceptual design of ECHo and motivate the strategies we have adopted to carry on the present medium scale experiment, ECHo-1K. In this experiment, the use of 1 kBq 163Ho will allow to reach a neutrino mass sensitivity below 10 eV/c 2. We then discuss how the results being achieved in ECHo-1k will guide the design of the next stage of the ECHo experiment, ECHo-1M, where a source of the order of 1 MBq 163Ho embedded in large MMCs arrays will allow to reach sub-eV sensitivity on the electron neutrino mass.

References

  1. Y. Fukuda et al., Super Kamiokande Collaboration, Phys. Rev. Lett. 81, 1562 (1998)

    ADS  Article  Google Scholar 

  2. Q.R. Ahmad et al., (SNO collaboration), Phys. Rev. Lett. 89, 011301 (2002)

    ADS  Article  Google Scholar 

  3. G.L. Fogli et al., Phys. Rev. D 84, 053007 (2011)

    ADS  Article  Google Scholar 

  4. K.N. Abazajian et al., Astropart. Phys. 35, 177 (2011)

    ADS  Article  Google Scholar 

  5. F.T. Avignone III et al., Rev. Mod. Phys. 80, 481 (2008)

    ADS  Article  Google Scholar 

  6. F. Simkovic et al., Phys. Rev. C 77, 045503 (2008)

    ADS  Article  Google Scholar 

  7. S. Eliseev et al., J. Phys. G: Nucl. Part. Phys. 39, 124003 (2012)

    ADS  Article  Google Scholar 

  8. G. Pagliaroli et al., Astropart. Phys. 33, 287 (2010)

    ADS  Article  Google Scholar 

  9. G. Drexlin et al., Adv. High Ener. Phys. 2013, 293986 (2013)

    Google Scholar 

  10. KATRIN Design Report, FZKA7090 (2004)

  11. Ch. Kraus et al., Eur. Phys. J. C 40, 447 (2005)

    ADS  Article  Google Scholar 

  12. Ch. Weinheimer, Prog. Part. Nucl. Phys. 57, 22 (2006)

    ADS  Article  Google Scholar 

  13. N. Aseev et al., Phys. Rev D 84, 112003 (2011)

    ADS  Article  Google Scholar 

  14. D.M. Asner et al., Phys. Rev. Lett. 114, 162501 (2015)

    ADS  Article  Google Scholar 

  15. S. Betts et al., arXiv:1307.4738[astro-ph.IM]

  16. P.T. Springer et al., Phys. Rev. A 35, 679 (1987)

    ADS  Article  Google Scholar 

  17. C.W. Reich, B. Singh, Nuclear Data Sheets 111, 1211 (2010)

    ADS  Article  Google Scholar 

  18. P.A. Baisden et al., Phys. Rev. C 28, 337 (1983)

    ADS  Article  Google Scholar 

  19. G. Audi et al., The Ame2012 atomic mass evaluation, Chinese Phys. C 36, 1157 (2012)

    Article  Google Scholar 

  20. J.U. Andersen et al., Phys. Lett. B 113, 72 (1982)

    ADS  Article  Google Scholar 

  21. F. Gatti et al., Phys. Lett. B 398, 415 (1997)

    ADS  Article  Google Scholar 

  22. P.C.-O. Ranitzsch et al., J. Low Temp. Phys. 167, 1004 (2012)

    ADS  Article  Google Scholar 

  23. S. Eliseev et al., Phys. Rev. Lett. 115, 062501 (2015)

    ADS  Article  Google Scholar 

  24. A. Faessler et al., Phys. Rev. C 91, 064302 (2015)

    ADS  Article  Google Scholar 

  25. C.L. Bennett et al., Phys. Lett. B 107, 19 (1981)

    ADS  Article  Google Scholar 

  26. S. Yasumi et al., Phys. Lett. B 122, 461 (1983)

    ADS  Article  Google Scholar 

  27. S. Yasumi et al., Phys. Lett. B 334, 229 (1994)

    ADS  Article  Google Scholar 

  28. A. De Rujula, M. Lusignoli, Phys. Lett. B 118, 429 (1982)

    ADS  Article  Google Scholar 

  29. A. De Rujula, arXiv:1305.4857 (2013)

  30. E. Laegsgaard et al., Proceeding of 7th International Conference on Atomic Masses and Fundamental Constants (AMCO-7) (1984)

