Line shape analysis of the Kβ transition in muonic hydrogen

The European Physical Journal D volume 72, Article number: 72 (2018) Cite this article

Abstract

The Kβ transition in muonic hydrogen was measured with a high-resolution crystal spectrometer. The spectrum is shown to be sensitive to the ground-state hyperfine splitting, the corresponding triplet-to-singlet ratio, and the kinetic energy distribution in the 3p state. The hyperfine splitting and triplet-to-singlet ratio are found to be consistent with the values expected from theoretical and experimental investigations and, therefore, were fixed accordingly in order to reduce the uncertainties in the further reconstruction of the kinetic energy distribution. The presence of high-energetic components was established and quantified in both a phenomenological, i.e. cascade-model-free fit, and in a direct deconvolution of the Doppler broadening based on the Bayesian method.

Graphical abstract

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

42,99 €

Tax calculation will be finalised during checkout.

References

  1. 1.

    H. Anderhub et al., Phys. Lett. B 143, 65 (1984)

    ADS  Article  Google Scholar 

  2. 2.

    N. Bregant et al., Phys. Lett. A 241, 344 (1998)

    ADS  Article  Google Scholar 

  3. 3.

    B. Lauss et al., Phys. Rev. Lett. 80, 3041 (1998)

    ADS  Article  Google Scholar 

  4. 4.

    E. Borie, M. Leon, Phys. Rev. A 21, 1460 (1980)

    ADS  Article  Google Scholar 

  5. 5.

    L. Bracchi, G. Fiorentini, Nuovo Cim. A 43, 9 (1978)

    ADS  Article  Google Scholar 

  6. 6.

    J.B. Czirr et al., Phys. Rev. 130, 341 (1963)

    ADS  Article  Google Scholar 

  7. 7.

    A. Badertscher et al., Europhys. Lett. 54, 313 (2001), and references therein

    ADS  Article  Google Scholar 

  8. 8.

    Th. Siems et al., Phys. Rev. Lett. 84, 4573 (2000)

    ADS  Article  Google Scholar 

  9. 9.

    D. Gotta, Prog. Part. Nucl. Phys. 52, 133 (2004)

    ADS  Article  Google Scholar 

  10. 10.

    D.S. Covita et al., Phys. Rev. Lett. 102, 023401 (2009)

    ADS  Article  Google Scholar 

  11. 11.

    PSI proposal R-98-01, www.fz-juelich.de/ikp/exotic-atoms

  12. 12.

    D. Gotta et al., Lect. Notes Phys. 745, 165 (2008)

    ADS  Article  Google Scholar 

  13. 13.

    Th. Strauch et al., Phys. Rev. Lett. 104, 142503 (2010)

    ADS  Article  Google Scholar 

  14. 14.

    Th. Strauch et al., Eur. Phys. J. A 87, 88 (2011)

    ADS  Article  Google Scholar 

  15. 15.

    J. Gasser, V.E. Lyubovitskij, A. Rusetsky, Phys. Rep. 456, 167 (2008)

    ADS  Article  Google Scholar 

  16. 16.

    T.S. Jensen, V.E. Markushin, Eur. Phys. J. D 21, 271 (2002)

    ADS  Article  Google Scholar 

  17. 17.

    T.S. Jensen, V.N. Pomerantsev, V.P. Popov, arXiv:nucl-th/0712.3010v1 (2007)

  18. 18.

    V.P. Popov, V.N. Pomerantsev, Phys. Rev. A 83, 032516 (2011)

    ADS  Article  Google Scholar 

  19. 19.

    V.P. Popov, V.N. Pomerantsev, Hyperfine Int. 209, 75 (2012)

    ADS  Article  Google Scholar 

  20. 20.

    V.P. Popov, V.N. Pomerantsev, Phys. Rev. A 95, 022506 (2017)

    ADS  Article  Google Scholar 

  21. 21.

    D. Gotta et al., AIP Conf. Proc. 1037, 162 (2008)

    ADS  Article  Google Scholar 

  22. 22.

    Th. Strauch et al., Hyperfine Int. 193, 47 (2009)

    ADS  Article  Google Scholar 

  23. 23.

