Skip to main content

Ab Initio Approaches to Nuclear Structure

  • Chapter
  • First Online:
The Euroschool on Exotic Beams, Vol. VI

Part of the book series: Lecture Notes in Physics ((LNP,volume 1005))

Abstract

Ab initio nuclear structure theory has experienced a phase of ground-breaking developments over the past decade. Compared to the situation in the early 2000s, we now have a rich variety of powerful and complementary tools that connect the underlying theory of the strong interaction to nuclear structure observables. This enables us to describe a much larger domain of nuclei and observables with controlled and quantified theoretical uncertainties—in the ab initio spirit. In this lecture we provide a pedagogical introduction into the ab initio toolbox with a focus on basis expansion approaches, particularly on configuration interaction methods, like the no-core shell model, and decoupling approaches, like the in-medium similarity renormalization group.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. S.R. Beane, W. Detmold, K. Orginos, M.J. Savage, Prog. Part. Nucl. Phys. 66, 1 (2011)

    Article  ADS  Google Scholar 

  2. M.J. Savage, Prog. Part. Nucl. Phys. 67, 140 (2012)

    Article  ADS  Google Scholar 

  3. T. Inoue, Few Body Syst. 62, 106 (2021)

    Article  ADS  Google Scholar 

  4. S. Weinberg, Phys. Lett. B 251, 288 (1990)

    Article  ADS  Google Scholar 

  5. H. Hergert, R. Roth, Phys. Lett. B 682, 27 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999)

    Article  ADS  Google Scholar 

  7. P.F. Bedaque, U. van Kolck, Ann. Rev. Nucl. Part. Sci. 52, 339 (2002)

    Article  ADS  Google Scholar 

  8. E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006)

    Article  ADS  Google Scholar 

  9. E. Epelbaum, H.W. Hammer, U.G. Meissner, Rev. Mod. Phys. 81, 1773 (2009)

    Article  ADS  Google Scholar 

  10. R. Machleidt, D.R. Entem, Phys. Rept. 503, 1 (2011)

    Article  ADS  Google Scholar 

  11. E. Epelbaum, U.G. Meissner, Ann. Rev. Nucl. Part. Sci. 62, 159 (2012)

    Article  ADS  Google Scholar 

  12. H.W. Hammer, S. König, U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020)

    Article  ADS  Google Scholar 

  13. Y. Nosyk, D.R. Entem, R. Machleidt, Phys. Rev. C 104, 054001 (2021)

    Article  ADS  Google Scholar 

  14. T. Hüther, K. Vobig, K. Hebeler, R. Machleidt, R. Roth, Phys. Lett. B 808, 135651 (2020)

    Article  Google Scholar 

  15. W.G. Jiang, A. Ekström, C. Forssén, G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. C 102, 054301 (2020)

    Article  ADS  Google Scholar 

  16. P. Reinert, H. Krebs, E. Epelbaum, Eur. Phys. J. A 54, 86 (2018)

    Article  ADS  Google Scholar 

  17. D.R. Entem, R. Machleidt, Y. Nosyk, Phys. Rev. C 96, 024004 (2017)

    Article  ADS  Google Scholar 

  18. M. Piarulli, L. Girlanda, R. Schiavilla, R. Navarro Pérez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. C 91, 024003 (2015)

    Article  ADS  Google Scholar 

  19. 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)

    Article  ADS  Google Scholar 

  20. E. Epelbaum, H. Krebs, U.G. Meißner, Phys. Rev. Lett. 115, 122301 (2015)

    Article  ADS  Google Scholar 

  21. A. Gezerlis, I. Tews, E. Epelbaum, M. Freunek, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. C 90, 054323 (2014)