  31. F.X. Hartmann, R.A. Naumann, Nucl. Instr. Meth. A 13, 237 (1992)

    ADS  Article  Google Scholar 

  32. L. Gastaldo et al., Nucl. Inst. and Meth. A 711, 150 (2013)

    ADS  Article  Google Scholar 

  33. L. Gastaldo et al., J. Low Temp. Phys. 176, 876 (2014)

    ADS  Article  Google Scholar 

  34. B. Alpert et al., Eur. Phys. J. C 75, 112 (2015)

    ADS  Article  Google Scholar 

  35. http://p25ext.lanl.gov/kunde/NuMECS/

  36. M.P. Croce et al., J. Low Temp. Phys. 184, 938 (2016)

    ADS  Article  Google Scholar 

  37. R.G.H. Robertson, Phys. Rev. C 91, 035504 (2015)

    ADS  Article  Google Scholar 

  38. A. Faessler, F. Simkovic, Phys. Rev. C 91, 045505 (2015)

    ADS  Article  Google Scholar 

  39. A. De Rujula, M. Lusignoli, arXiv:1510.05462 (2015)

  40. A. De Rujula, M. Lusignoli, arXiv:1601.04990 (2016)

  41. A. Faessler et al., J. Phys. G 42, 015108 (2015)

    ADS  Article  Google Scholar 

  42. R.D. Deslattes et al., Rev. Mod. Phys. 75, 35 (2003)

    ADS  Article  Google Scholar 

  43. A. Thompson et al., X-ray data booklet (2009), xdb.lbl.gov

  44. J. Campbell, T. Papp, At. Data Nucl. Data Tables 77, 1 (2001)

    ADS  Article  Google Scholar 

  45. R.L. Cohen et al., Phys. Rev. B 5, 1037 (1972)

    ADS  Article  Google Scholar 

  46. M. Lusignoli, M. Vignati, Phys. Lett. B 697, 11 (2011)

    ADS  Article  Google Scholar 

  47. A. Fleischmann et al., in Cryogenic Particle Detection (Springer Topics in Applied Physics 99) ed EnssC (Berlin: Springer) (2005), p. 151

