Skip to main content
SpringerLink
Log in

The importance of few-nucleon forces in chiral effective field theory

  • Regular Article –Theoretical Physics
  • Published:
The European Physical Journal A Aims and scope Submit manuscript

Abstract

We study the importance of few-nucleon forces in chiral effective field theory for describing many-nucleon systems. A combinatorial argument suggests that three-nucleon forces-which are conventionally regarded as next-to-next-to-leading order-should accompany the two-nucleon force already at leading order (LO) starting with mass number \(A\simeq \) 10–20. We find that this promotion enables the first realistic description of the \(^{16}\)O ground state based on a renormalization-group-invariant LO interaction. We also performed coupled-cluster calculations of the equation of state for symmetric nuclear matter and our results indicate that LO four-nucleon forces could play a crucial role for describing heavy-mass nuclei. The enhancement mechanism we found is very general and could be important also in other many-body problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data Availability

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Our work involves only theoretical arguments and numerical calculations. All the data and results are presented as figures and tables in the manuscript.]

Notes

  1. Not being renormalizable, this is sometimes referred to more accurately as Weinberg’s pragmatic proposal [5].

  2. For example, contributions from NN and NNN interactions appear as Eq. (A2) and (A4) of Ref. [55] in ab initio calculations.

  3. Note that \(c _{1,3,4}\) can change considerably when including higher-order corrections [68].

References

  1. H.-W. Hammer, S. König, U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020). https://doi.org/10.1103/RevModPhys.92.025004. arXiv:1906.12122 [nucl-th]

    Article  ADS  Google Scholar 

  2. E. Epelbaum, H.-W. Hammer, U.-G. Meißner, Rev. Mod. Phys. 81, 1773 (2009). https://doi.org/10.1103/RevModPhys.81.1773. arXiv:0811.1338 [nucl-th]

    Article  ADS  Google Scholar 

  3. H. Hergert, Front. Phys. 8, 379 (2020). https://doi.org/10.3389/fphy.2020.00379. arXiv:2008.05061 [nucl-th]

    Article  Google Scholar 

  4. I. Tews, Z. Davoudi, A. Ekström, J.D. Holt, J.E. Lynn, J. Phys. G 47, 103001 (2020). https://doi.org/10.1088/1361-6471/ab9079. arXiv:2001.03334 [nucl-th]

    Article  ADS  Google Scholar 

  5. H.W. Grießhammer, Few Body Syst. 63, 44 (2022). https://doi.org/10.1007/s00601-022-01739-z. arXiv:2111.00930 [nucl-th]

    Article  ADS  Google Scholar 

  6. S. Weinberg, Phys. Lett. B 251, 288 (1990). https://doi.org/10.1016/0370-2693(90)90938-3

    Article  ADS  Google Scholar 

  7. S. Weinberg, Nucl. Phys. B 363, 3 (1991). https://doi.org/10.1016/0550-3213(91)90231-l

    Article  ADS  Google Scholar 

  8. R. Machleidt, D.R. Entem, Phys. Rept. 503, 1 (2011). https://doi.org/10.1016/j.physrep.2011.02.001. arXiv:1105.2919 [nucl-th]

    Article  ADS  Google Scholar 

  9. E. Epelbaum, U.-G. Meißner, Ann. Rev. Nucl. Part. Sci. 62, 159 (2012). https://doi.org/10.1146/annurev-nucl-102010-130056. arXiv:1201.2136 [nucl-th]

    Article  ADS  Google Scholar 

  10. S. Binder, J. Langhammer, A. Calci, R. Roth, Phys. Lett. B 736, 119 (2014). https://doi.org/10.1016/j.physletb.2014.07.010

    Article  ADS  Google Scholar 

  11. V. Lapoux, V. Somà, C. Barbieri, H. Hergert, J.D. Holt, S.R. Stroberg, Phys. Rev. Lett. 117, 052501 (2016). https://doi.org/10.1103/PhysRevLett.117.052501. arXiv:1605.07885 [nucl-ex]