    Article  ADS  Google Scholar 

  22. A. Ekström, et al., Phys. Rev. Lett. 110, 192502 (2013)

    Article  ADS  Google Scholar 

  23. D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001 (2003)

    Article  ADS  Google Scholar 

  24. U. van Kolck, Front. in Phys. 8, 79 (2020)

    Article  ADS  Google Scholar 

  25. E. Epelbaum, H. Krebs, P. Reinert, Front. in Phys. 8, 98 (2020)

    Article  ADS  Google Scholar 

  26. 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)

    Google Scholar 

  27. E. Epelbaum, H. Krebs, U.G. Meißner, Eur. Phys. J. A 51, 53 (2015)

    Article  ADS  Google Scholar 

  28. S. Binder, et al., Phys. Rev. C 93, 044002 (2016)

    Article  ADS  Google Scholar 

  29. S. Binder, et al., Phys. Rev. C 98, 014002 (2018)

    Article  ADS  Google Scholar 

  30. R.J. Furnstahl, N. Klco, D.R. Phillips, S. Wesolowski, Phys. Rev. C 92, 024005 (2015)

    Article  ADS  Google Scholar 

  31. J.A. Melendez, S. Wesolowski, R.J. Furnstahl, Phys. Rev. C 96, 024003 (2017)

    Article  ADS  Google Scholar 

  32. S. Wesolowski, R.J. Furnstahl, J.A. Melendez, D.R. Phillips, J. Phys. G 46, 045102 (2019)

    Article  ADS  Google Scholar 

  33. J.A. Melendez, R.J. Furnstahl, D.R. Phillips, M.T. Pratola, S. Wesolowski, Phys. Rev. C 100, 044001 (2019)

    Article  ADS  Google Scholar 

  34. A. Ekström, G. Hagen, Phys. Rev. Lett. 123, 252501 (2019)

    Article  ADS  Google Scholar 

  35. S. Okubo, Prog. Theor. Phys. 12, 603 (1954)

    Article  ADS  Google Scholar 

  36. K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980)

    Article  ADS  Google Scholar 

  37. H. Feldmeier, T. Neff, R. Roth, J. Schnack, Nucl. Phys. A 632, 61 (1998)

    Article  ADS  Google Scholar 

  38. H. Hergert, R. Roth, Phys. Rev. C 75, 051001 (2007)

    Article  ADS  Google Scholar 

  39. R. Roth, T. Neff, H. Feldmeier, Prog. Part. Nucl. Phys. 65, 50 (2010)

    Article  ADS  Google Scholar 

  40. F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994)

    Article  ADS  Google Scholar 

  41. F.J. Wegner, Phys. Rep. 348, 77 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  42. S.D. Glazek, K.G. Wilson, Phys. Rev. D 48, 5863 (1993)

    Article  ADS  Google Scholar 

  43. S.K. Bogner, R.J. Furnstahl, R.J. Perry, Phys. Rev. C 75, 061001 (2007)

    Article  ADS  Google Scholar 

  44. S.K. Bogner, R.J. Furnstahl, A. Schwenk, Prog. Part. Nucl. Phys. 65, 94 (2010)

    Article  ADS  Google Scholar 

  45. R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navratil, Phys. Rev. Lett. 107, 072501 (2011)

    Article  ADS  Google Scholar 

  46. R. Wirth, R. Roth, Phys. Rev. C 100, 044313 (2019)

    Article  ADS  Google Scholar 

  47. W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)

    Article  Google Scholar 

  48. T.D. Morris, N. Parzuchowski, S.K. Bogner, Phys. Rev. C 92, 034331 (2015)

    Article  ADS  Google Scholar 

  49. S. Szpigel, R.J. Perry, Quantum Field Theory—A 20th Century Profile (Hindustan Book Agency, 2000), chap. The Similarity renormalization group, pp. 59–81

