Nuclear Physics and Atomic Energy

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
  Periodicity: 4 times per year

  Open access peer reviewed journal


 Home page   About 
Nucl. Phys. At. Energy 2012, volume 13, issue 3, pages 255-265.
Section: Nuclear Physics.
Received: 26.06.2012; Published online: 30.09.2012.
PDF Full text (ru)
https://doi.org/10.15407/jnpae2012.03.255

Evaluation of the effective range parameters and the analysis of neutron-proton scattering data in the low-energy region

V. A. Babenko, N. M. Petrov

Bogolyubov Institute for Theoretical Physics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine

Abstract: Singlet low-energy parameters of neutron-proton scattering are calculated on the basis of approximating the singlet effective-range function k cot δs by polynomials with the help of the latest experimental data on phase shifts of np-scattering from the SAID nucleon-nucleon database (data of the GWU group). The obtained values of the singlet low-energy parameters are as = -23.719085 fm, r0s = 2.625917 fm, ν2s = 0.0008677 fm3, ν3s = -0.01328 fm5, ν4s = 0.2370 fm7. With the obtained values of the low-energy parameters, precise description of singlet phase shift in the energy interval T ≲ 10 MeV is received by using the effective-range expansion. Low-energy neutron-proton scattering parameters for the experimental data from the SAID database differ markedly from the analogous results obtained for data of the Nijmegen group. Obtained effective range parameters corresponding to the experimental data from the SAID database lead to an extremely well description of experimental total cross section of neutron-proton scattering, which is in contrast to the set of the effective range parameters of the Nijmegen group.

Keywords: effective range parameters, singlet low-energy parameters of neutron-proton scattering, np-scattering, scattering phase shifts, T ≲ 10 MeV.

References:

1. Ситенко О. Г., Тартаковський В. К. Теорiя ядра (Київ: Либiдь, 2000) 608 с.

2. Гольдбергер М., Ватсон К. Теория столкновений. Пер. с англ. М. К. Поливанова и А. Т. Филиппова (Москва: Мир, 1967) 824 с.

3. Cohen T. D., Hansen J. M. Low Energy Theorems for Nucleon-Nucleon Scattering. Phys. Rev. C 59 (1999) 13. https://doi.org/10.1103/PhysRevC.59.13

4. Cohen T. D., Hansen J. M. Testing Low Energy Theorems in Nucleon-Nucleon Scattering. Phys. Rev. C 59 (1999) 3047. https://doi.org/10.1103/PhysRevC.59.3047

5. Bedaque P. F., van Kolck U. Effective Field Theory for Few-Nucleon Systems. Ann. Rev. Nucl. Part. Sci. 52 (2002) 339. https://doi.org/10.1146/annurev.nucl.52.050102.090637

6. U. van Kolck. Effective Field Theory of Short-Range Forces. Nucl. Phys. A 645 (1999) 273. https://doi.org/10.1016/S0375-9474(98)00612-5

7. Valderrama M. P., Arriola E. R. Determination of Low Energy Parameters for NN-Scattering at N4LO in All Partial Waves with j ≤ 5. arXiv:nucl-th/0407113v1 (2004) 19 p.

8. Valderrama M. P., Arriola E. R. Renormalization of Singlet NN-Scattering with One Pion Exchange and Boundary Conditions. Phys. Lett. B 580 (2004) 149. https://doi.org/10.1016/j.physletb.2003.11.037

9. Epelbaum E., Glöckle W., Meissner U. -G. Improving the Convergence of the Chiral Expansion for Nuclear Forces - II: Low Phases and the Deuteron. Eur. Phys. J. A 19 (2004) 401. https://doi.org/10.1140/epja/i2003-10129-8

10. Epelbaum E., Glöckle W., Meissner U. -G. The Two-Nucleon System at Next-To-Next-To-Next-To-Leading Order. Nucl. Phys. A 747 (2005) 362. https://doi.org/10.1016/j.nuclphysa.2004.09.107

11. Бабенко В. А., Петров Н. М. О триплетных низкоэнергетических параметрах нуклон-нуклонного рассеяния. Ядерная физика 69 (2006) 1586.

12. Arndt R. A., Briscoe W. J., Strakovsky I. I., Workman R. L. Partial-Wave Analysis Facility SAID, The George Washington University, Washington; http://gwdac.phys.gwu.edu

Arndt R. A., Strakovsky I. I., Workman R. L. Nucleon-Nucleon Elastic Scattering to 3 GeV. Phys. Rev. C 62 (2000) 034005. https://doi.org/10.1103/PhysRevC.62.034005

13. Nijmegen NN-Online program; http://nn-online.org

Stoks V. G. J., Klomp R. A. M., Rentmeester M. C. M., de Swart J. J. Partial-Wave Analysis of All Nucleon-Nucleon Scattering Data Below 350 MeV. Phys. Rev. C 48 (1993) 792. https://doi.org/10.1103/PhysRevC.48.792

14. Houk T. L. Neutron-Proton Scattering Cross Section at a Few Electron Volts and Charge Independence. Phys. Rev. C 3 (1971) 1886. https://doi.org/10.1103/PhysRevC.3.1886

15. Hurst P. Thesis. Fac. of Phys., Technische Universität München (1984);

Koester L., Waschkowski W., Meier J. Cross Sections for Neutrons of 1970 eV and Contributions to Fundamental Neutron Interactions. Z. Phys. A 337 (1990) 341. https://doi.org/10.1007/BF01289703

16. Dilg W. Measurement of the Neutron-Proton Total Cross Section at 132 eV. Phys. Rev. C 11 (1975) 103. https://doi.org/10.1103/PhysRevC.11.103

17. Кирилюк А. Л., Гребнев А. В., Ворона П. Н., Гнидак Н. Л. Изучение взаимодействия промежуточных нейтронов с тритием и водородом. Нейтронная физика: Материалы I Междунар. конф., Киев, 14 - 18 сент. 1987 г. (Москва, 1988) Т. II, c. 298.

