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Experiments of Few-Nucleon Scattering to Explore Three-Nucleon Forces

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Abstract

Few-nucleon scattering offers a good opportunities to study dynamical aspects of three-nucleon forces, that are momentum, spin and isospin dependent. In the paper, the experimental results of deuteron-proton elastic scattering at \(\sim ~\mathrm 100\) MeV/nucleon obtained in the course of the study are presented. The experimental study of few-nucleon scattering has been recently extended to the proton-\(^3 \textrm{He}\) scattering with the aim of approaching the isospin \(T=3/2\) channel in three-nucleon forces. The data are in comparison with the rigorous numerical calculations based on state-of-the-art nuclear potentials with three-nucleon forces.

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References

  1. H. Yukawa, On the interaction of elementary particles. I. Proc. Phys. Math. Soc. Jpn. 17, 48–57 (1935). https://doi.org/10.11429/ppmsj1919.17.0_48

    Article  Google Scholar 

  2. J. Fujita, H. Miyazawa, Pion theory of three-body forces. Progress Theoret. Phys. 17(3), 360–365 (1957). https://doi.org/10.1143/PTP.17.360

    Article  ADS  MathSciNet  Google Scholar 

  3. S. Coon, H. Han, Reworking the Tucson-Melbourne three-nucleon potential. Few-Body Syst. 30, 131 (2001)

    Article  ADS  Google Scholar 

  4. B.S. Pudliner, V.R. Pandharipande, J. Carlson, S.C. Pieper, R.B. Wiringa, Phys. Rev. C 56, 1720 (1997). https://doi.org/10.1103/PhysRevC.56.1720

    Article  ADS  Google Scholar 

  5. U. van Kolck, Few-nucleon forces from chiral Lagrangians. Phys. Rev. C 49, 2932 (1994). https://doi.org/10.1103/PhysRevC.49.2932

    Article  ADS  Google Scholar 

  6. E. Epelbaum, H.W. Hammer, U.G. Meißner, Modern theory of nuclear forces. Rev. Mod. Phys. 81, 1773 (2009). https://doi.org/10.1103/RevModPhys.81.1773

    Article  ADS  Google Scholar 

  7. C.R. Chen, G.L. Payne, J.L. Friar, B.F. Gibson, Phys. Rev. C 33, 1740 (1986). https://doi.org/10.1103/PhysRevC.33.1740

    Article  ADS  Google Scholar 

  8. T. Sasakawa, S. Ishikawa, Triton binding energy and three-nucleon potential. Few-Body Syst. 1(1), 3 (1986). https://doi.org/10.1007/BF01075288

    Article  ADS  Google Scholar 

  9. R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Accurate nucleon-nucleon potential with charge-independence breaking. Phys. Rev. C 51, 38 (1995). https://doi.org/10.1103/PhysRevC.51.38

    Article  ADS  Google Scholar 

  10. R. Machleidt, High-precision, charge-dependent Bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001). https://doi.org/10.1103/PhysRevC.63.024001

    Article  ADS  Google Scholar 

  11. V.G.J. Stoks, R.A.M. Klomp, C.P.F. Terheggen, J.J. de Swart, Construction of high-quality NN potential models. Phys. Rev. C 49, 2950–2962 (1994). https://doi.org/10.1103/PhysRevC.49.2950

    Article  ADS  Google Scholar 

  12. A. Nogga, H. Kamada, W. Glockle, B.R. Barrett, The \(\alpha \) particle based on modern nuclear forces. Phys. Rev. C 65, 054003 (2002). https://doi.org/10.1103/PhysRevC.65.054003

    Article  ADS  Google Scholar 

  13. S.C. Pieper, K. Varga, R.B. Wiringa, Quantum monte Carlo calculations of \(a=9,10\) nuclei. Phys. Rev. C 66, 044310 (2002). https://doi.org/10.1103/PhysRevC.66.044310

    Article  ADS  Google Scholar 

  14. P. Navrátil, W.E. Ormand, Ab initio shell model with a genuine three-nucleon force for the p-shell nuclei. Phys. Rev. C 68, 034305 (2003). https://doi.org/10.1103/PhysRevC.68.034305

    Article  ADS  Google Scholar 

  15. A. Akmal, V.R. Pandharipande, D.G. Ravenhall, Equation of state of nucleon matter and neutron star structure. Phys. Rev. C 58, 1804–1828 (1998). https://doi.org/10.1103/PhysRevC.58.1804

    Article  ADS  Google Scholar 

  16. S. Gandolfi, J. Carlson, S. Reddy, A.W. Steiner, R.B. Wiringa, The equation of state of neutron matter, symmetry energy, and neutron star structure. Eur. Phys. J. A 50, 10 (2014). https://doi.org/10.1140/epja/i2014-14010-5. arXiv:1307.5815 [nucl-th]