    Google Scholar 

  50. R. Roth, A. Calci, J. Langhammer, S. Binder, Phys. Rev. C 90, 024325 (2014)

    Article  ADS  Google Scholar 

  51. R. Roth, S. Binder, K. Vobig, A. Calci, J. Langhammer, P. Navratil, Phys. Rev. Lett. 109, 052501 (2012)

    Article  ADS  Google Scholar 

  52. I. Talmi, Helv. Phys. Acta 25, 185 (1952)

    Google Scholar 

  53. M. Moshinsky, Nucl. Phys. 13, 104 (1959)

    Article  Google Scholar 

  54. M. Moshinsky, Y.F. Smirnov, The Harmonic Oscillator in Modern Physics (Harwood Academic Publishers, Amsterdam, 1996)

    MATH  Google Scholar 

  55. G.P. Kamuntavicius, R.K. Kalinauskas, B.R. Barrett, S. Mickevicius, D. Germanas, Nucl. Phys. A 695, 191 (2001)

    Article  ADS  Google Scholar 

  56. P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980)

    Book  Google Scholar 

  57. J. Suhonen, From Nucleons to Nucleus: Concepts of Microscopic Nuclear Theory. Theoretical and Mathematical Physics (Springer, Berlin, Germany, 2007)

    Book  MATH  Google Scholar 

  58. R. Roth, P. Papakonstantinou, N. Paar, H. Hergert, T. Neff, H. Feldmeier, Phys. Rev. C 73, 044312 (2006)

    Article  ADS  Google Scholar 

  59. C. Constantinou, M.A. Caprio, J.P. Vary, P. Maris, Nucl. Sci. Tech. 28, 179 (2017)

    Article  Google Scholar 

  60. A. Tichai, J. Müller, K. Vobig, R. Roth, Phys. Rev. C 99, 034321 (2019)

    Article  ADS  Google Scholar 

  61. I. Shavitt, R.J. Bartlett, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory. Cambridge Molecular Science (Cambridge University Press, Cambridge, 2009)

    Book  Google Scholar 

  62. S. Binder, J. Langhammer, A. Calci, P. Navratil, R. Roth, Phys. Rev. C 87, 021303 (2013)

    Article  ADS  Google Scholar 

  63. S. Binder, J. Langhammer, A. Calci, R. Roth, Phys. Lett. B 736, 119 (2014)

    Article  ADS  Google Scholar 

  64. W. Kutzelnigg, D. Mukherjee, J. Chem. Phys. 107, 432 (1997)

    Article  ADS  Google Scholar 

  65. D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997)

    Article  ADS  Google Scholar 

  66. L. Kong, M. Nooijen, D. Mukherjee, J. Chem. Phys. 132, 234107 (2010)

    Article  ADS  Google Scholar 

  67. E. Gebrerufael, A. Calci, R. Roth, Phys. Rev. C 93, 031301 (2016)

    Article  ADS  Google Scholar 

  68. B.R. Barrett, P. Navratil, J.P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)

    Article  ADS  Google Scholar 

  69. P. Navratil, S. Quaglioni, I. Stetcu, B.R. Barrett, J. Phys. G 36, 083101 (2009)

    Article  ADS  Google Scholar 

  70. R. Roth, P. Navratil, Phys. Rev. Lett. 99, 092501 (2007)

    Article  ADS  Google Scholar 

  71. R. Roth, Phys. Rev. C 79, 064324 (2009)

    Article  ADS  Google Scholar 

  72. C. Stumpf, J. Braun, R. Roth, Phys. Rev. C 93, 021301 (2016)

    Article  ADS  Google Scholar 

  73. P. Navratil, G.P. Kamuntavicius, B.R. Barrett, Phys. Rev. C 61, 044001 (2000)

    Article  ADS  Google Scholar 

  74. C. Forssén, B.D. Carlsson, H.T. Johansson, D. Sääf, A. Bansal, G. Hagen, T. Papenbrock, Phys. Rev. C 97, 034328 (2018)

