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The Faddeev–Yakubovsky Symphony

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Abstract

We briefly summarize the main steps leading to the Faddeev–Yakubovsky equations in configuration space for \(\hbox {N}=3, 4\) and 5 interacting particles.

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Notes

  1. Usually denoted by \(K_{ij,k}^l\equiv \varPhi _{ij,k}^l\) and \(H_{ij,kl}\equiv \varPhi _{ij,kl}\).

References

  1. L.D. Faddeev, JETP 39, 1459 (1960)

    Google Scholar 

  2. L.D. Faddeev, Sov. Phys. JETP 12, 1014 (1961)

    Google Scholar 

  3. L.D. Faddeev, Mathematical Aspects of the Three-body Problem in the Quantum Scattering Theory. Israel Program for Scientic Translations, Jerusalem (1965)

  4. L.D. Faddeev, S.P. Merkuriev, Quantum Scattering Theory for Several Particle Systems (Kluwer, Dordrecht, 1993)

    MATH  Google Scholar 

  5. O.A. Yakubovsky, Sov. J. Nucl. Phys. 5, 937 (1967)

    Google Scholar 

  6. R. Lazauskas, Few Body Syst. 59, 13 (2018)

    ADS  Google Scholar 

  7. R. Lazauskas, Phys. Rev. C 97, 044002 (2018)

    ADS  Google Scholar 

  8. R. Lazauskas, E. Hiyama, J. Carbonell, Phys. Lett. B 791, 335 (2019)

    ADS  Google Scholar 

  9. S.P. Merkuriev, Theor. Math. Phys. 8, 798 (1971)

    Google Scholar 

  10. S.P. Merkuriev, Sov. J. Nucl. Phys. 19, 22 (1974)

    Google Scholar 

  11. C. Gignoux, A. Laverne, Phys. Rev. Lett. 29, 436 (1972)

    ADS  Google Scholar 

  12. C. Gignoux, A. Laverne, S.P. Merkuriev, Phys. Rev. Lett. 33, 1350 (1974)

    ADS  Google Scholar 

  13. S.P. Merkurev, C. Gignoux, A. Laverne, Ann. Phys. 99, 30 (1976)

    ADS  Google Scholar 

  14. W. Glöckle, The Quantum Mechanical Few-Body Problems (Springer, Berlin, 1983)

    Google Scholar 

  15. F. Ciesielski, J. Carbonell, Phys. Rev. C 58, 58 (1998)

    ADS  Google Scholar 

  16. R. Lazauskas, PhD Univ. J. Fourier Grenoble (2003)

  17. R. Lazauskas, J. Carbonell, Phys. Rev. C 70, 044002 (2004)

    ADS  Google Scholar 

  18. S.P. Merkuriev, Ann. Phys. (N.Y.) 130, 395 (1980)

    ADS  MathSciNet  Google Scholar 

  19. S.P. Merkuriev, Acta Physica Aust. Suppl. XXIII, 65 (1981)

    MathSciNet  Google Scholar 

  20. P. Doleschall, Z. Papp, Phys. Rev. C 72(4), 044003 (2005)

    ADS  Google Scholar 

  21. A. Kvitsninsky, J. Carbonell, C. Gignoux, Phys. Rev. A 46, 1310 (1992)

    ADS  Google Scholar 

  22. M. Valdes et al., Phys. Rev. A 97, 012709 (2018)

    ADS  Google Scholar 

  23. V.A. Gradusov et al., J. Phys. B Atomic Mol. Opt. Phys. 52, 055202 (2019)

    ADS  Google Scholar 

  24. P. Noyes, H. Fideldey, in Proceedings of Texas Additive Manufacturing Conference, ed. by J. Gillespie, J. Nuttall (Benjamin, New York, 1968), pp. 195–293

  25. L.D. Faddeev, in Proceedings of the First International Conference of the Three Body Problems in Nuclear and Particle Physics, Birmingham, 8–10 July (1969), Ed. by J.S.C. Mc Kee, P.M. Rolph, North-Holland, London, p. 154 (1970)