  17. J.E. Lynn, I. Tews, J. Carlson, S. Gandolfi, A. Gezerlis, K.E. Schmidt, A. Schwenk, Chiral three-nucleon interactions in light nuclei, neutron-\(\alpha \) scattering, and neutron matter. Phys. Rev. Lett. 116, 062501 (2016). https://doi.org/10.1103/PhysRevLett.116.062501

    Article  ADS  Google Scholar 

  18. K. Hebeler, Three-nucleon forces: Implementation and applications to atomic nuclei and dense matter. Phys. Rep. 890, 1–116 (2021). https://doi.org/10.1016/j.physrep.2020.08.009

    Article  ADS  Google Scholar 

  19. H. Witała, W. Glockle, D. Huber, J. Golak, H. Kamada, Cross section minima in elastic \(\mathit{Nd}\) scattering: possible evidence for three-nucleon force effects. Phys. Rev. Lett. 81, 1183 (1998). https://doi.org/10.1103/PhysRevLett.81.1183

    Article  ADS  Google Scholar 

  20. N. Kalantar-Nayestanaki, E. Epelbaum, J.G. Messchendorp, A. Nogga, Signatures of three-nucleon interactions in few-nucleon systems. Rep. Prog. Phys. 75(1), 016301 (2011). https://doi.org/10.1088/0034-4885/75/1/016301

    Article  ADS  Google Scholar 

  21. H. Okamura et al., Development of the RIKEN polarized ion source. AIP Conf. Proc. 293, 84 (1993). https://doi.org/10.1063/1.45151

    Article  ADS  Google Scholar 

  22. T. Ichihara et al., Spin isospin resonance observed in the (\(d\),\(^{2}{{\rm He}}\)) and (\(^{12}\)C, \(^{12}\)N) reactions at \(E/A = 135~{{\rm MeV}}\). Nucl. Phys. A 569, 287c (1994). https://doi.org/10.1016/0375-9474(94)90119-8

    Article  ADS  Google Scholar 

  23. ...K. Sekiguchi, H. Sakai, H. Witała, W. Glockle, J. Golak, M. Hatano, H. Kamada, H. Kato, Y. Maeda, J. Nishikawa, A. Nogga, T. Ohnishi, H. Okamura, N. Sakamoto, S. Sakoda, Y. Satou, K. Suda, A. Tamii, T. Uesaka, T. Wakasa, K. Yako, Complete set of precise deuteron analyzing powers at intermediate energies: comparison with modern nuclear force predictions. Phys. Rev. C 65, 034003 (2002). https://doi.org/10.1103/PhysRevC.65.034003

    Article  ADS  Google Scholar 

  24. ...K. Sekiguchi, H. Sakai, H. Witała, K. Ermisch, W. Glöckle, J. Golak, M. Hatano, H. Kamada, N. Kalantar-Nayestanaki, H. Kato, Y. Maeda, J. Nishikawa, A. Nogga, T. Ohnishi, H. Okamura, T. Saito, N. Sakamoto, S. Sakoda, Y. Satou, K. Suda, A. Tamii, T. Uchigashima, T. Uesaka, T. Wakasa, K. Yako, Polarization transfer measurement for \(dp\) elastic scattering at 135 \({{\rm MeV}}/{{\rm nucleon}}\) and three-nucleon force effects. Phys. Rev. C 70, 014001 (2004). https://doi.org/10.1103/PhysRevC.70.014001

    Article  ADS  Google Scholar 

  25. K. Sekiguchi, H. Sakai, H. Witała, W. Glockle, J. Golak, K. Hatanaka, M. Hatano, K. Itoh, H. Kamada, H. Kuboki, Y. Maeda, A. Nogga, H. Okamura, T. Saito, N. Sakamoto, Y. Sakemi, M. Sasano, Y. Shimizu, K. Suda, A. Tamii, T. Uesaka, T. Wakasa, K. Yako, Resolving the discrepancy of 135 \({\rm MeV}pd\) elastic scattering cross sections and relativistic effects. Phys. Rev. Lett. 95, 162301 (2005). https://doi.org/10.1103/PhysRevLett.95.162301

    Article  ADS  Google Scholar 

  26. Y. Maeda, H. Sakai, K. Fujita, M.B. Greenfield, K. Hatanaka, M. Hatano, J. Kamiya, T. Kawabata, H. Kuboki, H. Okamura, J. Rapaport, T. Saito, Y. Sakemi, M. Sasano, K. Sekiguchi, Y. Shimizu, K. Suda, Y. Tameshige, A. Tamii, T. Wakasa, K. Yako, J. Blomgren, P. Mermod, A. Öhrn, M. Österlund, H. Witała, A. Deltuva, A.C. Fonseca, P.U. Sauer, W. Glockle, J. Golak, H. Kamada, A. Nogga, R. Skibiń ński, Differential cross section and analyzing power measurements for \(\stackrel{\rightarrow }{n}d\) elastic scattering at 248 \({{\rm MeV}}\). Phys. Rev. C 76, 014004 (2007). https://doi.org/10.1103/PhysRevC.76.014004