    D. Gotta et al., Hyperfine Int. 209, 57 (2012)

    ADS  Article  Google Scholar 

  24. 24.

    M. Hennebach et al., Eur. Phys. J. A 50, 190 (2014)

    ADS  Article  Google Scholar 

  25. 25.

    R.D. Cousins, Am. J. Phys. 63, 398 (1995)

    ADS  MathSciNet  Article  Google Scholar 

  26. 26.

    D.S. Covita et al., Hyperfine Int. 193, 61 (2009)

    ADS  Article  Google Scholar 

  27. 27.

    G.J. Babu, Bayesian and frequentist approaches, in Online Proceedings of the Astronomical Data Analysis Conference (ADA VII) (2012)

  28. 28.

    F.J. Hartmann, in Proceedings of Physics of Exotic Atoms on Electromagnetic Cascade and Chemistry, Erice, Italy, 1989 (Plenum Press, New York, 1990), p. 23 and 127, and references therein

  29. 29.

    G.Ya. Korenman, V.P. Popov, Muon Catal. Fusion 4, 145 (1989)

    Google Scholar 

  30. 30.

    G.Ya. Korenman, V.P. Popov, G.A. Fesenko, Muon Catal. Fusion 7, 179 (1992)

    Google Scholar 

  31. 31.

    J.S. Cohen, Phys. Rev. 59, 1160 (1999)

    ADS  Article  Google Scholar 

  32. 32.

    J.S. Cohen, Rep. Prog. Phys. 67, 1769 (2004)

    ADS  Article  Google Scholar 

  33. 33.

    F. Kottmann et al., Hyperfine Int. 119, 3 (1999)

    ADS  Article  Google Scholar 

  34. 34.

    F. Kottmann et al., Hyperfine Int. 138, 55 (2001)

    ADS  Article  Google Scholar 

  35. 35.

    R. Pohl et al., Nature 466, 213 (2010)

    ADS  Article  Google Scholar 

  36. 36.

    R. Pohl et al., Hyperfine Int. 138, 35 (2001)

    ADS  Article  Google Scholar 

  37. 37.

    H.-Ch. Schröder et al., Eur. Phys. J C 21, 473 (2001)

    ADS  Article  Google Scholar 

  38. 38.

    R. Pohl et al., Phys. Rev. Lett. 97, 193402 (2006)

    ADS  Article  Google Scholar 

  39. 39.

    M. Leon, H.A. Bethe, Phys. Rev. 127, 636 (1962)

    ADS  Article  Google Scholar 

  40. 40.

    T.S. Jensen, V.E. Markushin, Lect. Notes Phys. 627, 37 (2003)

    ADS  Article  Google Scholar 

  41. 41.

    T.P. Terada, R.S. Hayano, Phys. Rev. C 55, 73 (1997)

    ADS  Article  Google Scholar 

  42. 42.

    J.F. Crawford et al., Phys. Rev. D 43, 46 (1991)

    ADS  Article  Google Scholar 

  43. 43.

    D.J. Abbott et al., Phys. Rev. A 55, 165 (1997)

    Article  Google Scholar 

  44. 44.

    R. Pohl, Ph.D. thesis, ETH Zürich No. 14096, 2001

  45. 45.

    V.E. Markushin, Phys. Rev. A 50, 1137 (1994)

    ADS  Article  Google Scholar 

  46. 46.

    A.V. Kravtsov, A.I. Mikhailov, L.I. Ponomarev, E.A. Solovyov, Hyperfine Int. 138, 99 (2001)

    ADS  Article  Google Scholar 

  47. 47.

    T.S. Jensen, V.E. Markushin, Eur. Phys. J. D 21, 261 (2002)

    ADS  Article  Google Scholar 

  48. 48.

    G.Ya. Korenman, V.N. Pomerantsev, V.P. Popov, JETP Lett. 81, 543 (2005)

    ADS  Article  Google Scholar 

  49. 49.

    V.N. Pomerantsev, V.P. Popov, JETP Lett. 83, 331 (2006)

    Article  Google Scholar 

  50. 50.

    V.N. Pomerantsev, V.P. Popov, Phys. Rev. A 73, 040501(R) (2006)

    ADS  Article  Google Scholar 

  51. 51.

