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Nucleon—Nucleon Potentials from Phase Shifts and Inversion

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Part of the book series: Lecture Notes in Physics ((LNP,volume 427))

Abstract

We determine energy independent local nucleon-nucleon (NN) potentials for radial Schrödinger equations with Gelfand-Levitan and Marchenko inversion from today’s optimum phase shifts. Based on four phase shift sets, quantitative and complete results for all partial waves, with J ≤ 3, and all charge states are presented. The potential results are confronted with known features and other NN potentials. A first application to triton binding energy and bremsstrahlung calculations falls well within our expectations.

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References

  1. K. Holinde, Nucl. Phys. A 543, 143 (1992)

    Article  ADS  Google Scholar 

  2. J. Wambach, see this Proceedings and cited references

    Google Scholar 

  3. A. de Shalit and H. Feshbach, Theoretical nuclear physics: Nuclear structure, Wiley (1974)

    Google Scholar 

  4. H. Feshbach, Theoretical nuclear physics: Nuclear reactions, Wiley (1992)

    Google Scholar 

  5. B. Gibson, Nucl. Phys. A 543, l (1992)

    Google Scholar 

  6. A.J. Sarty ibid 49c, I. Slaus and A. Marusic, ibid 213c

    Google Scholar 

  7. V. Stoks and J. de Swart, Phys. Rev. C 47, 761 (1993)

    Article  ADS  Google Scholar 

  8. I.M. Gelfand and B.M. Levitan, On the determination of a differential equation by its spectral function, Amer. Math. Soc. Trans. Ser. 21, 253 (1955)

    MathSciNet  Google Scholar 

  9. Z.S. Agranovich and V.A. Marchenko, The Inverse Problem of Scattering Theory, Gordon and Breach (1963)

    Google Scholar 

  10. K. Chadan and P.C. Sabatier, Inverse problems in quantum scattering theory, Springer (1977), 2nd Ed. (1989)

    Google Scholar 

  11. B.N. Zakhariev and A.A. Suzko, Direct and Inverse Problems, Springer (1990).

    Google Scholar 

  12. M. Coz, J. Kuberczyk and H.V. von Geramb, Z. Phys A 326, 345 (1987), ibid A328, 259 and 265 (1987)

    Google Scholar 

  13. Th. Kirst, Nukleon-Nukleon Potentiale aus der Inversion, Thesis, Hamburg (1989)

    Google Scholar 

  14. Th. Kirst, J. Math. Phys. 32, 1318 (1991)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  15. Th. Kirst et al., Phys. Rev. C 40, 912 (1989)

    Article  ADS  Google Scholar 

  16. Th. Kirst, H. Kohlhoff and H.V. von Geramb, in Inverse Methods in Action, P.C. Sabatier (Ed.), Springer (1990)

    Google Scholar 

  17. M. Küker, Proton-Proton Inversions-Potentiale, Diplomarbeit, Hamburg (1992)

    Google Scholar 

  18. M. Küker, H. Kohlhoff and H.V. von Geramb, Nucleon Nucleon Potentials from Inversion: pp and np Single Channel Potentials, XIII. Int. Conf. Few Body Problems in Physics, Adelaide ( Australia ), January (1992)

    Google Scholar 

  19. H. Kohlhoff, M. Küker, H. Freitag and H.V. von Geramb, PhysicaScripta 48, 238 (1993)

    Article  ADS  Google Scholar 

  20. H. Kohlhoff, Nukleon-Nukleon Potentiale und Quanteninversion der Streumatrix, Thesis, Hamburg (1993) and Rationale Darstellungen der NN S-Matrizen, Diplomarbeit (1989)