  48. A. Fleischmann et al., AIP Conf. Proc. 1185, 571 (2009)

    ADS  Article  Google Scholar 

  49. C. Pies et al., J. Low Temp. Phys. 167, 269 (2012)

    ADS  Article  Google Scholar 

  50. J.A.B. Mates et al., Appl. Phys. Lett. 92, 023514 (2008)

    ADS  Article  Google Scholar 

  51. A. Fleischmann et al., in preparation

  52. C. Enss, in Cryogenic Particle Detection, Top. Appl. Phys. (2005), Vol. 99

  53. A. Enss, D. Mac Cammon, J. Low Temp. Phys. 151, 5 (2008)

    ADS  Article  Google Scholar 

  54. K.D. Irwin, G.C. Hilton, Top. Appl. Phys. 99, 63 (2005)

    Google Scholar 

  55. J.-P. Porst et al., J. Low Temp. Phys. 176, 617 (2014)

    ADS  Article  Google Scholar 

  56. J.-P. Porst et al., Nucl. Phys. B (Proc. Suppl.) 229-232, 446 (2012)

    ADS  Article  Google Scholar 

  57. L. Gastaldo et al., AIP Conf. Proc. 1185, 607 (2009)

    ADS  Article  Google Scholar 

  58. A. Fleischmann et al., J. Low Temp. Phys. 118, 7 (2000)

    ADS  Article  Google Scholar 

  59. G. Hölzer et al., Phys. Rev. A 56, 4554 (1997)

    ADS  Article  Google Scholar 

  60. E. Kugler, Hyperfine Interact. 129, 23 (2000)

    ADS  Article  Google Scholar 

  61. A.G. Kozorezov et al., Phys. Rev. B 87, 104504 (2013)

    ADS  Article  Google Scholar 

  62. P.C.-O. Ranitzsch, arXiv:1409.0071[physics.ins-det] (2014)

  63. D. Drung et al., IEEE Trans. Appl. Supercond. 17, 699 (2007)

    ADS  Article  Google Scholar 

  64. C. Hassel et al., J. Low Temp. Phys. 184, 910 (2016)

    ADS  Article  Google Scholar 

  65. K. Prasai et al., Rev. Sci. Instr. 84, 083905 (2013)

    ADS  Article  Google Scholar 

  66. I.M. Band, M.B. Trzhaskovskaya, Atomic Data and Nuclear Data Tables 35, 1 (1986)

    ADS  Article  Google Scholar 

  67. J. Clarke, A.I. Braginski, eds., in The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems (Wiley-VCH, Weinheim, 2004)

  68. S. Kempf et al., Supercond. Sci. Technol. 28, 045008 (215)

  69. D. Drung, M. Mück, SQUID electronics in The SQUID Handbook: Fundamentals and Technology of SQUIDs and SQUID Systems, edited by J. Clarke and A.I. Braginski (Wiley-VCH, Weinheim, 2004)

  70. S.R. Bandler et al., J. Low Temp. Phys. 167, 254 (2012)

    ADS  Article  Google Scholar 

  71. J. Beyer, D. Drung, Supercond. Sci. Technol. 21, 105022 (2008)

    ADS  Article  Google Scholar 

  72. J.-P. Porst et al., IEEE Trans. Appl. Supercond. 23, 2500905 (2013)

    Article  Google Scholar 

  73. K.D. Irwin, K.W. Lehnert, Appl. Phys. Lett. 85, 2107 (2004)

    ADS  Article  Google Scholar 

  74. K.W. Lehnert et al., IEEE Trans. Appl. Supercond. 17, 705 (2007)

    ADS  Article  Google Scholar 

  75. J.M. Goodkind, D.L. Stolfa, Rev. Sci. Instrum. 41, 799 (1970)

    ADS  Article  Google Scholar 

  76. P.K. Hansma, J. Appl. Phys. 44, 4191 (1973)

    ADS  Article  Google Scholar 

  77. R. Rifkin et al., J. Appl. Phys. 47, 2645 (1976)

    ADS  Article  Google Scholar 

  78. S. Kempf et al., J. Low Temp. Phys. 175, 850 (2014)

    ADS  Article  Google Scholar 

  79. J.A.B. Mates et al., J. Low Temp. Phys. 167, 707 (2012)

    ADS  Article  Google Scholar 

  80. B.A. Mazin et al., Nucl. Instr. Meth. A 559, 799 (2006)

    ADS  Article  Google Scholar 

  81. S.J.C. Yates et al., Appl. Phys. Lett. 95, 042504 (2009)

    ADS  Article  Google Scholar 

  82. R. Duan et al., Proc. of SPIE 7741, 77411 (2010)

    Article  Google Scholar 

  83. S. Kempf et al., J. Low Temp. Phys. 176, 426 (2014)

    ADS  Article  Google Scholar 

  84. S. Kempf et al., AIP Advances 7, 015007 (2017)

    ADS  Article  Google Scholar 

  85. C. Bueno, Radiographic Testing, in Nondestructive testing handbook, 3rd edn (The American Society for Nondestructive Testing, Columbus, OH, USA, 2002), Vol. 4