    Article  ADS  Google Scholar 

  75. M. Shao, H.M. Aktulga, C. Yang, E.G. Ng, P. Maris, J.P. Vary, Comput. Phys. Commun. 222, 1 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  76. K. Tsukiyama, S.K. Bogner, A. Schwenk, Phys. Rev. Lett. 106, 222502 (2011)

    Article  ADS  Google Scholar 

  77. H. Hergert, S.K. Bogner, S. Binder, A. Calci, J. Langhammer, R. Roth, A. Schwenk, Phys. Rev. C 87, 034307 (2013)

    Article  ADS  Google Scholar 

  78. H. Hergert, S.K. Bogner, T.D. Morris, A. Schwenk, K. Tsukiyama, Phys. Rept. 621, 165 (2016)

    Article  ADS  Google Scholar 

  79. H. Hergert, S.K. Bogner, J.G. Lietz, T.D. Morris, S. Novario, N.M. Parzuchowski, F. Yuan, Lect. Notes Phys. 936, 477 (2017)

    Article  ADS  Google Scholar 

  80. H. Hergert, Phys. Scripta 92, 023002 (2017)

    Article  ADS  Google Scholar 

  81. K. Tsukiyama, S.K. Bogner, A. Schwenk, Phys. Rev. C 85, 061304 (2012)

    Article  ADS  Google Scholar 

  82. S.R. Stroberg, A. Calci, H. Hergert, J.D. Holt, S.K. Bogner, R. Roth, A. Schwenk, Phys. Rev. Lett. 118, 032502 (2017)

    Article  ADS  Google Scholar 

  83. H. Hergert, S. Binder, A. Calci, J. Langhammer, R. Roth, Phys. Rev. Lett. 110, 242501 (2013)

    Article  ADS  Google Scholar 

  84. H. Hergert, S.K. Bogner, T.D. Morris, S. Binder, A. Calci, J. Langhammer, R. Roth, Phys. Rev. C 90, 041302 (2014)

    Article  ADS  Google Scholar 

  85. E. Gebrerufael, K. Vobig, H. Hergert, R. Roth, Phys. Rev. Lett. 118, 152503 (2017)

    Article  ADS  Google Scholar 

  86. G. Hagen, T. Papenbrock, M. Hjorth-Jensen, D.J. Dean, Rept. Prog. Phys. 77, 096302 (2014)

    Article  ADS  Google Scholar 

  87. V. Somà, Front. in Phys. 8, 340 (2020)

    Article  ADS  Google Scholar 

  88. A. Tichai, R. Roth, T. Duguet, Front. in Phys. 8, 164 (2020)

    Article  ADS  Google Scholar 

  89. S. Gandolfi, D. Lonardoni, A. Lovato, M. Piarulli, Front. Phys. 8, 117 (2020)

    Article  Google Scholar 

  90. T.A. Lähde, U.G. Meißner, Nuclear Lattice Effective Field Theory: An Introduction, vol. 957 (Springer, Berlin, 2019)

    MATH  Google Scholar 

  91. H. Hergert, Front. Phys. 8, 379 (2020)

    Article  Google Scholar 

  92. E. Epelbaum, et al., Phys. Rev. C 99, 024313 (2019)

    Article  ADS  Google Scholar 

  93. P. Maris, et al., Phys. Rev. C 103, 054001 (2021)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Supported by the DFG through the Sonderforschungsbereich (SFB) 1245 (Project ID 279384907) and the BMBF through Verbundprojekt 05P2021 (ErUM-FSP T07, Contract No. 05P21RDFNB). Calculations were performed using the Lichtenberg II high-performance computer at the Technische Universität Darmstadt.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Robert Roth .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Roth, R. (2022). Ab Initio Approaches to Nuclear Structure. In: Lenzi, S.M., Cortina-Gil, D. (eds) The Euroschool on Exotic Beams, Vol. VI. Lecture Notes in Physics, vol 1005. Springer, Cham. https://doi.org/10.1007/978-3-031-10751-1_3

Download citation

Publish with us

Policies and ethics