Ядерна фізика та енергетика Nuclear Physics and Atomic Energy   ISSN: 1818-331X (Print), 2074-0565 (Online)   Publisher: Institute for Nuclear Research of the National Academy of Sciences of Ukraine   Languages: Ukrainian, English, Russian   Periodicity: 4 times per year   Open access peer reviewed journal

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Abstract: Charge dependence of the pion-nucleon coupling constants and the ¹S₀-state low-energy nucleon-nucleon scattering parameters are studied on the basis of the Yukawa meson theory. The charge independence breaking effect in the pion-nucleon coupling constants is entirely explained by the mass difference between the charged and the neutral pions and by the mass difference between the proton and the neutron. Using of well-known pseudovector pion-nucleon coupling constant f ²_ppπ⁰=0.0749(7), which characterize the proton-proton nuclear interaction, we calculate the charged f ²_c=0.0802(7) and the neutral f ²₀=0.0750(7) pion-nucleon coupling constants, and also the pion-nucleon coupling constant f ²_nnπ⁰=0.0751(7), which characterize the neutron-neutron nuclear interaction. With the help of the obtained coupling constants, we also calculate values of the low-energy np- and nn-scattering parameters, which appear to be in good agreement with the experiment.

1. H. Yukawa, On the Interaction of Elementary Particles, Proc. Phys. Math. Soc. Jap. 17 (1935) 48 - 57.

2. L. Hulthen, M. Sugawara, The Two-Nucleon Problem, in Encyclopedia of Physics, Vol. 39: Structure of Atomic Nuclei (Ed. S. Flugge), Berlin-Gettingen-Heidelberg: Springer-Verlag (1957) 1 - 143. Google books

3. A. Bohr, B.R. Mottelson, Nuclear Structure, Vol. 1, New York: Benjamin (1969), 471 p. Google books

4. T. Ericson, W. Weise, Pions and Nuclei, Oxford: Clarendon Press (1988), 479 p. Google books

5. G.A. Miller, B.M.K. Nefkens, I. Slaus, Charge Symmetry, Quarks and Mesons, Phys. Rept. 194, No. 1-2 (1990) 1 - 116. https://doi.org/10.1016/0370-1573(90)90102-8

6. R. Machleidt, I. Slaus, The Nucleon-Nucleon Interaction, J. Phys. G 27, No. 5 (2001) R69 - R108. https://doi.org/10.1088/0954-3899/27/5/201

7. J.J. de Swart, M.C.M. Rentmeester, R.G.E. Timmermans, The Status of the Pion-Nucleon Coupling Constant, arXiv:nucl-th/9802084 (1998), 19 p. https://arxiv.org/abs/nucl-th/9802084

8. J. Blomgren (Ed.), Proc. Workshop on Critical Issues in the Determination of the Pion-Nucleon Coupling Constant, Uppsala, Sweden, June 7-8, 1999, Phys. Scr. T87 (2000) 5 - 77. http://iopscience.iop.org/issue/1402-4896/2000/T87

9. V. Limkaisang, K. Harada, J. Nagata et al., Phase-Shift Analysis of pp Scattering at T_L = 25-500 MeV, Prog. Theor. Phys. 105, No. 2 (2001) 233 - 242. https://doi.org/10.1143/PTP.105.233

10. J.R. Bergervoet, P.C. van Campen, R.A.M. Klomp et al., Phase Shift Analysis of All Proton-Proton Scattering Data Below T_lab = 350 MeV, Phys. Rev. C 41, No. 4 (1990) 1435 - 1452. https://doi.org/10.1103/PhysRevC.41.1435

11. R.A. Arndt, I.I. Strakovsky, R.L. Workman, Extraction of the πNN Coupling Constant from NN Scattering Data, Phys. Rev. C 52, No. 4 (1995) 2246 - 2249. https://doi.org/10.1103/PhysRevC.52.2246

12. R. Machleidt, M.K. Banerjee, Charge Dependence of the πNN Coupling Constant and Charge Dependence of the Nucleon-Nucleon Interaction, Few-Body Syst. 28, No. 3 (2000) 139 - 146. https://doi.org/10.1007/s006010070019

13. O. Dumbrajs, R. Koch, H. Pilkuhn et al., Compilation of Coupling Constants and Low-Energy Parameters, Nucl. Phys. B 216, No. 2 (1983) 277 - 335. https://doi.org/10.1016/0550-3213(83)90288-2

14. D.V. Bugg, A.A. Carter, J.R. Carter, New Values of Pion-Nucleon Scattering Lengths and f², Phys. Lett. B 44, No. 3 (1973) 278 - 280. https://doi.org/10.1016/0370-2693(73)90225-6

15. R. Koch, E. Pietarinen, Low-Energy πN Partial Wave Analysis, Nucl. Phys. A 336, No. 3 (1980) P. 331 - 346. https://doi.org/10.1016/0375-9474(80)90214-6

16. V. Stoks, R. Timmermans, J.J. de Swart, Pion-Nucleon Coupling Constant, Phys. Rev. C 47, No. 2 (1993) 512 - 520. https://doi.org/10.1103/PhysRevC.47.512