  86. D. Rowe, Appl. Energ. 40, 241 (1991)

    Article  Google Scholar 

  87. J. Runke et al., J. Radioanal. Nucl. Chem. 299, 1081 (2014)

    Article  Google Scholar 

  88. J. Magill et al., Karlsruher Nuklidkarte, 8th edn. (Nucleonica GmbH, 76344 Eggenstein-Leopoldshafen, Germany, 2012)

  89. J.W. Engle et al., Nucl. Instrum. Meth. B 311, 131 (2013)

    ADS  Article  Google Scholar 

  90. S. Niese et al., J. Radioanal. Nucl. Chem. 233, 167 (1998)

    Article  Google Scholar 

  91. G. Heusser. Annu. Rev. Nucl. Part. Sci. 45, 543 (1995)

    ADS  Article  Google Scholar 

  92. J. Korkisch. CRC Handbook of Ion Exchange Resins, Vol. I-V (CRC Press, Boca Raton, FL, USA, 1988)

  93. V. Mocko et al., Radiochim. Acta 103, 577 (2015)

    Article  Google Scholar 

  94. H.L. Ravn et al., AIP Conf. Proc. 99, 1 (1983)

    ADS  Article  Google Scholar 

  95. M. Fujioka et al., CYRIC Ann. Rep. 1981, 25 (1981)

    Google Scholar 

  96. M. Blann, H.K. Vonach, Phys. Rev. C 28, 1475 (1983)

    ADS  Article  Google Scholar 

  97. K. Katsube et al., CYRIC Ann. Rep. 1982, 28 (1982)

    Google Scholar 

  98. F. Tárkányi et al., Appl. Radiat. Isot. 98, 87 (2015)

    Article  Google Scholar 

  99. O. Kawakami et al., Phys. Rev. C 38, 1857 (1988)

    ADS  Article  Google Scholar 

  100. A. Koning et al., TALYS-1.0 (EDP Sciences, 2007), p. 58

  101. Z. Szucs et al., in Proceedings of the third international conference on application of radiotracers and energetic beams in sciences: extended abstracts of the plenary lectures and contributed papers (2014)

  102. M. Maiti et al., in International Conference on Modern Trends in Activation Analysis 14 (MTAA 14) (2015)

  103. M. Maiti et al., J. Radioanal. Nucl. Chem. 307, 1667 (2016)

    Article  Google Scholar 

  104. S. Lahiri et al., Appl. Radiat. Isot. 51, 27 (1999)

    Article  Google Scholar 

  105. S. Lahiri et al., Appl. Radiat. Isot. 61, 1157 (2004)

    Article  Google Scholar 

  106. R.A. Naumann et al., J. Inorg. Nucl. Chem. 15, 195 (1960)

    Article  Google Scholar 

  107. N. Holden, Neutron Scattering and Absorption Properties, in CRC Handbook of Chemistry and Physics, cd-rom edn. (CRC Press, Boca Raton, FL, USA, 2006), p. 11