    Article  ADS  Google Scholar 

  12. B.D. Carlsson, A. Ekström, C. Forssén, D.F. Strömberg, G.R. Jansen, O. Lilja, M. Lindby, B.A. Mattsson, K.A. Wendt, Phys. Rev. X 6, 011019 (2016). https://doi.org/10.1103/PhysRevX.6.011019

    Article  Google Scholar 

  13. R. Machleidt, Nucl. Theor. 37, 62 (2018). arXiv:1901.01473 [nucl-th]

    Google Scholar 

  14. V. Somà, P. Navrátil, F. Raimondi, C. Barbieri, T. Duguet, Phys. Rev. C 101, 014318 (2020). https://doi.org/10.1103/PhysRevC.101.014318. arXiv:1907.09790 [nucl-th]

    Article  ADS  Google Scholar 

  15. A. Ekström, G.R. Jansen, K.A. Wendt, G. Hagen, T. Papenbrock, B.D. Carlsson, C. Forssén, M. Hjorth-Jensen, P. Navrátil, W. Nazarewicz, Phys. Rev. C 91, 051301 (2015). https://doi.org/10.1103/PhysRevC.91.051301. arXiv:1502.04682 [nucl-th]

    Article  ADS  Google Scholar 

  16. U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999). https://doi.org/10.1016/S0146-6410(99)00097-6. arXiv:nucl-th/9902015

    Article  ADS  Google Scholar 

  17. A. Ekström, G. Hagen, T.D. Morris, T. Papenbrock, P.D. Schwartz, Phys. Rev. C 97, 024332 (2018). https://doi.org/10.1103/PhysRevC.97.024332. arXiv:1707.09028 [nucl-th]

    Article  ADS  Google Scholar 

  18. W.G. Jiang, A. Ekström, C. Forssén, G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. C 102, 054301 (2020). https://doi.org/10.1103/PhysRevC.102.054301. arXiv:2006.16774 [nucl-th]

    Article  ADS  Google Scholar 

  19. U. van Kolck, Front. Phys. 8, 79 (2020). https://doi.org/10.3389/fphy.2020.00079. arXiv:2003.06721 [nucl-th]

    Article  Google Scholar 

  20. D.B. Kaplan, M.J. Savage, M.B. Wise, Nucl. Phys. B 478, 629 (1996). https://doi.org/10.1016/0550-3213(96)00357-4. arXiv:nucl-th/9605002

    Article  ADS  Google Scholar 

  21. S.R. Beane, P.F. Bedaque, M.J. Savage, U. van Kolck, Nucl. Phys. A 700, 377 (2002). https://doi.org/10.1016/S0375-9474(01)01324-0. arXiv:nucl-th/0104030

    Article  ADS  Google Scholar 

  22. A. Nogga, R.G.E. Timmermans, U. van Kolck, Phys. Rev. C 72, 054006 (2005). https://doi.org/10.1103/PhysRevC.72.054006. arXiv:nucl-th/0506005

    Article  ADS  Google Scholar 

  23. M. Pavón Valderrama, E. Ruiz Arriola, Phys. Rev. C 74, 064004 (2006), note [Erratum: Phys.Rev.C 75, 059905 (2007)], https://doi.org/10.1103/PhysRevC.74.064004. arXiv:nucl-th/0507075

  24. C.J. Yang, C. Elster, D.R. Phillips, Phys. Rev. C 80, 034002 (2009). https://doi.org/10.1103/PhysRevC.80.034002. arXiv:0901.2663 [nucl-th]

    Article  ADS  Google Scholar 

  25. C.J. Yang, C. Elster, D.R. Phillips, Phys. Rev. C 80, 044002 (2009). https://doi.org/10.1103/PhysRevC.80.044002. arXiv:0905.4943 [nucl-th]

    Article  ADS  Google Scholar 

  26. C. Zeoli, R. Machleidt, D.R. Entem, Few Body Syst. 54, 2191 (2013). https://doi.org/10.1007/s00601-012-0481-4. arXiv:1208.2657 [nucl-th]

