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Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons

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Abstract.

The Effective Field Theory “without pions” at next-to-leading order is used to analyze universal bound-state and scattering properties of the 3- and 4-nucleon system. Results of a variety of phase shift equivalent nuclear potentials are presented for bound-state properties of 3H and 4He , and for the singlet S -wave 3He -neutron scattering length a 0(3He-n) . The calculations are performed with the Refined Resonating Group Method and include a full treatment of the Coulomb interaction and the leading-order 3-nucleon interaction. The results compare favorably with data and values from AV18(+UIX) model calculations. A new correlation between a 0(3He-n) and the 3H binding energy is found. Furthermore, we confirm at next-to-leading order the correlations, already found at leading order, between the 3H binding energy and the 3H charge radius, and the Tjon line. With the 3H binding energy as input, we get predictions of the effective field theory “without pions” at next-to-leading order for the root mean square charge radius of 3H of (1.6±0.2) fm, for the 4He binding energy of (28±2.5) MeV, and for Re{a 0(3He-n)} of (7.5±0.6) fm. Including the Coulomb interaction, the splitting in binding energy between 3H and 3He is found to be (0.66±0.03) MeV. The discrepancy to data of (0.10±0.03) MeV is model independently attributed to higher-order charge independence breaking interactions. We also demonstrate that different results for the same observable stem from higher-order effects, and carefully assess that numerical uncertainties are negligible. Our results demonstrate the convergence and usefulness of the pion-less theory at next-to-leading order in the 4He channel. We conclude that no 4-nucleon interaction is needed to renormalize the theory at next-to-leading order in the 4-nucleon sector.

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References

  1. U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999)

    Article  ADS  Google Scholar 

  2. S.R. Beane, P.F. Bedaque, W.C. Haxton, D.R. Phillips, M.J. Savage, From hadrons to nuclei: Crossing the border, in At the Frontier of Particle Physics, edited by M. Shifman, Vol. 1 (World Scientific, 2000) pp. 133--269, arXiv:nucl-th/0008064

  3. P.F. Bedaque, U. van Kolck, Ann. Rev. Nucl. Part. Sci. 52, 339 (2002)

    Article  ADS  Google Scholar 

  4. L. Platter, Few Body Syst. 46, 139 (2009)

    Article  ADS  Google Scholar 

  5. H.W. Hammer, E. Braaten, Phys. Rep. 428, 259 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  6. E. Epelbaum, H.W. Hammer, U.G. Meißner, Rev. Mod. Phys. 81, 1773 (2009)

    Article  ADS  Google Scholar 

  7. E. Epelbaum, Nucl. Phys. A 737, 43 (2004)

    Article  ADS  Google Scholar 

  8. E. Epelbaum, arXiv:1001.3229 [nucl-th]

  9. G. Rupak, Nucl. Phys. A 678, 405 (2000)

    Article  ADS  Google Scholar 

  10. L. Platter, H.W. Hammer, U.G. Meißner, Phys. Lett. B 607, 254 (2005)

    Article  ADS  Google Scholar 

  11. I. Stetcu, B.R. Barrett, U. van Kolck, Phys. Lett. B 653, 358 (2007)

    Article  ADS  Google Scholar 

  12. J.A. Tjon, Phys. Lett. B 56, 217 (1975)

    Article  ADS  Google Scholar 

  13. A.C. Phillips, Nucl. Phys. A 107, 209 (1968)

    Article  ADS  Google Scholar 

  14. H.W. Hammer, L. Platter, arXiv:1001.1981 [nucl-th]

  15. V. Efimov, Sov. J. Nucl. Phys. 12, 589 (1971)

    Google Scholar 

  16. P.F. Bedaque, H.W. Hammer, U. van Kolck, Phys. Rev. Lett. 82, 463 (1999)

    Article  ADS  Google Scholar 

  17. V.F. Kharchenko, Sov. J. Nucl. Phys. 16, 173 (1973)

    Google Scholar 

  18. H.M. Hofmann, in Proceedings of Models and Methods in Few-Body Physics, Lisboa, Portugal, edited by L.S. Ferreira, A.C. Fonseca, L. Streit (Berlin, New York, Springer, 1986) p. 243