    Google Scholar 

  21. M. Sander, Nukleonen Potentiale für die Praxis, Diplomarbeit, Hamburg (1993)

    Google Scholar 

  22. The central server of the Nuclear Theory Group, an IBM RISC-6000 workstation, can be reached by INTERNET and anonymous ftp. Use: ftp I04KTHA.DESY.DE or 131.169.81.53; user: anonymous; password: give your home-address. Change directory: pub, this subdirectory contains several subdirectories, change directory: INVERSION_POTENTIALS, contains 5 directories referring to 4 phase shift inversion potential sets ARNDT_PHASESHIFTS_1992, NIJMEGEN_PHASESHIFTS_NIJ3_REIDLIKE, BONN_BONNB_POTENTIAL_PHASESHIFTS PARIS_POTENTIAL_PHASESHIFTS and OPEP. Select and change directory for potential files. The first letter signals P/N (proton-proton/neutron-proton systems) and thereafter follows the configuration. Coupled channels use C as identifier and the rest is a source identifier. Each of these files contain a header line and thereafter 800 lines with: R [fm] and V(R) [MeV]. The directory OPEP contains a Fortran routine OPEP potential which is optional for J 4. In case of questions, please forward an E-mail to I04GERODHHDESY3.BITNET or I04GERODSYIBM.DESY.DE (131.169.93.32).

    Google Scholar 

  23. R.A. Arndt and L.D. Roper, Nucleon-nucleon partial-wave analysis to 1 GeV, Phys. Rev. D 28, 97 (1983)

    Article  Google Scholar 

  24. R.A. Arndt, J.S. Hyslop III and D.L. Roper, Nucleon-nucleon partial-wave analysis to 1100 MeV, Phys. Rev. D 35, 128 (1986)

    Article  Google Scholar 

  25. R.A. Arndt, Nucleon-nucleon partial-wave analysis to 1.6 GeV, Phys. Rev. D 45, 3995 (1992)

    Article  Google Scholar 

  26. R.A. Arndt, Scattering Analysis Interactive Dial-in (SAID) with interpolation files -93, Virginia Polytechnic Institute, Blacksbury, access via Telnet: 128.173.7.3 (VTINTE.PHYS.VT.EDU), Logon: PHYSICS, Password: QUANTUM). private communication (1992)

    Google Scholar 

  27. J. Bystricky et al., Nucleon-Nucleon phase shift analysis, J. Physique 48, 199 (1987)

    Article  Google Scholar 

  28. D.V. Bugg, np phase shifts, 142 to 800 Me V, Phys. Rev. C 41, 2708 (1990)

    Google Scholar 

  29. V. Stoks and J.J. de Swart, Nijmegen NN potential subroutine code, we use option #3/nonrelativistic and follow their suggestion to call this local potential Nijmegen-3 alias Nijm-3 which is equivalent to NijmRdl, private communication (1992)

    Google Scholar 

  30. J.J. de Swart, R.A.M. Klomp, T.A. Rijken and V.G.J. Stoks, A New partial wave analysis and the nucleon-nucleon interaction, Few-Body Systems Suppl. 6, 105 (1992)

    Article  Google Scholar 

  31. J.R. Bergervoet, P.C. van Campen, R.A.M. Klomp, J.L. de Kok, T.A. Rijken, V.G.J. Stoks and J.J. de Swart, Phase shift analysis of all proton-proton scattering data below T(lab) = 350-MeV, Phys. Rev. C 41, 1435 (1990)

    Google Scholar 

  32. T.A. Rijken, V.G.J. Stoks, R.A.M. Klomp, J.L. De Kok, J.J. De Swart, The Nijmegen NN phase shift analyses, Nucl. Phys. A 508, 173 (1990)

    Google Scholar 

  33. J.R. Bergervoet, P.C. van Campen, W.A. van der Sanden and J.J. de Swart, Phase shift analysis of O-30 MeV pp scattering data, Phys. Rev. C 38, 15 (1989)

    Google Scholar 

  34. J.R. Bergervoet, P.C. Van Campen, T.A. Rijken and J.J. De Swart, Optimal polynomial theory applied to O-MEV - 350 MeV pp scattering, Phys. Rev. C 38, 770 (1988)

    Google Scholar 

  35. J. Raynal, DWBA-92, a nonlocal microscopic optical model and inelastic scattering code, CEA-Saclay (1992)

    Google Scholar 

  36. W.R. Theis, Z. f. Naturforschung 11, 889 (1956).

    ADS  MATH  Google Scholar 

  37. G.A. Baker and P. Graves-Morris, Padé-Approximants, Part I: Basic Theory, and Padé-Approximants, Part II: Extensions and Applications, Encyclopedia of Mathematics and its Applications, Vols. 13 and 14, Addison-Wesley (1981)

    Google Scholar 

  38. W.B. Gragg, SIAM Review 14, 1 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  39. Y.L. Luke, Algorithms for the Computation of Mathematical Functions, Academic Press (1977) and Mathematical Functions and their Approximations, Academic Press (1975)