  27. K. Sekiguchi, Y. Wada, J. Miyazaki, H. Witała, M. Dozono, U. Gebauer, J. Golak, H. Kamada, S. Kawase, Y. Kubota, C.S. Lee, Y. Maeda, T. Mashiko, K. Miki, A. Nogga, H. Okamura, T. Saito, H. Sakai, S. Sakaguchi, N. Sakamoto, M. Sasano, Y. Shimizu, R. Skibiński, H. Suzuki, T. Taguchi, K. Takahashi, T.L. Tang, T. Uesaka, T. Wakasa, K. Yako, Complete set of deuteron analyzing powers for \(dp\) elastic scattering at 250–294 \(\rm MeV \)/nucleon and the three-nucleon force. Phys. Rev. C 89, 064007 (2014). https://doi.org/10.1103/PhysRevC.89.064007

    Article  ADS  Google Scholar 

  28. K. Sekiguchi, H. Witała, T. Akieda, D. Eto, H. Kon, Y. Wada, A. Watanabe, S. Chebotaryov, M. Dozono, J. Golak, H. Kamada, S. Kawakami, Y. Kubota, Y. Maeda, K. Miki, E. Milman, A. Ohkura, H. Sakai, S. Sakaguchi, N. Sakamoto, M. Sasano, Y. Shindo, R. Skibiński, H. Suzuki, M. Tabata, T. Uesaka, T. Wakasa, K. Yako, T. Yamamoto, Y. Yanagisawa, J. Yasuda, Complete set of deuteron analyzing powers from \(\vec{d}p\) elastic scattering at \(190~{{\rm MeV}}/{{\rm nucleon}}\). Phys. Rev. C 96, 064001 (2017). https://doi.org/10.1103/PhysRevC.96.064001

    Article  ADS  Google Scholar 

  29. K. Ermisch, H.R. Amir-Ahmadi, A.M. van den Berg, R. Castelijns, B. Davids, E. Epelbaum, E. van Garderen, W. Glöckle, J. Golak, M.N. Harakeh, M. Hunyadi, M.A. de Huu, N. Kalantar-Nayestanaki, H. Kamada, M. Kis, M. Mahjour-Shafiei, A. Nogga, R. Skibiński, H. Witała, H.J. Wörtche, Systematic investigation of the elastic proton-deuteron differential cross section at intermediate energies. Phys. Rev. C 68, 051001 (2003). https://doi.org/10.1103/PhysRevC.68.051001

    Article  ADS  Google Scholar 

  30. A. Ramazani-Moghaddam-Arani, H.R. Amir-Ahmadi, A.D. Bacher, C.D. Bailey, A. Biegun, M. Eslami-Kalantari, I. Gašsparić, L. Joulaeizadeh, N. Kalantar-Nayestanaki, S. Kistryn, A. Kozela, H. Mardanpour, J.G. Messchendorp, A.M. Micherdzinska, H. Moeini, S.V. Shende, E. Stephan, E.J. Stephenson, R. Sworst, Elastic proton-deuteron scattering at intermediate energies. Phys. Rev. C 78, 014006 (2008). https://doi.org/10.1103/PhysRevC.78.014006

    Article  ADS  Google Scholar 

  31. S. Binder, et al., Few-nucleon systems with state-of-the-art chiral nucleon-nucleon forces. Phys. Rev. C 93(4), 044002 (2016). https://doi.org/10.1103/PhysRevC.93.044002. arXiv:1505.07218 [nucl-th]

  32. E. Epelbaum, J. Golak, K. Hebeler, H. Kamada, H. Krebs, U.G. Meißner, A. Nogga, P. Reinert, R. Skibiński, K. Topolnicki, Y. Volkotrub, H. Witala, Towards high-order calculations of three-nucleon scattering in chiral effective field theory. Eur. Phys. J. A 56(3), 92 (2020). https://doi.org/10.1140/epja/s10050-020-00102-2

    Article  ADS  Google Scholar 

  33. A. Deltuva, A.C. Fonseca, Ab initio four-body calculation of \(n\)-\(^{3}{{\rm He}}\), \(p\)-\(^{3}{{\rm H}}\), and \(d-d\) scattering. Phys. Rev. C 76, 021001 (2007). https://doi.org/10.1103/PhysRevC.76.021001