    Article  ADS  Google Scholar 

  27. M.C. Birse, Phys. Rev. C 74, 014003 (2006). https://doi.org/10.1103/PhysRevC.74.014003. arXiv:nucl-th/0507077

    Article  ADS  Google Scholar 

  28. M.C. Birse, Phys. Rev. C 76, 034002 (2007). https://doi.org/10.1103/PhysRevC.76.034002. arXiv:0706.0984 [nucl-th]

    Article  ADS  Google Scholar 

  29. B. Long, U. van Kolck, Ann. Phys. 323, 1304 (2008). https://doi.org/10.1016/j.aop.2008.01.003. arXiv:0707.4325 [quant-ph]

    Article  ADS  Google Scholar 

  30. M. Pavón Valderrama, Phys. Rev. C 83, 024003 (2011). https://doi.org/10.1103/PhysRevC.83.024003. arXiv:0912.0699 [nucl-th]

    Article  ADS  Google Scholar 

  31. M. Pavón Valderrama, Phys. Rev. C 84, 064002 (2011). https://doi.org/10.1103/PhysRevC.84.064002. arXiv:1108.0872 [nucl-th]

    Article  ADS  Google Scholar 

  32. B. Long, C.J. Yang, Phys. Rev. C 84, 057001 (2011). https://doi.org/10.1103/PhysRevC.84.057001. arXiv:1108.0985 [nucl-th]

    Article  ADS  Google Scholar 

  33. B. Long, C.J. Yang, Phys. Rev. C 85, 034002 (2012). https://doi.org/10.1103/PhysRevC.85.034002. arXiv:1111.3993 [nucl-th]

    Article  ADS  Google Scholar 

  34. B. Long, C.J. Yang, Phys. Rev. C 86, 024001 (2012). https://doi.org/10.1103/PhysRevC.86.024001. arXiv:1202.4053 [nucl-th]

    Article  ADS  Google Scholar 

  35. S. Wu, B. Long, Phys. Rev. C 99, 024003 (2019). https://doi.org/10.1103/PhysRevC.99.024003. arXiv:1807.04407 [nucl-th]

    Article  ADS  Google Scholar 

  36. Y.-H. Song, R. Lazauskas, U. van Kolck, Phys. Rev. C 96, 024002 (2017), note [Erratum: Phys.Rev.C 100, 019901 (2019)], https://doi.org/10.1103/PhysRevC.96.024002. arXiv:1612.09090 [nucl-th]

  37. C.-J. Yang, A. Ekström, C. Forssén, G. Hagen, Phys. Rev. C 103, 054304 (2021). https://doi.org/10.1103/PhysRevC.103.054304. arXiv:2011.11584 [nucl-th]

    Article  ADS  Google Scholar 

  38. I. Stetcu, B.R. Barrett, U. van Kolck, Phys. Lett. B 653, 358 (2007). https://doi.org/10.1016/j.physletb.2007.07.065. arXiv:nucl-th/0609023

    Article  ADS  Google Scholar 

  39. L. Contessi, A. Lovato, F. Pederiva, A. Roggero, J. Kirscher, U. van Kolck, Phys. Lett. B 772, 839 (2017). https://doi.org/10.1016/j.physletb.2017.07.048. arXiv:1701.06516 [nucl-th]

    Article  ADS  Google Scholar 

  40. A. Bansal, S. Binder, A. Ekström, G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. C 98, 054301 (2018). https://doi.org/10.1103/PhysRevC.98.054301. arXiv:1712.10246 [nucl-th]

    Article  ADS  Google Scholar 

  41. M.C. Birse, Eur. Phys. J. A 46, 231 (2010). https://doi.org/10.1140/epja/i2010-11034-9. arXiv:1007.0540 [nucl-th]

    Article  ADS  Google Scholar 

  42. B. Long, Phys. Rev. C 88, 014002 (2013). https://doi.org/10.1103/PhysRevC.88.014002. arXiv:1304.7382 [nucl-th]

    Article  ADS  Google Scholar 

  43. M. Sánchez Sánchez, C.-J. Yang, B. Long, U. van Kolck, Phys. Rev. C 97, 024001 (2018). https://doi.org/10.1103/PhysRevC.97.024001. arXiv:1704.08524 [nucl-th]

    Article  ADS  Google Scholar 

  44. P.F. Bedaque, H.W. Hammer, U. van Kolck, Nucl. Phys. A 676, 357 (2000). https://doi.org/10.1016/S0375-9474(00)00205-0. arXiv:nucl-th/9906032