    V.P. Popov, V.N. Pomerantsev, arXiv:0809.0742 (2008)

  52. 52.

    V.P. Popov, V.N. Pomerantsev, Hyperfine Int. 101/102, 133 (1996)

    ADS  Article  Google Scholar 

  53. 53.

    V.P. Popov, V.N. Pomerantsev, Hyperfine Int. 119, 133 (1999)

    ADS  Article  Google Scholar 

  54. 54.

    V.P. Popov, V.N. Pomerantsev, Hyperfine Int. 119, 137 (1999)

    ADS  Article  Google Scholar 

  55. 55.

    V.V. Gusev, V.P. Popov, V.N. Pomerantsev, Hyperfine Int. 119, 141 (1999)

    ADS  Article  Google Scholar 

  56. 56.

    T.S. Jensen, V.E. Markushin, Eur. Phys. J. D 19, 165 (2002)

    ADS  Google Scholar 

  57. 57.

    V.P. Popov, V.N. Pomerantsev, arXiv:0712.3111 (2007)

  58. 58.

    D. Taqqu, AIP Conf. Proc. 181, 217 (1989)

    ADS  Article  Google Scholar 

  59. 59.

    S. Jonsell, J. Wallenius, P. Froelich, Phys. Rev. A 59, 3440 (1999)

    ADS  Article  Google Scholar 

  60. 60.

    R. Pohl, Hyperfine Int. 193, 115 (2009)

    ADS  Article  Google Scholar 

  61. 61.

    M. Diepold et al., Phys. Rev A 88, 042520 (2013)

    ADS  Article  Google Scholar 

  62. 62.

    S. Kilic, J.-P. Karr, L. Hilico, Phys. Rev. A 70, 042506 (2004)

    ADS  Article  Google Scholar 

  63. 63.

    E. Lindroth, J. Wallenius, S. Jonsell, Phys. Rev. A 68, 032502 (2003)

    ADS  Article  Google Scholar 

  64. 64.

    E. Lindroth, J. Wallenius, S. Jonsell, Phys. Rev. A 69, 059903(E) (2004)

    ADS  Article  Google Scholar 

  65. 65.

    L.M. Simons, Phys. Scr. T22, 90 (1988)

    ADS  Article  Google Scholar 

  66. 66.

    L.M. Simons, Hyperfine Int. 81, 253 (1993)

    ADS  Article  Google Scholar 

  67. 67.

    H. Gorke et al., AIP Conf. Proc. 793, 341 (2005)

    ADS  Article  Google Scholar 

  68. 68.

    D.E. Gotta, L.M. Simons, Spectrochim. Acta. B 120, 9 (2016)

    ADS  Article  Google Scholar 

  69. 69.

    J. Eggs, K. Ulmer, Z. Angew. Phys. 20, 118 (1965)

    Google Scholar 

  70. 70.

    G. Zschornack, Nucl. Instrum. Methods 200, 481 (1982)

    Article  Google Scholar 

  71. 71.

    N. Nelms et al., Nucl. Instrum. Methods A 484, 419 (2002)

    ADS  Article  Google Scholar 

  72. 72.

    A.D. Holland, M.J.L. Turner, A.F. Abbey, P.J. Pool, Proc. SPIE 2808, 414 (1996)

    ADS  Article  Google Scholar 

  73. 73.

    P. Indelicato et al., Rev. Sci. Instrum. 77, 043107 (2006)

    ADS  Article  Google Scholar 

  74. 74.

    D.S. Covita et al., Rev. Scient. Instrum. 79, 033102 (2008)

    ADS  Article  Google Scholar 

  75. 75.

    P. Indelicato, unpublished (2008)

  76. 76.

    A.P. Martynenko, R.N. Faustov, JETP 98, 39 (2004)

    ADS  Article  Google Scholar 

  77. 77.

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

    ADS  Article  Google Scholar 

  78. 78.

    G. Basile et al., Phys. Rev. Lett. 72, 3133 (1994)

    ADS  Article  Google Scholar 

  79. 79.