  108. U. Köster et al., Radiother. Oncol. 102, S102 (2012)

    Article  Google Scholar 

  109. P. Armbruster et al., Phys. Rev. Lett. 54, 406 (1985)

    ADS  Article  Google Scholar 

  110. N. Trautmann, H. Folger, Nucl. Instrum. Meth. A 282, 102 (1989)

    ADS  Article  Google Scholar 

  111. K. Eberhardt et al., Nucl. Instrum. Meth. A 521, 208 (2004)

    ADS  Article  Google Scholar 

  112. K. Zimmer. Ph.D. thesis, Johannes Gutenberg-Universität Mainz, 1995

  113. F. Schneider et al., Nucl. Instrum. Meth. B 376, 388 (2016)

    ADS  Article  Google Scholar 

  114. H. Dorrer et al., to be submitted in Radiochim. Acta

  115. L. Monz et al., Spectrochim. Acta B 48, 1655 (1993)

    ADS  Article  Google Scholar 

  116. K. Wendt. Eur. J. Mass Spectrom. 8, 273 (2002)

    Article  Google Scholar 

  117. T. Gottwald et al., AIP Conf. Proc. 1104, 138 (2009)

    ADS  Article  Google Scholar 

  118. T. Kieck et al., to be submitted to NIM B

  119. D. Liebe et al., Nucl. Instrum. Meth. A 590, 145 (2008)

    ADS  Article  Google Scholar 

  120. F. Schneider et al., Eur. Phys. J. A 51, 89 (2015)

    ADS  Article  Google Scholar 

  121. J. Repp et al., Appl. Phys. B 107, 983 (2012)

    ADS  Article  Google Scholar 

  122. C. Sailer, Diploma thesis, Physikalisches Institut der Eberhard Karls Universität Tübingen, 2008

  123. M. Köhler et al., Appl. Rad. Isot. 67, 736 (2009)

    Article  Google Scholar 

  124. S. Agostinelli et al., Nucl. Instr. Meth. A 506, 250 (2003)

    ADS  Article  Google Scholar 

  125. J. Allison et al., IEEE Trans. Nucl. Sci. 53, 270 (2006)

    ADS  Article  Google Scholar 

  126. D.S. Leonard et al. (EXO-Collaboration), Nucl. Inst. Meth. A 591, 490 (2008)

    ADS  Article  Google Scholar 

  127. International Commission on Radiation Units and Measurements, Stopping Powers for Electrons and Positrons, ICRU Report 37 (1984)

  128. http://www.nndc.bnl.gov/

  129. C.M. Baglin, Nuclear Data Sheets for A = 166, Nucl. Data Sheets 109, 1103 (2008)

    ADS  Article  Google Scholar 

  130. S.Y.F. Chu, L.P. Ekström, R.B. Firestone, The Lund/LBNL Nuclear Data Search, Version 2.0, Feb. 1999, http://nucleardata.nuclear.lu.se/toi/xray.asp