18. Koester L., Waschkowski W., Meier J. Cross Sections for Neutrons of 1970 eV and Contributions to Fundamental Neutron Interactions. Z. Phys. A 337 (1990) 341. https://doi.org/10.1007/BF01289703

19. Fujita Y., Kobayashi K., Oosaki T., Block R. C. Measurement of the Neutron-Proton Total Cross Section Using 24 keV Iron Filtered Neutrons. Nucl. Phys. A 258 (1976) 1. https://doi.org/10.1016/0375-9474(76)90521-2

20. Engelke C. E., Benenson R. E., Melkonian E., Lebowitz J. M. Precision Measurements of the n-p Total Cross Section at 0.4926 and 3.205 MeV. Phys. Rev. 129 (1963) 324. https://doi.org/10.1103/PhysRev.129.324

21. Fields R. E., Becker R. L., Adair R. K. Measurement of the Neutron-Proton Cross Section at 1.0 and 2.5 MeV. Phys. Rev. 94 (1954) 389. https://doi.org/10.1103/PhysRev.94.389

22. Davis J. C., Weaver K. A., Hilscher D. et al. Total Cross Section of Protons for 2.5-MeV Neutrons. Phys. Rev. C 4 (1971) 1061. https://doi.org/10.1103/PhysRevC.4.1061

23. Davis J. C., Barschall H. H. Adjustments in the n-p singlet effective range. Phys. Lett. B 27 (1968) 636. https://doi.org/10.1016/0370-2693(68)90301-8

24. Hafner E. M., Hornyak W. F., Falk C. E. et al. The Total n-p Scattering Cross Section at 4.75 Mev. Phys. Rev. 89 (1953) 204. https://doi.org/10.1103/PhysRev.89.204

25. Ландау Л. Д., Смородинский Я. А. Рассеяние протонов протонами. ЖЭТФ 14 (1944) 269.

26. Schwinger J. S. A Variational Principle for Scattering Problems. Phys. Rev. 72 (1947) 742.

27. Blatt J. M., Jackson J. D. On the Interpretation of Neutron-Proton Scattering Data by the Schwinger Variational Method. Phys. Rev. 76 (1949) 18. https://doi.org/10.1103/PhysRev.76.18

28. Bethe H. A. Theory of the Effective Range in Nuclear Scattering. Phys. Rev. 76 (1949) 38. https://doi.org/10.1103/PhysRev.76.38

29. Хюльтен Л., Сугавара М. Проблема взаимодействия двух нуклонов. Строение атомного ядра. Пер. с англ.; Под ред А. С. Давыдова (Москва: ИЛ, 1959) С. 7.

30. Dumbrajs O., Koch R., Pilkuhn H. et al. Compilation of Coupling Constants and Low-Energy Parameters. Nucl. Phys. B 216 (1983) 277. https://doi.org/10.1016/0550-3213(83)90288-2

31. J. J. de Swart., Terheggen C. P. F., Stoks V. G. J. The Low-Energy Neutron-Proton Scattering Parameters and the Deuteron. arXiv:nucl-th/9509032v1 (1995) 10 p. https://doi.org/10.48550/arXiv.nucl-th/9509032

32. Machleidt R. High-Precision, Charge-Dependent Bonn Nucleon-Nucleon Potential. Phys. Rev. C 63 (2001) 024001. https://doi.org/10.1103/PhysRevC.63.024001

33. Machleidt R. A Consistent Meson-Theoretic Description of the NN-Interaction. Few-Body Problems in Physics: Proceedings of the IX European Conference, Tbilisi, 25 - 31 Aug. 1984 (World Sci., Singapore; Philadelphia, 1984) p. 218.

34. Stoks V. G. J., Klomp R. A. M., Terheggen C. P. F., J. J. de Swart. Construction of High-Quality NN Potential Models. Phys. Rev. C 49 (1994) 2950. https://doi.org/10.1103/PhysRevC.49.2950

35. Wiringa R. B., Stoks V. G. J., Schiavilla R. Accurate Nucleon-Nucleon Potential with Charge-Independence Breaking. Phys. Rev. C 51 (1995) 38. https://doi.org/10.1103/PhysRevC.51.38

36. Machleidt R., Sammarruca F., Song Y. Nonlocal Nature of the Nuclear Force and its Impact on Nuclear Structure. Phys. Rev. C 53 (1996) R1483. https://doi.org/10.1103/PhysRevC.53.R1483

37. Kukulin V. I., Pomerantsev V. N., Faessler A. Generalized Orthogonality-Condition Model for the NN Interaction. Phys. Rev. C 59 (1999) 3021; https://doi.org/10.1103/PhysRevC.59.3021

The Complete Version of Moscow NN Potential. arXiv:nucl-th/9903056v1 (1999) 40 p.

38. Hackenburg R. W. Neutron-Proton Effective Range Parameters and Zero-Energy Shape Dependence. Phys. Rev. C 73 (2006) 044002. https://doi.org/10.1103/PhysRevC.73.044002

39. Бабенко В. А., Петров Н. М. Определение низкоэнергетических параметров np-рассеяния из современных экспериментальных данных фазового анализа. Ядерная физика 70 (2007) 699.