    M. Sanchez del Rio, R.J. Dejus, Proc. SPIE Int. Soc. Opt. Eng. 3448, 246 (1998)

    ADS  Google Scholar 

  80. 80.

    M. Sanchez del Rio, R.J. Dejus, Proc. SPIE Int. Soc. Opt. Eng. 5536, 171 (2004)

    ADS  Google Scholar 

  81. 81.

    M. Sanchez del Rio, R.J. Dejus, Proc. SPIE Int. Soc. Opt. Eng. http://www.esrf.eu/computing/scientific/xop2.1

  82. 82.

    WM.J. Veigele, At. Data Tables 5, 51 (1973)

    ADS  Article  Google Scholar 

  83. 83.

    S. Biri, L. Simons, D. Hitz, Rev. Sci. Instrum. 71, 1116 (2000)

    ADS  Article  Google Scholar 

  84. 84.

    D.F. Anagnostopulos et al., Nucl. Instrum. Methods A 545, 217 (2005)

    ADS  Article  Google Scholar 

  85. 85.

    M. Trassinelli et al., J. Phys. Conf. Ser. 58, 129 (2007)

    Article  Google Scholar 

  86. 86.

    D.S. Covita, High-precision spectroscopy of the 3p–1s transition in muonic hydrogen, Ph.D. thesis, University of Coimbra, 2008, http://hdl.handle.net/10316/7521.

  87. 87.

    A. Antognini et al., Ann. Phys. 331, 127 (2013)

    ADS  Article  Google Scholar 

  88. 88.

    A.P. Martynenko, Phys. Rev. A 71, 022506 (2005)

    ADS  Article  Google Scholar 

  89. 89.

    C. Peset, A. Pineda, arXiv:1612.05206v1 (2016)

  90. 90.

    K. Pachucki, Phys. Rev. A 53, 2092 (1996)

    ADS  Article  Google Scholar 

  91. 91.

    J. Beringer et al. (PDG), Phys. Rev. D 86, 01001 (2012)

    Article  Google Scholar 

  92. 92.

    B. Efron, Am. Stat. 40, 11 (1986)

    Google Scholar 

  93. 93.

    F. James, A unified approach to understanding statistics, in PHYSTAT2003 (SLAC), Stanford, California (2003)

  94. 94.

    G. Bohm, G. Zech, Introduction to statistics and data analysis for physicists (Verlag Deutsches Elektronen Synchrotron, 2010)

  95. 95.

    M. Trassinelli, Nucl. Instrum. Methods B 408, 301 (2017)

    ADS  Article  Google Scholar 

  96. 96.

    F. James, M. Roos, Comput. Phys. Commun. 10, 343 (1975)

    ADS  Article  Google Scholar 

  97. 97.

    J. Skilling, in American institute of physics conference series (2004), Vol. 735, p. 395

  98. 98.

    M. Theisen, Fakultät für Mathematik, Informatik und Naturwisssenschaften der RWTH Aachen, Diploma thesis, 2013

  99. 99.

    H. Jeffreys, in The theory of probability, 3rd edn. (Oxford University Press, USA, 1961)

  100. 100.

    R.E. Kass, A.E. Raftery, J. Stat. Am. Assoc. 90, 773 (1995)

    Article  Google Scholar 

  101. 101.

    D. Sivia, J. Skilling, in Data analysis: a Bayesian tutorial (Oxford University Press, 2006)

  102. 102.

    M.R. Stoneking, D. Hartogh, Rev. Sci. Instrum. 68, 914 (1997)

    ADS  Article  Google Scholar 

  103. 103.

    S. Baker, R.D. Cousins, Nucl. Instrum. Methods Phys. Res. 221, 437 (1984)

    ADS  Article  Google Scholar 

  104. 104.

    T. Hauschild, M. Jentschel, Nucl. Instrum. Methods A 457, 384 (2001)

    ADS  Article  Google Scholar 

  105. 105.

    U.C. Bergmann, K. Riisager, Nucl. Instrum. Methods A 489, 444 (2002)

    ADS  Article  Google Scholar 

  106. 106.

    R. Trotta, Contemp. Phys. 49, 71 (2008)

    ADS  Article  Google Scholar 

  107. 107.