17. R.A. Arndt, W.J. Briscoe, I.I. Strakovsky et al., Dispersion Relation Constrained Partial Wave Analysis of πN Elastic and πN → ηN Scattering Data: The Baryon Spectrum, Phys. Rev. C 69, No. 3 (2004) 035213. https://doi.org/10.1103/PhysRevC.69.035213

18. R.A. Arndt, W.J. Briscoe, I.I. Strakovsky, R.L. Workman, Extended Partial-Wave Analysis of πN Scattering Data, Phys. Rev. C 74, No. 4 (2006) 045205. https://doi.org/10.1103/PhysRevC.74.045205

19. D.V. Bugg, The Pion Nucleon Coupling Constant, Eur. Phys. J. C 33, No. 4 (2004) 505 - 509. https://doi.org/10.1140/epjc/s2004-01666-y

20. V. Baru, C. Hanhart, M. Hoferichter et al., Precision Calculation of Threshold πd^- Scattering, πN Scattering Lengths, and the GMO Sum Rule, Nucl. Phys. A 872, No. 1 (2011) 69 - 116. https://doi.org/10.1016/j.nuclphysa.2011.09.015

21. T.E.O. Ericson, B. Loiseau, J. Nilsson et al., πNN Coupling from High Precision np Charge Exchange at 162 MeV, Phys. Rev. Lett. 75, No. 6 (1995) 1046 - 1049. https://doi.org/10.1103/PhysRevLett.75.1046

22. J. Rahm, J. Blomgren, H. Conde et al., np Scattering Measurements at 162 MeV and the πNN Coupling Constant, Phys. Rev. C 57, No. 3 (1998) 1077 - 1096. https://doi.org/10.1103/PhysRevC.57.1077

23. J. Rahm, J. Blomgren, H. Conde et al., np Scattering Measurements at 96 MeV, Phys. Rev. C 63, No. 4 (2001) 044001. https://doi.org/10.1103/PhysRevC.63.044001

24. E. Matsinos, G. Rasche, Systematic Effects in the Low-Energy Behavior of the Current SAID Solution for the Pion-Nucleon System, Int. J. Mod. Phys. E 26, No. 3 (2017) 1750002. https://doi.org/10.1142/S0218301317500021

25. E. Matsinos, G. Rasche, Update of the Phase-Shift Analysis of the Low-Energy πN Data, arXiv: 1706.05524 [nucl-th] (2017), 76 p. https://arxiv.org/abs/1706.05524

26. V.A. Babenko, N.M. Petrov, Charge Dependence of the Pion-Nucleon Coupling Constant, Yaderna Fizyka ta Energetyka (Nucl. Phys. At. Energy) 16, No. 2 (2015) 136 - 143. (Rus) http://jnpae.kinr.kiev.ua/16.2/Articles_PDF/jnpae-2015-16-0136-Babenko.pdf

27. V.A. Babenko, N.M. Petrov, Study of the Charge Dependence of the Pion-Nucleon Coupling Constant on the Basis of Data on Low-Energy Nucleon-Nucleon Interactions, Physics of Atomic Nuclei 79, No. 1 (2016) 67 - 71. https://doi.org/10.1134/S1063778815090033

28. V.A. Babenko, N.M. Petrov, Study of the Pion-Nucleon Coupling Constant Charge Dependence on the Basis of the Low-Energy Data on Nucleon-Nucleon Interaction, arXiv:1604.02912 [nucl-th] (2016), 10 p. https://arxiv.org/abs/1604.02912

29. V.A. Babenko, N.M. Petrov, Isospin Breaking in the Pion-Nucleon Coupling Constant and the Nucleon-Nucleon Scattering Length, Yaderna Fizyka ta Energetyka (Nucl. Phys. At. Energy) 17, No. 2 (2016) 143 - 149. (Rus) http://jnpae.kinr.kiev.ua/17.2/Articles_PDF/jnpae-2016-17-0143-Babenko.pdf

30. V.A. Babenko, N.M. Petrov, Relation between the Charged and Neutral Pion-Nucleon Coupling Constants in the Yukawa Model, Phys. Part. Nucl. Lett. 14, No. 1 (2017) 58 - 65. https://doi.org/10.1134/S1547477117010083

31. E.R. Arriola, J.E. Amaro, R.N. Perez, Three Pion Nucleon Coupling Constants, Mod. Phys. Lett. A 31, No. 28 (2016) 1630027. https://doi.org/10.1142/S0217732316300275

32. T.E.O. Ericson, M. Rosa-Clot, The Deuteron Asymptotic D-state as a Probe of the Nucleon-Nucleon Force, Nucl. Phys. A 405, No. 3 (1983) 497 - 533. https://doi.org/10.1016/0375-9474(83)90516-X

33. M. Naghdi, Nucleon-Nucleon Interaction: A Typical/Concise Review, Phys. Part. Nucl. 45, No. 5 (2014) 924 - 971. https://doi.org/10.1134/S1063779614050050

