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Nucleon polarizabilities from deuteron Compton scattering within a Green’s function hybrid approach

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Abstract.

We examine elastic Compton scattering from the deuteron for photon energies ranging from zero to 100MeV, using state-of-the-art deuteron wave functions and NN potentials. Nucleon-nucleon rescattering between emission and absorption of the two photons is treated by Green’s functions in order to ensure gauge invariance and the correct Thomson limit. With this Green’s function hybrid approach, we fulfill the low-energy theorem of deuteron Compton scattering and there is no significant dependence on the deuteron wave function used. Concerning the nucleon structure, we use the chiral effective field theory with explicit \( \Delta\)(1232) degrees of freedom within the small-scale expansion up to leading-one-loop order. Agreement with available data is good at all energies. Our 2-parameter fit to all elastic \( \gamma\) d data leads to values for the static isoscalar dipole polarizabilities which are in excellent agreement with the isoscalar Baldin sum rule. Taking this value as additional input, we find \( \alpha_{E}^{s}\) = (11.3±0.7(stat)±0.6(Baldin)±1(theory)).10-4 fm^3 and \( \beta_{M}^{s}\) = (3.2±0.7(stat)±0.6(Baldin)±1(theory)).10-4 fm^3 and conclude by comparison to the proton numbers that neutron and proton polarizabilities are the same within rather small errors.

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References

  1. H.W. Grießhammer, T.R. Hemmert, Phys. Rev. C 65, 045207 (2002)

    Article  ADS  Google Scholar 

  2. R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, B. Pasquini, Eur. Phys. J. A 20, 293 (2004)

    Article  ADS  Google Scholar 

  3. M. Schumacher, Prog. Part. Nucl. Phys. 55, 567 (2005)

    Article  ADS  Google Scholar 

  4. Olmos de Leon et al., Eur. Phys. J. A 10, 207 (2001)

    Article  ADS  Google Scholar 

  5. T.R. Hemmert, B.R. Holstein, J. Kambor, Phys. Lett. B 395, 89 (1997)

    Article  ADS  Google Scholar 

  6. T.R. Hemmert, B.R. Holstein, J. Kambor, J. Phys. G 24, 1831 (1998)

    Article  ADS  Google Scholar 

  7. M. Lucas, PhD Thesis, University of Illinois (1994)

  8. M. Lundin et al., Phys. Rev. Lett. 90, 192501 (2003)

    Article  ADS  Google Scholar 

  9. D.L. Hornidge et al., Phys. Rev. Lett. 84, 2334 (2000)

    Article  ADS  Google Scholar 

  10. H.R. Weller, M.W. Ahmed, H. Gao, W. Tornow, Y.K. Wu, M. Gai, R. Miskimen, Prog. Part. Nucl. Phys. 62, 257 (2009)

    Article  ADS  Google Scholar 

  11. H. Weller, HIGS-E-18-09

  12. R. Miskimen, HIGS-E-06-09

  13. R. Miskimen, Measuring the Spin-Polarizabilities of the Proton at , presentation at the INT Workshop on Soft Photons and Light Nuclei, 17 June 2008