    D. Madigan, A.E. Raftery, J. Am. Stat. Assoc. 89, 1335 (1994)

    Article  Google Scholar 

  108. 108.

    P. Mukherjee et al., MNRAS 369, 1725 (2006)

    ADS  Article  Google Scholar 

  109. 109.

    F. Feroz, M.P. Hobson, MNRAS 384, 449 (2008)

    ADS  Article  Google Scholar 

  110. 110.

    F. Feroz et al., MNRAS 398, 2009 2049

    ADS  Article  Google Scholar 

  111. 111.

    F. Feroz, J. Skilling, arXiv:1312.5638v (2013)

  112. 112.

    F. Feroz et al., arXiv:1306.2144v1 (2013)

  113. 113.

    W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, in Numerical recipies, 2nd edn. (Cambridge University Press, 1992)

Download references

Author information

Affiliations

  1. LIBPhys, Physics Department, University of Coimbra, 3004-526, Coimbra, Portugal

    Daniel S. Covita & Joaquim M. F. dos Santos

  2. Laboratory for Particle Physics, Paul Scherrer Institut, CH-5232, Villigen, Switzerland

    Daniel S. Covita, Thomas S. Jensen, Valeri E. Markushin & Leopold M. Simons

  3. Department of Materials Science and Engineering, University of Ioannina, 45110, Ioannina, Greece

    Dimitrios F. Anagnostopoulos

  4. Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, 1090, Vienna, Austria

    Hermann Fuhrmann, Alexander Gruber, Albert Hirtl, Tomoichi Ishiwatari, Philipp Schmid & Johann Zmeskal

  5. Zentralinstitut für Elektronik, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    Hubert Gorke

  6. Institut für Kernphysik, Forschungszentrum Jülich, 52425, Jülich, Germany

    Detlev Gotta, Michael Nekipelov & Marian Theisen

  7. Laboratoire Kastler Brossel, Sorbonne Universités, UPMC Univ. Paris 06, Case 74, 4 Place Jussieu, 75005, Paris, France

    Paul Indelicato & Eric-Olivier Le Bigot

  8. Laboratoire Kastler Brossel, CNRS, 75005, Paris, France

    Paul Indelicato

  9. Laboratoire Kastler Brossel, Département de Physique de l’École Normale Supérieure, 24 Rue Lhomond, 75005, Paris, France

    Paul Indelicato

  10. Institut für Theoretische Physik Universität Zürich, CH-8057, Zürich, Switzerland

    Thomas S. Jensen

  11. Skobeltsyn Institut of Nuclear Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Vladimir N. Pomerantsev & Vladimir P. Popov

  12. Institut des NanoSciences de Paris, CNRS-UMR 7588, Sorbonne Universités, UPMC Univ. Paris 06, 75005, Paris, France

    Martino Trassinelli

  13. I3N, Department of Physics, Aveiro University, 3810, Aveiro, Portugal

    Joao F. C. A. Veloso

Authors
  1. Daniel S. Covita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dimitrios F. Anagnostopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hermann Fuhrmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hubert Gorke
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Detlev Gotta
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Alexander Gruber
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Albert Hirtl
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Tomoichi Ishiwatari
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Paul Indelicato
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Thomas S. Jensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Eric-Olivier Le Bigot
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Valeri E. Markushin
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Michael Nekipelov
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Vladimir N. Pomerantsev
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Vladimir P. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Joaquim M. F. dos Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. Philipp Schmid
    View author publications

    You can also search for this author in PubMed Google Scholar

  18. Leopold M. Simons
    View author publications

    You can also search for this author in PubMed Google Scholar

  19. Marian Theisen
    View author publications

    You can also search for this author in PubMed Google Scholar

  20. Martino Trassinelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  21. Joao F. C. A. Veloso
    View author publications

    You can also search for this author in PubMed Google Scholar

  22. Johann Zmeskal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Detlev Gotta.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Covita, D.S., Anagnostopoulos, D.F., Fuhrmann, H. et al. Line shape analysis of the Kβ transition in muonic hydrogen. Eur. Phys. J. D 72, 72 (2018). https://doi.org/10.1140/epjd/e2018-80593-1

Download citation

Keywords

  • Atomic Physics