  19. D.R. Phillips, Czech. J. Phys. 52, B49 (2002)

    Article  Google Scholar 

  20. C. Ordonez, L. Ray, U. van Kolck, Phys. Rev. Lett. 72, 1982 (1994)

    Article  ADS  Google Scholar 

  21. P.F. Bedaque, H.W. Hammer, U. van Kolck, Nucl. Phys. A 646, 444 (1999)

    Article  ADS  Google Scholar 

  22. P.F. Bedaque, G. Rupak, H.W. Grießhammer, H.W. Hammer, Nucl. Phys. A 714, 589 (2003)

    Article  MATH  ADS  Google Scholar 

  23. H.W. Hammer, T. Mehen, Phys. Lett. B 516, 353 (2001)

    Article  ADS  Google Scholar 

  24. L. Platter, Phys. Rev. C 74, 037001 (2006)

    Article  ADS  Google Scholar 

  25. L. Platter, D.R. Phillips, Few Body Syst. 40, 35 (2006)

    Article  ADS  Google Scholar 

  26. G.P. Lepage, How to renormalize the Schroedinger equation, in Lectures given at the 9th Jorge Andre Swieca Summer School: Particles and Fields, Sao Paulo, Brazil, 16-28 Feb 1997, arXiv:nucl-th/9706029

  27. S. Christlmeier, H.W. Grießhammer, Phys. Rev. C 77, 064001 (2008)

    Article  ADS  Google Scholar 

  28. H.W. Grießhammer, Nucl. Phys. A 744, 192 (2004)

    Article  ADS  Google Scholar 

  29. S. Weinberg, Phys. Lett. B 251, 2 (1990)

    MathSciNet  Google Scholar 

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

    Article  MATH  ADS  Google Scholar 

  31. D.R. Phillips, T.D. Cohen, Phys. Lett. B 390, 7 (1997)

    Article  ADS  Google Scholar 

  32. A.R. Edmonds, Angular Momentum in Quantum Mechanics (Princton University Press, 1996)

  33. R.G. Newton. Scattering Theory of Waves and Particles (Dover Publications, 2002) Chapt. 14.6

  34. C. Winkler, H.M. Hofmann, Phys. Rev. C 55, 684 (1997)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. R. Machleidt, K. Holinde, C. Elster, Phys. Rep. 149, 1 (1987)