    Google Scholar 

  40. R. Newton, Scattering Theory of Waves and Particles, Springer, 2nd Ed. (1982)

    Google Scholar 

  41. C.E. Froeberg, Introduction to Numerical Analysis, Addison-Wesley (1979)

    Google Scholar 

  42. E.B. Saff and R.S. Varga, On the zeros and Poles of Padé-Approximants to ez, Num. Math. 25, 1 (1975), ibid 30, 241 (1978)

    MATH  MathSciNet  Google Scholar 

  43. E.B. Saff and Varga, R. S. (Eds.), Padé and Rational Approximation, Academic Press (1977)

    Google Scholar 

  44. M.Z. Nashed, Generalized Inverses and Applications, Academic Press (1976)

    Google Scholar 

  45. A. Tikhonov and V. Arsenin, Solutions of ill-posed problems, Winston Wiley (1977)

    Google Scholar 

  46. A. Tikhonov and A. Goncharskij, Improperly posed problems in natural sciences, Mir, Moscow (1987)

    Google Scholar 

  47. K. Clancey and I. Gohberg, Factorization of matrix functions and singular integral operators, OT3, Birkhäuser (1981)

    Google Scholar 

  48. M. Lacombe et al., Phys. Rev. C 21, 861 (1980)

    Article  ADS  Google Scholar 

  49. R. Machleidt,R. Holinde and Ch. Elster, Phys. Rep. 149, 1 (1987)

    Article  ADS  Google Scholar 

  50. R. Machleidt, The Meson Theory of Nuclear Forces and Nuclear Structure, Adv. Nuclear Physics, E. Voigt and J. Negele (Eds.), 19, 189 (1989)

    Google Scholar 

  51. L. Mathelitsch and B.L. VerWest, Phys. Rev. C 29, 739 (1984)

    Article  ADS  Google Scholar 

  52. H.V. von Geramb and K.A. Amos, Phys. Rev.C 41, 1384 (1990), ibid C 44 (1), 73 (1991)

    Google Scholar 

  53. I. Slaus, Phys. At. Nucl. 56, 948 (1993)

    Google Scholar 

  54. V.G.J. Stoks, P.C. Van Campen, T.A. Rijken and J.J. de Swart, Phys. Rev. Lett. 61, 1702 (1988)

    Article  ADS  Google Scholar 

  55. M. Jetter, see this Proceedings and cited references

    Google Scholar 

  56. I. Slaus, R. Machleidt, W. Tornow, W. Glöckle, W. Witala, Comments Nucl. Part. Phys. 20, 85 (1991)

    Google Scholar 

  57. H. Kamada, H. Witala and W. Glöckle, Phys. At. Nucl. 56, 873 (1993)

    Google Scholar 

  58. W. Glöckle and H. Kamada, Universität Bochum, private communication (1992)

    Google Scholar 

  59. W. Glöckle, T. Cornelius and H. Witala, Nucl. A 508, 115 (1990)

    Article  ADS  Google Scholar 

  60. H. Witala, W. Tornow and W. Glöckle, Few Body Systems 13

    Google Scholar 

  61. B.H.J. Mckellar and W. Glöckle, Nucl. Phys. A 416, 435 (1984) 11 and 189 (1992)

    Google Scholar 

  62. J. Strate et al., Nucl. Phys. A 501, 51 (1989)

    Article  ADS  Google Scholar 

  63. B. Gibson, Theory Division, LAMPF. private communication (1993)

    Google Scholar 

  64. B. Gibson and H.V. von Geramb, in preparation is an extensive study with 5, 9, 18 and 32 channels using genuine and inversion potentials — a correlation between PD, deuteron D-state probability, and lack of triton binding energy is manifest

    Google Scholar 

  65. V.R. Pandharipande, Nucl. Phys. A 553, 191c (1993)

    Article  ADS  Google Scholar 

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© 1994 Springer-Verlag Berlin Heidelberg

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von Geramb, H.V., Kohlhoff, H. (1994). Nucleon—Nucleon Potentials from Phase Shifts and Inversion. In: von Geramb, H.V. (eds) Quantum Inversion Theory and Applications. Lecture Notes in Physics, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13969-1_18

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