  26. S. Weinberg, Phys. Rev. 130, 776 (1963)

    ADS  MathSciNet  Google Scholar 

  27. S. Weinberg, Phys. Rev. 131, 440 (1963)

    ADS  MathSciNet  Google Scholar 

  28. I.M. Narodetsky, O.A.Yakubovksy, ITEP-1-1980 (preprint) (1980)

  29. S.P. Merkuriev, S.L. Yakovlev, Akad. Nauk (SSSR) 261, 591 (1982)

    Google Scholar 

  30. S.P. Merkuriev, S.L. Yakovlev, Theor. Math. Phys. 56, 673 (1983)

    Google Scholar 

  31. S.P. Merkuriev, S.L. Yakovlev, C. Gignoux, Nucl. Phys. A 431, 125 (1984)

    ADS  Google Scholar 

  32. A. Nogga et al., Phys. Rev. C 65, 054003 (2002)

    ADS  Google Scholar 

  33. E. Uzu et al., Phys. Rev. C 68, 061001 (2003)

    ADS  Google Scholar 

  34. A. Deltuva, A.C. Fonseca, Phys. Rev. C 86, 011001 (2012)

    ADS  Google Scholar 

  35. R. Lazauskas, Phys. Rev. C 91, 041001 (2015)

    ADS  Google Scholar 

  36. T. Sasakawa, Prog. Theor. Phys. Suppl 61, 149 (1977)

    ADS  MathSciNet  Google Scholar 

  37. R. Lazauskas, in Application of the Complex Scaling Method in Quantum Scattering Theory, Habilitation Thesis (2019). arXiv:1904.04675 [nucl-th]

  38. Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, 2003)

    MATH  Google Scholar 

  39. N.W. Schellingerhout, L.P. Kok, G.D. Bosveld, Phys. Rev. A 40, 5568 (1989)

    ADS  MathSciNet  Google Scholar 

  40. R. Lazauskas. http://tel.ccsd.cnrs.fr/documents/archives0/00/00/41/78/, Univ. J. Fourier, Grenoble (2003)

  41. W. Glockle, H. Witala, D. Huber, H. Kamada, J. Golak, Phys. Rep. 274, 107 (1996)

    ADS  Google Scholar 

  42. W. Glockle, H. Kamada, Phys. Rev. Lett. 71, 971 (1993)

    ADS  Google Scholar 

  43. W. Glockle, H. Kamada, Nucl. A 560, 541 (1993)

    ADS  Google Scholar 

  44. A. Nogga, D. Huber, H. Kamada, W. Glockle, PLB 409, 19 (1997)

    Google Scholar 

  45. E.O. Alt, P. Grassberger, W. Sandhas, Nucl. Phys. B 2, 167 (1967)

    ADS  Google Scholar 

  46. A. Deltuva, A.C. Fonseca, Phys. Rev. C 76, 021001(R) (2007)

    ADS  Google Scholar 

  47. A. Deltuva, A.C. Fonseca, Phys. Rev. C 95, 024003 (2017)

    ADS  Google Scholar 

  48. B.S. Pudliner et al., Phys. Rev. C 56, 1720 (1997)

    ADS  Google Scholar 

  49. K.M. Nollett et al., Phys. Rev. Lett. 99, 022502 (2007)

    ADS  Google Scholar 

  50. M. Gattobigio, A. Kievsky, M. Viviani, Few Body Syst. 54, 657 (2013)

    ADS  Google Scholar 

  51. A. Kievsky et al., J. Phys. G 35, 063101 (2008)

    ADS  Google Scholar 

  52. E. Hiyama, Y. Kino, M. Kamimura, Prog. Theor. Phys. 51, 223 (2003)

    Google Scholar 

  53. P. Navrátil et al., Phys. Rev. C 61, 044001 (2000)

    ADS  Google Scholar 

  54. P. Navrátil et al., Physica Scr. 5, 053002 (2016)

    ADS  Google Scholar 

  55. G. Hupin, S. Quaglioni, P. Navrátil, Nat. Commun. 10, 351 (2019)

    ADS  Google Scholar 

  56. V.D. Efros, W. Leidemann, G. Orlandini, Phys. Lett. B 338, 130 (1994)

    ADS  Google Scholar 

  57. G. Orlandini, in An Advanced Course in Computational Nuclear Physics, Lecture Notes in Physics, vol. 936, p. 263 (2017)

    Google Scholar 

  58. A. Kievsky et al., Nucl. Phys. A 577, 511 (1994)

    ADS  Google Scholar 

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Authors and Affiliations

  1. IPHC, IN2P3-CNRS, Université de Strasbourg, BP 28, 67037, Strasbourg Cedex 2, France

    Rimantas Lazauskas

  2. IN2P3-CNRS, Institut de Physique Nucléaire, Univ Paris-Sud, 91406, Orsay Cedex, France

    Jaume Carbonell

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  1. Rimantas Lazauskas
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  2. Jaume Carbonell
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Correspondence to Rimantas Lazauskas.

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Lazauskas, R., Carbonell, J. The Faddeev–Yakubovsky Symphony. Few-Body Syst 60, 62 (2019). https://doi.org/10.1007/s00601-019-1529-5

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