  14. H. Gao, HIGS-E-07-10

  15. M. Ahmed, HIGS-E-06-10

  16. G. Feldman et al., Few Body Syst. 44, 325 (2008)

    Article  ADS  Google Scholar 

  17. MAXlab experiment NP-006, http://www.maxlab.lu.se/kfoto/Experimental Program/PAC\_info.html

  18. A. Richter, P. von Neumann-Cosel, private communication (2005)

  19. R. Beck, Nucleon Compton Scattering at MAMI, talk at the INT Workshop on Soft Photons and Light Nuclei, 17 June 2008

  20. M.I. Levchuk, A.I. L’vov, Nucl. Phys. A 674, 449 (2000)

    Article  ADS  Google Scholar 

  21. K. Kossert et al., Eur. Phys. J. A 16, 259 (2003)

    Article  ADS  Google Scholar 

  22. R.P. Hildebrandt, H.W. Grießhammer, T.R. Hemmert, D.R. Phillips, Nucl. Phys. A 748, 573 (2005)

    Article  ADS  Google Scholar 

  23. V. Bernard, N. Kaiser, J. Kambor, U.-G. Meißner, Nucl. Phys. B 388, 315 (1992)

    Article  ADS  Google Scholar 

  24. D.R. Phillips, J. Phys. G 36, 104004 (2009)

    Article  ADS  Google Scholar 

  25. J.J. Karakowski, G.A. Miller, Phys. Rev. C 60, 014001 (1999)

    Article  ADS  Google Scholar 

  26. J.J. Karakowski, PhD Thesis, preprint nt@uw-99-6 (1999) [nucl-th/9901011]

  27. S.R. Beane, M. Malheiro, D.R. Phillips, U. van Kolck, Nucl. Phys. A 656, 367 (1999)

    Article  ADS  Google Scholar 

  28. S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Phys. Lett. B 567, 200 (2003)

    Article  ADS  Google Scholar 

  29. S.R. Beane, M. Malheiro, J.A. McGovern, D.R. Phillips, U. van Kolck, Nucl. Phys. A 747, 311 (2005)

    Article  ADS  Google Scholar 

  30. S. Weinberg, Phys. Lett. B 251, 288 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  31. S. Weinberg, Nucl. Phys. B 363, 3 (1991)