    Article  Google Scholar 

  37. G.L. Greene, E.G. Kessler, R.D. Deslattes, H. Börner, Phys. Rev. Lett. 56, 819 (1986)

    Article  ADS  Google Scholar 

  38. O. Dumbrajs, R. Koch, H. Pilkuhn, G.C. Oades, H. Behrens, J.J. de Swart, P. Kroll, Nucl. Phys. B 216, 277 (1983)

    Article  ADS  Google Scholar 

  39. V.G.J. Stoks, R.A.M. Klomp, M.C.M. Rentmeester, J.J. de Swart, Phys. Rev. C 48, 792 (1993)

    Article  ADS  Google Scholar 

  40. Nijmegen PWA online database, accessed 11/2008, http://nn-online.org/

  41. L. Platter, H.W. Hammer, Nucl. Phys. A 766, 132 (2006)

    Article  ADS  Google Scholar 

  42. D.R. Tilley, H.R. Weller, H.H. Hasan, Nucl. Phys. A 474, 1 (1987)

    Article  ADS  Google Scholar 

  43. A.H. Wapstra, G. Audi, Nucl. Phys. A 432, 1 (1985)

    Article  ADS  Google Scholar 

  44. G.L. Payne, J.L. Friar, B.F. Gibson, I.R. Afnan, Phys. Rev. C 22, 823 (1980)

    Article  ADS  Google Scholar 

  45. C.R. Chen, G.L. Payne, J.L. Friar, B.F. Gibson, Phys. Rev. C 31, 2266 (1985)

    Article  ADS  Google Scholar 

  46. J.L. Friar, B.F. Gibson, C.R. Chen, G.L. Payne, Phys. Lett. B 161, 241 (1985)

    Article  ADS  Google Scholar 

  47. B.S. Pudliner, V.R. Pandharipande, J. Carlson, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 56, 1720 (1997)

    Article  ADS  Google Scholar 

  48. G.H. Berthold, A. Stadler, H. Zankel, Phys. Rev. C 38, 444 (1988)

    Article  ADS  Google Scholar 

  49. J.L. Friar, G.L. Payne, U. van Kolck, Phys. Rev. C 71, 024003 (2005)

    Article  ADS  Google Scholar 

  50. G.A. Miller, A.K. Opper, E.J. Stephenson, Annu. Rev. Nucl. Part. Sci. 56, 253 (2006)

    Article  ADS  Google Scholar 

  51. S. Fiarman, W.E. Meyerhof, Nucl. Phys. A 206, 1 (1973)

    Article  ADS  Google Scholar 

  52. J. Kirscher, Diploma Thesis, FAU Erlangen, 2006, http://theorie3.physik.uni-erlangen.de/theses/ data/Dip-2006-01.pdf

  53. A. Deltuva, A.C. Fonseca, Phys. Rev. C 75, 014005 (2007)

    Article  ADS  Google Scholar 

  54. H.M. Hofmann, G.M. Hale, Phys. Rev. C 77, 044002 (2008)

    Article  ADS  Google Scholar 

  55. S.C. Pieper, V.R. Pandharipande, R.B. Wiringa, J. Carlson, Phys. Rev. C 64, 014001 (2001)

    Article  ADS  Google Scholar 

  56. P.R. Huffman et al., Phys. Rev. C 70, 014004 (2004)

    Article  ADS  Google Scholar 

  57. O. Zimmer, G. Ehlers, B. Farago, H. Humblot, W. Ketter, R. Scherm, EPJ direct 4, No. 1, 1 (2002)

    Article  Google Scholar 

  58. J. Kirscher, H.W. Grießhammer, H.M. Hofmann, in preparation

  59. C.A. Bertulani, H.W. Hammer, U. Van Kolck, Nucl. Phys. A 712, 37 (2002)

    Article  ADS  Google Scholar 

  60. T. Shima et al., Phys. Rev. C 72, 044004 (2005)

    Article  ADS  Google Scholar 

  61. S. Quaglioni, W. Leidemann, G. Orlandini, N. Barnea, V.D. Efros, Phys. Rev. C 69, 044002 (2004)

    Article  ADS  Google Scholar 

  62. W. Sandhas, W. Schadow, G. Ellerkmann, L.L. Howell, S.A. Sofianos, Nucl. Phys. A 631, 210c (1998)

    Article  ADS  Google Scholar 

  63. C. Reiss, H.M. Hofmann, Nucl. Phys. A 716, 107 (2003)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

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

    J. Kirscher & H. W. Grießhammer

  2. Department of Physics and Astronomy, University of North Carolina, 27599-3255, Chapel Hill, NC, USA

    D. Shukla

  3. Institut für Theoretische Physik III, Department für Physik, Universität Erlangen-Nürnberg, D-91058, Erlangen, Germany

    H. M. Hofmann

Authors
  1. J. Kirscher
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  2. H. W. Grießhammer
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  3. D. Shukla
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  4. H. M. Hofmann
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Correspondence to J. Kirscher.

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Communicated by M.C. Birse

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Kirscher, J., Grießhammer, H.W., Shukla, D. et al. Universal correlations in pion-less EFT with the resonating group method: Three and four nucleons. Eur. Phys. J. A 44, 239–256 (2010). https://doi.org/10.1140/epja/i2010-10939-5

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  • DOI: https://doi.org/10.1140/epja/i2010-10939-5

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