    Article  ADS  Google Scholar 

  45. A. Kievsky, M. Viviani, M. Gattobigio, L. Girlanda, Phys. Rev. C 95, 024001 (2017). https://doi.org/10.1103/PhysRevC.95.024001. arXiv:1610.09858 [nucl-th]

    Article  ADS  Google Scholar 

  46. A. Kievsky, M. Viviani, D. Logoteta, I. Bombaci, L. Girlanda, Phys. Rev. Lett. 121, 072701 (2018). https://doi.org/10.1103/PhysRevLett.121.072701. arXiv:1806.02636 [nucl-th]

    Article  ADS  Google Scholar 

  47. U. van Kolck, Eur. Phys. J. A 56, 97 (2020). https://doi.org/10.1140/epja/s10050-020-00092-1. arXiv:2003.09974 [nucl-th]

    Article  ADS  Google Scholar 

  48. C.J. Yang, Eur. Phys. J. A 56, 96 (2020). https://doi.org/10.1140/epja/s10050-020-00104-0. arXiv:1905.12510 [nucl-th]

    Article  ADS  Google Scholar 

  49. A. Manohar, H. Georgi, Nucl. Phys. B 234, 189 (1984). https://doi.org/10.1016/0550-3213(84)90231-1

    Article  ADS  Google Scholar 

  50. H. Georgi, L. Randall, Nucl. Phys. B 276, 241 (1986). https://doi.org/10.1016/0550-3213(86)90022-2

    Article  ADS  Google Scholar 

  51. S. Weinberg, Phys. Rev. Lett. 63, 2333 (1989). https://doi.org/10.1103/physrevlett.63.2333

    Article  ADS  Google Scholar 

  52. H. Georgi, Phys. Lett. B 298, 187 (1993). https://doi.org/10.1016/0370-2693(93)91728-6

    Article  ADS  Google Scholar 

  53. U. van Kolck, Phys. Rev. C 49, 2932 (1994). https://doi.org/10.1103/PhysRevC.49.2932

    Article  ADS  Google Scholar 

  54. E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, U.-G. Meißner, H. Witała, Phys. Rev. C 66, 064001 (2002). https://doi.org/10.1103/PhysRevC.66.064001

    Article  ADS  Google Scholar 

  55. P. Navratil, G.P. Kamuntavicius, B.R. Barrett, Phys. Rev. C 61, 044001 (2000). https://doi.org/10.1103/PhysRevC.61.044001. arXiv:nucl-th/9907054

    Article  ADS  Google Scholar 

  56. J.L. Friar, Few-Body Syst. 22, 161 (1997). https://doi.org/10.1007/s006010050059

    Article  ADS  Google Scholar 

  57. E. Epelbaum, Phys. Lett. B 639, 456 (2006). https://doi.org/10.1016/j.physletb.2006.06.046. arXiv:nucl-th/0511025

    Article  ADS  Google Scholar 

  58. J.R. Bergervoet, P.C. van Campen, R.A.M. Klomp, J.-L. de Kok, T.A. Rijken, V.G.J. Stoks, J.J. de Swart, Phys. Rev. C 41, 1435 (1990). https://doi.org/10.1103/physrevc.41.1435

    Article  ADS  Google Scholar 

  59. P. Navrátil, J.P. Vary, B.R. Barrett, Phys. Rev. Lett. 84, 5728 (2000). https://doi.org/10.1103/physrevlett.84.5728

    Article  ADS  Google Scholar 

  60. P. Navratil, J.P. Vary, B.R. Barrett, Phys. Rev. C 62, 054311 (2000). https://doi.org/10.1103/PhysRevC.62.054311

    Article  ADS  Google Scholar 

  61. H. Kümmel, K.H. Lührmann, J.G. Zabolitzky, Phys. Rep. 36, 1 (1978). https://doi.org/10.1016/0370-1573(78)90081-9

    Article  ADS  Google Scholar 

  62. R.J. Bartlett, M. Musiał, Rev. Mod. Phys. 79, 291 (2007). https://doi.org/10.1103/revmodphys.79.291

    Article  ADS  Google Scholar 

  63. G. Hagen, T. Papenbrock, M. Hjorth-Jensen, D.J. Dean, Rep. Prog. Phys. 77, 096302 (2014). https://doi.org/10.1088/0034-4885/77/9/096302