34. J. Beringer, J.-F. Arguin, R.M. Barnett et al. (Particle Data Group), Review of Particle Physics, Phys. Rev. D 86, No. 1 (2012) 010001. https://doi.org/10.1103/PhysRevD.86.010001

35. A.W. Thomas, P. Bickerstaff, A. Gersten, New Source of Charge-Symmetry Violation in the Nucleon-Nucleon System, Phys. Rev. D 24, No. 9 (1981) 2539 - 2541. https://doi.org/10.1103/PhysRevD.24.2539

36. L.K. Morrison, Radiative Corrections to Pion-Nucleon Coupling Constants, Ann. Phys. 50, No. 1 (1968) 6 - 50. https://doi.org/10.1016/0003-4916(68)90315-1

37. L.A. Sliv, Charge Independence and Charge Symmetry of Nuclear Forces, Izv. Akad. Nauk SSSR, Ser. Fiz. 38, No. 1 (1974) 2 - 14. (Rus)

38. V.V. Babikov, Variable Phase Approach in Quantum Mechanics, Moskva: Nauka (1976), 288 p. (Rus)

39. A.G. Sitenko, V.K. Tartakovskii, Lectures on the Theory of the Nucleus, Oxford, New York: Pergamon Press (1975), 304 p. Google Books

40. W.O. Lock, D.F. Measday, Intermediate Energy Nuclear Physics, London: Methuen (1970), 320 p. Google Books

41. V.A. Babenko, N.M. Petrov, Determination of Low-Energy Parameters of Neutron-Proton Scattering on the Basis of Modern Experimental Data from Partial-Wave Analyses, Physics of Atomic Nuclei 70, No. 4 (2007) 669 - 675. https://doi.org/10.1134/S1063778807040072

42. V.A. Babenko, N.M. Petrov, Determination of Low-Energy Parameters of Neutron-Proton Scattering in the the Shape-Parameter Approximation from Present-Day Experimental Data, Physics of Atomic Nuclei 73, No. 9 (2010) 1499 - 1506. https://doi.org/10.1134/S1063778810090048

43. B. Gabioud, J.-C. Alder, C. Joseph et al., n-n Effective Range from the Photon Spectrum of the Reaction π^-d → γnn, Phys. Lett. B 103, No. 1 (1981) 9 - 12. https://doi.org/10.1016/0370-2693(81)90182-9

44. V.A. Babenko, N.M. Petrov, Determination of Low-Energy Parameters of Neutron-Neutron Scattering from an Analysis of the Binding-Energy Difference between the ³H and ³He Mirror Nuclei, Physics of Atomic Nuclei 77, No. 5 (2014) 549 - 554. https://doi.org/10.1134/S1063778814050068

45. V.A. Babenko, N.M. Petrov, Mirror Nuclei ³H and ³He Binding Energies Difference and Low Energy Parameters of Neutron-Neutron Scattering, Phys. Part. Nucl. Lett. 12, No. 4 (2015) 584 - 590. https://doi.org/10.1134/S1547477115040068

46. B. Kuhn, Measurements of the Neutron-Neutron Scattering Wave Length and the Problem of Charge Dependence of Nuclear Forces, Phys. Part. Nucl. 6, No. 2 (1975) 347 - 392.

47. C.R. Howell, Q. Chen, T.S. Carman et al., Toward a Resolution of the Neutron-Neutron Scattering-Length Issue, Phys. Lett. B 444, No. 3 (1998) 252 - 259. https://doi.org/10.1016/S0370-2693(98)01386-0

48. D.E. Gonzalez Trotter, F. Salinas, Q. Chen et al., New Measurement of the ¹S₀ Neutron-Neutron Scattering Length Using the Neutron-Proton Scattering Length as a Standard, Phys. Rev. Lett. 83, No. 19 (1999) 3788 - 3791. https://doi.org/10.1103/PhysRevLett.83.3788

49. V. Huhn, L. Watzold, Ch. Weber et al., New Investigation of the Neutron-Neutron and Neutron-Proton Final-State Interaction in the n-d Breakup Reaction, Phys. Rev. C 63, No. 1 (2001) 014003. https://doi.org/10.1103/PhysRevC.63.014003

50. W. von Witsch, X. Ruan, H. Witala, Neutron-Neutron Final-State Interaction in the ²H(n,p)2n Reaction at E_n = 17.4 MeV, Phys. Rev. C 74, No. 1 (2006) 014001. https://doi.org/10.1103/PhysRevC.74.014001

51. D.E. Gonzalez Trotter, F. Salinas Meneses, W. Tornow et al., Neutron-Deuteron Breakup Experiment at E_n = 13 MeV: Determination of the ¹S₀ Neutron-Neutron Scattering Length a_nn, Phys. Rev. C 73, No. 3 (2006) 034001. https://doi.org/10.1103/PhysRevC.73.034001

52. V.A. Babenko, N.M. Petrov, Low-Energy Parameters of Neutron-Neutron Interaction in the Effective-Range Approximation, Physics of Atomic Nuclei 76, No. 6 (2013) 684 - 689. https://doi.org/10.1134/S1063778813060033