    Article  ADS  Google Scholar 

  34. R. Lazauskas, Elastic proton scattering on tritium below the \(n\text{- }^{3}{{\rm He}} \) threshold. Phys. Rev. C 79, 054007 (2009). https://doi.org/10.1103/PhysRevC.79.054007

    Article  ADS  Google Scholar 

  35. M. Viviani, A. Kievsky, S. Rosati, E.A. George, L.D. Knutson, The \({A}_{y}\) problem for \({p}-^{3}{{\rm He}} \) elastic scattering. Phys. Rev. Lett. 86, 3739–3742 (2001). https://doi.org/10.1103/PhysRevLett.86.3739

    Article  ADS  Google Scholar 

  36. A. Deltuva, A.C. Fonseca, Calculation of proton-\({}^{3}{{\rm He}}\) elastic scattering between 7 and 35\({{\rm MeV}}\). Phys. Rev. C 87, 054002 (2013). https://doi.org/10.1103/PhysRevC.87.054002

    Article  ADS  Google Scholar 

  37. A.C. Fonseca, A. Deltuva, Numerical exact ab initio four-nucleon scattering calculations: from dream to reality. Few-Body Syst. 58(2), 46 (2017). https://doi.org/10.1007/s00601-017-1211-8

    Article  ADS  Google Scholar 

  38. A. Watanabe, S. Nakai, Y. Wada, K. Sekiguchi, A. Deltuva, T. Akieda, D. Etoh, M. Inoue, Y. Inoue, K. Kawahara, H. Kon, K. Miki, T. Mukai, D. Sakai, S. Shibuya, Y. Shiokawa, T. Taguchi, H. Umetsu, Y. Utsuki, M. Watanabe, S. Goto, K. Hatanaka, Y. Hirai, T. Ino, D. Inomoto, A. Inoue, S. Ishikawa, M. Itoh, H. Kanda, H. Kasahara, N. Kobayashi, Y. Maeda, S. Mitsumoto, S. Nakamura, K. Nonaka, H.J. Ong, H. Oshiro, Y. Otake, H. Sakai, A. Taketani, A. Tamii, D.T. Tran, T. Wakasa, Y. Wakabayashi, T. Wakui, Proton-\(^{3}{{\rm He}} \) elastic scattering at intermediate energies. Phys. Rev. C 103, 044001 (2021). https://doi.org/10.1103/PhysRevC.103.044001

    Article  ADS  Google Scholar 

  39. A. Watanabe, S. Nakai, K. Sekiguchi, A. Deltuva, S. Goto, K. Hatanaka, Y. Hirai, T. Ino, D. Inomoto, M. Inoue, S. Ishikawa, M. Itoh, H. Kanda, H. Kasahara, Y. Maeda, K. Miki, K. Nonaka, H.J. Ong, H. Oshiro, D. Sakai, H. Sakai, S. Shibuya, D.T. Tran, H. Umetsu, Y. Utsuki, T. Wakasa, Spin correlation coefficient for proton-\(^{3}{{\rm He}}\) elastic scattering at \(100~{{\rm MeV}}\). Phys. Rev. C 106, 054002 (2022). https://doi.org/10.1103/PhysRevC.106.054002

    Article  ADS  Google Scholar 

  40. P. Doleschall, Influence of the short range nonlocal nucleon-nucleon interaction on the elastic \(n-d\) scattering: below \(30{{\rm MeV}} \). Phys. Rev. C 69, 054001 (2004). https://doi.org/10.1103/PhysRevC.69.054001

    Article  ADS  Google Scholar 

  41. P. Reinert, H. Krebs, E. Epelbaum, Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order. Eur. Phys. J. A 54(5), 86 (2018). https://doi.org/10.1140/epja/i2018-12516-4

    Article  ADS  Google Scholar 

  42. A. Deltuva, R. Machleidt, P.U. Sauer, Realistic two-baryon potential coupling two-nucleon and nucleon-\(\Delta \)-isobar states: fit and applications to three-nucleon system. Phys. Rev. C 68, 024005 (2003). https://doi.org/10.1103/PhysRevC.68.024005

    Article  ADS  Google Scholar 

  43. S. Nemoto, Elastic nucleon-deuteron scattering with \(\Delta \)-isobar excitation. Ph.D. thesis, Hannover University (1999)

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Acknowledgements

This work is supported financially in part by JSPS KAKENHI Grants No. JP25105502, No. JP16H02171, No. JP18H05404, No. JP20H05636, Japan, and JST ERATO Grant No. JPMJER2304, Japan.

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Sekiguchi, K. Experiments of Few-Nucleon Scattering to Explore Three-Nucleon Forces. Few-Body Syst 65, 45 (2024). https://doi.org/10.1007/s00601-024-01910-8

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