    Article  ADS  Google Scholar 

  64. G. Hagen, T. Papenbrock, D. Dean, A. Schwenk, A. Nogga, M. Wloch, P. Piecuch, Phys. Rev. C 76, 034302 (2007). https://doi.org/10.1103/PhysRevC.76.034302. arXiv:0704.2854 [nucl-th]

    Article  ADS  Google Scholar 

  65. S. Binder, J. Langhammer, A. Calci, P. Navratil, R. Roth, Phys. Rev. C 87, 021303 (2013). https://doi.org/10.1103/PhysRevC.87.021303. arXiv:1211.4748 [nucl-th]

    Article  ADS  Google Scholar 

  66. A.G. Taube, R.J. Bartlett, J. Chem. Phys. 128, 044110 (2008). https://doi.org/10.1063/1.2830236

    Article  ADS  Google Scholar 

  67. G. Hagen, T. Papenbrock, A. Ekström, K.A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, C.J. Horowitz, Phys. Rev. C (2014). https://doi.org/10.1103/physrevc.89.014319

    Article  Google Scholar 

  68. M. Hoferichter, J. Ruiz de Elvira, B. Kubis, U.-G. Meißner, Phys. Rev. Lett. 115, 192301 (2015). https://doi.org/10.1103/PhysRevLett.115.192301. arXiv:1507.07552 [nucl-th]

    Article  ADS  Google Scholar 

  69. J. Fujita, H. Miyazawa, Prog. Theor. Phys. 17, 360 (1957). https://doi.org/10.1143/PTP.17.360

    Article  ADS  Google Scholar 

  70. L. Platter, H.W. Hammer, U.-G. Meissner, Phys. Lett. B 607, 254 (2005). https://doi.org/10.1016/j.physletb.2004.12.068. arXiv:nucl-th/0409040

    Article  ADS  Google Scholar 

  71. P. Navratil, V.G. Gueorguiev, J.P. Vary, W.E. Ormand, A. Nogga, Phys. Rev. Lett. 99, 042501 (2007). https://doi.org/10.1103/PhysRevLett.99.042501. arXiv:nucl-th/0701038

    Article  ADS  Google Scholar 

  72. A. Nogga, P. Navratil, B.R. Barrett, J.P. Vary, Phys. Rev. C 73, 064002 (2006). https://doi.org/10.1103/PhysRevC.73.064002. arXiv:nucl-th/0511082

    Article  ADS  Google Scholar 

  73. S. Wesolowski, I. Svensson, A. Ekström, C. Forssén, R. J. Furnstahl, J. A. Melendez, D. R. Phillips, Fast & rigorous constraints on chiral three-nucleon forces from few-body observables. (2021), arXiv:2104.04441 [nucl-th]

  74. T.A. Lähde, E. Epelbaum, H. Krebs, D. Lee, U.-G. Meißner, G. Rupak, Phys. Lett. B 732, 110 (2014). https://doi.org/10.1016/j.physletb.2014.03.023. arXiv:1311.0477 [nucl-th]

    Article  ADS  Google Scholar 

  75. R. Machleidt, P. Liu, D.R. Entem, E. Ruiz Arriola, Phys. Rev. C 81, 024001 (2010). https://doi.org/10.1103/PhysRevC.81.024001. arXiv:0910.3942 [nucl-th]

    Article  ADS  Google Scholar 

  76. J. Hu, Y. Zhang, E. Epelbaum, U.-G. Meißner, J. Meng, Phys. Rev. C 96, 034307 (2017). https://doi.org/10.1103/PhysRevC.96.034307. arXiv:1612.05433 [nucl-th]

  77. K. Hebeler, S.K. Bogner, R.J. Furnstahl, A. Nogga, A. Schwenk, Phys. Rev. C 83, 031301 (2011). https://doi.org/10.1103/PhysRevC.83.031301. arXiv:1012.3381 [nucl-th]