    Article  ADS  Google Scholar 

  32. V.G. Stoks, R.A. Klomp, C.P. Terheggen, J.J. de Swart, Phys. Rev. C 49, 2950 (1994)

    Article  ADS  Google Scholar 

  33. R. Machleidt, F. Sammarruca, Y. Song, Phys. Rev. C 53, 1483 (1996)

    Article  ADS  Google Scholar 

  34. R.B. Wiringa, V.G. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995)

    Article  ADS  Google Scholar 

  35. S.R. Beane, V. Bernard, E. Epelbaum, U.-G. Meißner, D.R. Phillips, Nucl. Phys. A 720, 399 (2003)

    Article  ADS  Google Scholar 

  36. D.R. Phillips, Phys. Lett. B 567, 12 (2003)

    Article  ADS  Google Scholar 

  37. M. Rho, in Proceedings of the 10th Taiwan Nuclear Physics Spring School, Hualien, Taiwan, China (2002)

  38. R.P. Hildebrandt, PhD Thesis, TU München, mediaTUM\_disshab\_000000000003041 (2005) [nucl-th/0512064]

  39. A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005)

    Article  ADS  Google Scholar 

  40. M.C. Birse, Phys. Rev. C 74, 014003 (2006) [arXiv:nucl-th/0507077]

    Article  ADS  Google Scholar 

  41. H.W. Grießhammer, in preparation

  42. H.W. Grießhammer, arXiv:nucl-th/0611074

  43. H.W. Grießhammer, arXiv:0710.2924 [nucl-th]

  44. S.R. Beane, M.J. Savage, Nucl. Phys. A 694, 511 (2001)

    Article  MATH  ADS  Google Scholar 

  45. H.W. Grießhammer, G. Rupak, Phys. Lett. B 529, 57 (2002)

    Article  ADS  Google Scholar 

  46. J. Chen, X. Ji, Y. Li, Phys. Rev. C 71, 044321 (2005)

    Article  ADS  Google Scholar 

  47. J.L. Friar, Ann. Phys. (N.Y.) 95, 170 (1975)

    Article  ADS  Google Scholar 

  48. A.J.F. Siegert, Phys. Rev. 52, 787 (1937)

    Article  ADS  Google Scholar 

  49. H. Arenhövel, Z. Phys. A 297, 129 (1980)

    Article  ADS  Google Scholar 

  50. M. Weyrauch, H. Arenhövel, Nucl. Phys. A 408, 425 (1983)

    Article  ADS  Google Scholar 

  51. V. Bernard, N. Kaiser, U.-G. Meißner, Int. J. Mod. Phys. E 4, 193 (1995)

    Article  ADS  Google Scholar 

  52. T.R. Hemmert, B.R. Holstein, J. Kambor, G. Knöchlein, Phys. Rev. D 57, 5746 (1998)

    Article  ADS  Google Scholar 

  53. E. Epelbaum, W. Glöckle, U.-G. Meissner Eur. Phys. J. A19125

    Article  Google Scholar 

  54. M.E. Rose, Elementary Theory of Angular Momentum (John Wiley & Sons, Inc., New York, London, Sydney, 1957)

  55. T. Ericson, W. Weise, Pions and Nuclei (Clarendon Press, Oxford, 1988) ISBN 0-19-852008-5

  56. D.R. Phillips, J. Phys. G 34, 365 (2007)

    Article  ADS  Google Scholar 

  57. T.-S. Park, K. Kubodera, D.-P. Min, M. Rho, Nucl. Phys. A 646, 83 (1999)

    Article  ADS  Google Scholar 

  58. E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 671, 295 (2000)

    Article  ADS  Google Scholar 

  59. J.A. McGovern, H.W. Grießhammer, D.R. Phillips, D. Shukla, arXiv:0910.1184 [nucl-th].

  60. H. Grießhammer, J. McGovern, D.R. Phillips, D. Shukla, in preparation

  61. J.J. Sakurai, Modern Quantum Mechanics (Addison-Wesley Publishing Company, 1994) ISBN 0-201-53929-2

  62. A.R. Edmonds, Angular Momentum in Quantum Mechanics, (University Press, Princeton, 1996) ISBN 0-691-07912-9

  63. F. Partovi, Ann. Phys. 27, 79 (1964)

    Article  ADS  Google Scholar 

  64. P. Marin, G.R. Bishop, H. Halban, Proc. Phys. Soc. London, Ser. A 67, 1113 (1954)

    Article  ADS  Google Scholar 

  65. Y. Birenbaum et al., Phys. Rev. C 32, 1825 (1985)

    Article  ADS  Google Scholar 

  66. R. Bernabei et al., Phys. Rev. Lett. 57, 1542 (1986)

    Article  ADS  Google Scholar 

  67. H.O. Meyer et al., Phys. Rev. C 31, 309 (1985)

    Article  ADS  Google Scholar 

  68. E. de Sanctis et al., Phys. Rev. C 34, 413 (1986)

    Article  ADS  Google Scholar 

  69. R. Moreh, T.J. Kennett, W.V. Prestwick, Phys. Rev. C 39, 1247 (1989)

    Article  ADS  Google Scholar 

  70. A.H. Snell, E.C. Barker, R.L. Sternberg, Phys. Rev. 80, 637 (1950)

    Article  ADS  Google Scholar 

  71. W.R. McMurray, C.H. Collie, Proc. Phys. Soc. London, Ser. A 68, 181 (1955)

    Article  ADS  Google Scholar 

  72. H. Arenhövel, M. Sanzone, Photodisintegration of the Deuteron, Few Body Syst. Suppl. 3 (Springer-Verlag, Wien, New York, 1991) ISBN 3-211-82276-3

  73. G.E. Brown, A.D. Jackson, The Nucleon-Nucleon Interaction (North-Holland Publishing Company, Amsterdam, Oxford, 1976) ISBN 0 7204 03359

  74. H.A. Bethe, Phys. Rev. 76, 38 (1949)

    Article  MATH  ADS  Google Scholar 

  75. H.A. Bethe, C. Longmire, Phys. Rev. 77, 647 (1950)

    Article  MATH  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Institut für Theoretische Physik (T39), Physik-Department, Technische Universität München, D-85747, Garching, Germany

    R. P. Hildebrandt, H. W. Grießhammer & T. R. Hemmert

  2. Institut für Theoretische Physik III, Naturwissenschaftliche Fakultät I, Universität Erlangen-Nürnberg, D-91058, Erlangen, Germany

    H. W. Grießhammer

  3. Center for Nuclear Studies, Department of Physics, The George Washington University, 20052, Washington DC, USA

    H. W. Grießhammer

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  1. R. P. Hildebrandt
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  2. H. W. Grießhammer
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Communicated by M.C. Birse

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Hildebrandt, R.P., Grießhammer, H.W. & Hemmert, T.R. Nucleon polarizabilities from deuteron Compton scattering within a Green’s function hybrid approach. Eur. Phys. J. A 46, 111–137 (2010). https://doi.org/10.1140/epja/i2010-11024-y

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