  131. K. Blaum, Phys. Rep. 425, 1 (2006)

    ADS  Article  Google Scholar 

  132. K. Blaum et al., Phys. Scr. T152, 014017 (2013)

    ADS  Article  Google Scholar 

  133. L.S. Brown, G. Gabrielse, Rev. Mod. Phys. 58, 233 (1986)

    ADS  Article  Google Scholar 

  134. L.S. Brown, G. Gabrielse, Phys. Rev. A 25, 2423 (1982)

    ADS  Article  Google Scholar 

  135. M. König et al., Int. J. Mass Spectrom. 142, 95 (1995)

    ADS  Article  Google Scholar 

  136. K. Blaum et al., Eur. Phys. J. A 15, 245 (2002)

    ADS  Article  Google Scholar 

  137. H. Dehmelt, F. Walls, Phys. Rev. Lett. 21, 127 (1968)

    ADS  Article  Google Scholar 

  138. M. Kretzschmar, Int. J. Mass Spectrom. 264, 122 (2007)

    ADS  Article  Google Scholar 

  139. S. George et al., Phys. Rev. Lett. 98, 162501 (2007)

    ADS  Article  Google Scholar 

  140. S. George et al., Int. J. Mass Spectrom. 264, 110 (2007)

    ADS  Article  Google Scholar 

  141. S. Eliseev et al., Phys. Rev. Lett. 110, 082501 (2013)

    ADS  Article  Google Scholar 

  142. S. Eliseev et al., Appl. Phys. B 114, 107 (2014)

    ADS  Article  Google Scholar 

  143. M. Block et al., Eur. Phys. J. D 45, 39 (2007)

    ADS  Article  Google Scholar 

  144. W. Shi et al., Phys. Rev. A 72, 022510 (2005)

    ADS  Article  Google Scholar 

  145. S. Streubel et al., Appl. Phys. B 114, 137 (2014)

    ADS  Article  Google Scholar 

  146. S. Sturm et al., Nature 506, 467 (2014)

    ADS  Article  Google Scholar 

  147. F. Hartmann, R. Naumann Phys. Rev. C 31, 1594 (1985)

    ADS  Article  Google Scholar 

  148. S. Yasumi et al., Phys. Lett. B 181, 169 (1986)

    ADS  Article  Google Scholar 

  149. F. Bosch, M. Jung, GSI Annual Rep. 65, 1993

  150. J. Ketelaer et al., Nucl. Instr. Meth. A 594, 162 (2008)

    ADS  Article  Google Scholar 

  151. A. Chaudhuri et al., Eur. Phys. J. D 45, 47 (2007)

    ADS  Article  Google Scholar 

  152. G. Savard et al., Phys. Lett. A 158, 247 (1991)

    ADS  Article  Google Scholar 

  153. K. Blaum et al., J. Phys. B 36, 921 (2003)

    ADS  Article  Google Scholar 

  154. C. Roux et al., Appl. Phys. B 107, 997 (2012)

    ADS  Article  Google Scholar 

  155. Th. A. Carlson et al., Phys. Rev. 169, 27 (1968)

    ADS  Article  Google Scholar 

  156. Th. A. Carlson, C. W. Nestor, Phys. Rev. A 8, 2887 (1973)

    ADS  Article  Google Scholar 

  157. I. P. Grant, Adv. Phys. 19, 747 (1970)

    ADS  Article  Google Scholar 

  158. J. P. Desclaux, Comp. Phys. Com. 9, 31 (1975)

    ADS  Article  Google Scholar 

  159. A.L. Ankudinov et al., Comp. Phys. Com. 98, 359 (1996)

    ADS  Article  Google Scholar 

  160. P.-O. Loewdin Phys. Rev. Lett. 97, 1474 (1955)

    ADS  Google Scholar 

  161. E. Vatai, Nucl. Phys. A156, 541 (1970)

    ADS  Article  Google Scholar 

  162. E. Vatai, Nucl. Phys. A402, 1 (1983)

    ADS  Article  Google Scholar 

  163. K. Blaum K et al., Contem. Phys. 51, 149 (2010)

    ADS  Article  Google Scholar 

  164. www.dreebit.com

  165. J.R. Crespo Lopez-Urrutia et al., Hyperfine Interact. 127, 497 (2000)

    ADS  Article  Google Scholar 

  166. S. Sturm et al., Phys. Rev. Lett. 107, 143003 (2011)

    ADS  Article  Google Scholar 

  167. K.N. Abazajian et al., arXiv:1204.5379 [hep-ph] (2012)

  168. S. Gariazzo et al., J. Phys. G 43, 033001 (2016)

    ADS  Article  Google Scholar 

  169. R. Adhikari et al., JCAP 01, 025 (2017)

    ADS  Article  Google Scholar 

  170. L. Gastaldo et al., JHEP 06, 061 (2016)

    ADS  Article  Google Scholar 

  171. C. Giunti et al., Phys. Rev. D 86, 113014 (2012)

    ADS  Article  Google Scholar 

  172. C. Giunti et al., Phys. Rev. D 87, 013004 (2013)

    ADS  Article  Google Scholar 

  173. C. Kraus et al., Eur. Phys. J. C 73, 2323 (2013)

    ADS  Article  Google Scholar 

  174. A.I. Belesev et al., JETP Lett. 97, 67 (2013)

    ADS  Article  Google Scholar 

  175. A.I. Belesev et al., J. Phys. G 41, 015001 (2014)

    ADS  Article  Google Scholar 

  176. A. Esmaili, O. Peres, Phys. Rev. D 85, 117301 (2012)

    ADS  Article  Google Scholar 

  177. P.E. Filianin et al., J. Phys. G 41, 095004 (2014)

    ADS  Article  Google Scholar 

  178. L. Fleischmann et al., IEEE Trans. Appl. Supercond. 19, 63 (2009)

    ADS  Article  Google Scholar 

  179. P. Filianin et al., Phys. Lett. B 758, 457 (2016)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to L. Gastaldo.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gastaldo, L., Blaum, K., Chrysalidis, K. et al. The electron capture in 163Ho experiment – ECHo. Eur. Phys. J. Spec. Top. 226, 1623–1694 (2017). https://doi.org/10.1140/epjst/e2017-70071-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2017-70071-y