  78. G. Baardsen, A. Ekström, G. Hagen, M. Hjorth-Jensen, Phys. Rev. C (2013). https://doi.org/10.1103/physrevc.88.054312

    Article  Google Scholar 

  79. C. Drischler, K. Hebeler, A. Schwenk, Phys. Rev. Lett. 122, 042501 (2019). https://doi.org/10.1103/PhysRevLett.122.042501. arXiv:1710.08220 [nucl-th]

    Article  ADS  Google Scholar 

  80. F. Sammarruca, R. Millerson, Front. Phys. 7, 213 (2019). https://doi.org/10.3389/fphy.2019.00213

    Article  Google Scholar 

  81. F. Sammarruca, R. Millerson, Phys. Rev. C 102, 034313 (2020). https://doi.org/10.1103/PhysRevC.102.034313. arXiv:2005.01958 [nucl-th]

    Article  ADS  Google Scholar 

  82. C. Drischler, J.A. Melendez, R.J. Furnstahl, D.R. Phillips, Phys. Rev. C 102, 054315 (2020). https://doi.org/10.1103/PhysRevC.102.054315. arXiv:2004.07805 [nucl-th]

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank H. Grießhammer, D. Lee, T. Papenbrock and R. Stroberg for useful discussions. This work was supported in part by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (Grant agreement No. 758027); the Swedish Research Council (Grant No. 2017-04234); the Czech Science Foundation GACR grant 19-19640 S and 22-14497 S; the Extreme Light Infrastructure Nuclear Physics (ELI-NP) Phase II, a project co-financed by the Romanian Government and the European Union through the European Regional Development Fund - the Competitiveness Operational Programme (1/07.07.2016, COP, ID 1334); the Romanian Ministry of Research and Innovation: PN23210105 (Phase 2, the Program Nucleu); the U.S. Department of Energy, Office of Science, Office of Nuclear Physics, under award numbers DE-FG02-04ER41338, desc0018223 (NUCLEI SciDAC-4 collaboration), the Field Work Proposal ERKBP72 at Oak Ridge National Laboratory (ORNL); and the U.S. National Science Foundation grants PHY-1913620, PHY-2209184. The computations were enabled by resources provided by the project “eInfrastruktura CZ” (e-INFRA CZ LM2018140) supported by the Ministry of Education, Youth and Sports of the Czech Republic, IT4Innovations at Czech National Supercomputing Center under project number OPEN24-21 1892, the Swedish National Infrastructure for Computing (SNIC) at C3SE and Tetralith partially funded by the Swedish Research Council, and CINECA under PRACE EHPCBEN-2023B05-023.

Author information

Authors and Affiliations

  1. Department of Physics, Chalmers University of Technology, 412 96, Göteborg, Sweden

    C.-J. Yang, A. Ekström & C. Forssén

  2. Nuclear Physics Institute of the Czech Academy of Sciences, 25069, Řež, Czech Republic

    C.-J. Yang

  3. ELI-NP, “Horia Hulubei” National Institute for Physics and Nuclear Engineering, 30 Reactorului Street, 077125, Bucharest-Magurele, Romania

    C.-J. Yang

  4. Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA

    G. Hagen

  5. Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, 37996, USA

    G. Hagen

  6. Department of Physics & Astronomy and HPC2 Center for Computational Sciences, Mississippi State University, Mississippi State, MS, 39762, USA

    G. Rupak

  7. Université Paris-Saclay, CNRS/IN2P3, IJCLab, 91405, Orsay, France

    U. van Kolck

  8. Department of Physics, University of Arizona, Tucson, AZ, 85721, USA

    U. van Kolck

Authors
  1. C.-J. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Ekström
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. C. Forssén
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. G. Hagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. G. Rupak
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. U. van Kolck
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to C.-J. Yang.

Additional information

Communicated by Vittorio Somà.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, CJ., Ekström, A., Forssén, C. et al. The importance of few-nucleon forces in chiral effective field theory. Eur. Phys. J. A 59, 233 (2023). https://doi.org/10.1140/epja/s10050-023-01149-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epja/s10050-023-01149-7

Search

Navigation