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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S.R. Beane, W. Detmold, K. Orginos, M.J. Savage, Prog. Part. Nucl. Phys. 66, 1 (2011)
M.J. Savage, Prog. Part. Nucl. Phys. 67, 140 (2012)
T. Inoue, Few Body Syst. 62, 106 (2021)
S. Weinberg, Phys. Lett. B 251, 288 (1990)
H. Hergert, R. Roth, Phys. Lett. B 682, 27 (2009)
U. van Kolck, Prog. Part. Nucl. Phys. 43, 337 (1999)
P.F. Bedaque, U. van Kolck, Ann. Rev. Nucl. Part. Sci. 52, 339 (2002)
E. Epelbaum, Prog. Part. Nucl. Phys. 57, 654 (2006)
E. Epelbaum, H.W. Hammer, U.G. Meissner, Rev. Mod. Phys. 81, 1773 (2009)
R. Machleidt, D.R. Entem, Phys. Rept. 503, 1 (2011)
E. Epelbaum, U.G. Meissner, Ann. Rev. Nucl. Part. Sci. 62, 159 (2012)
H.W. Hammer, S. König, U. van Kolck, Rev. Mod. Phys. 92, 025004 (2020)
Y. Nosyk, D.R. Entem, R. Machleidt, Phys. Rev. C 104, 054001 (2021)
T. Hüther, K. Vobig, K. Hebeler, R. Machleidt, R. Roth, Phys. Lett. B 808, 135651 (2020)
W.G. Jiang, A. Ekström, C. Forssén, G. Hagen, G.R. Jansen, T. Papenbrock, Phys. Rev. C 102, 054301 (2020)
P. Reinert, H. Krebs, E. Epelbaum, Eur. Phys. J. A 54, 86 (2018)
D.R. Entem, R. Machleidt, Y. Nosyk, Phys. Rev. C 96, 024004 (2017)
M. Piarulli, L. Girlanda, R. Schiavilla, R. Navarro Pérez, J.E. Amaro, E. Ruiz Arriola, Phys. Rev. C 91, 024003 (2015)
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)
E. Epelbaum, H. Krebs, U.G. Meißner, Phys. Rev. Lett. 115, 122301 (2015)
A. Gezerlis, I. Tews, E. Epelbaum, M. Freunek, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. C 90, 054323 (2014)
A. Ekström, et al., Phys. Rev. Lett. 110, 192502 (2013)
D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001 (2003)
U. van Kolck, Front. in Phys. 8, 79 (2020)
E. Epelbaum, H. Krebs, P. Reinert, Front. in Phys. 8, 98 (2020)
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)
E. Epelbaum, H. Krebs, U.G. Meißner, Eur. Phys. J. A 51, 53 (2015)
S. Binder, et al., Phys. Rev. C 93, 044002 (2016)
S. Binder, et al., Phys. Rev. C 98, 014002 (2018)
R.J. Furnstahl, N. Klco, D.R. Phillips, S. Wesolowski, Phys. Rev. C 92, 024005 (2015)
J.A. Melendez, S. Wesolowski, R.J. Furnstahl, Phys. Rev. C 96, 024003 (2017)
S. Wesolowski, R.J. Furnstahl, J.A. Melendez, D.R. Phillips, J. Phys. G 46, 045102 (2019)
J.A. Melendez, R.J. Furnstahl, D.R. Phillips, M.T. Pratola, S. Wesolowski, Phys. Rev. C 100, 044001 (2019)
A. Ekström, G. Hagen, Phys. Rev. Lett. 123, 252501 (2019)
S. Okubo, Prog. Theor. Phys. 12, 603 (1954)
K. Suzuki, S.Y. Lee, Prog. Theor. Phys. 64, 2091 (1980)
H. Feldmeier, T. Neff, R. Roth, J. Schnack, Nucl. Phys. A 632, 61 (1998)
H. Hergert, R. Roth, Phys. Rev. C 75, 051001 (2007)
R. Roth, T. Neff, H. Feldmeier, Prog. Part. Nucl. Phys. 65, 50 (2010)
F. Wegner, Ann. Phys. (Leipzig) 3, 77 (1994)
F.J. Wegner, Phys. Rep. 348, 77 (2001)
S.D. Glazek, K.G. Wilson, Phys. Rev. D 48, 5863 (1993)
S.K. Bogner, R.J. Furnstahl, R.J. Perry, Phys. Rev. C 75, 061001 (2007)
S.K. Bogner, R.J. Furnstahl, A. Schwenk, Prog. Part. Nucl. Phys. 65, 94 (2010)
R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navratil, Phys. Rev. Lett. 107, 072501 (2011)
R. Wirth, R. Roth, Phys. Rev. C 100, 044313 (2019)
W. Magnus, Commun. Pure Appl. Math. 7, 649 (1954)
T.D. Morris, N. Parzuchowski, S.K. Bogner, Phys. Rev. C 92, 034331 (2015)
S. Szpigel, R.J. Perry, Quantum Field Theory—A 20th Century Profile (Hindustan Book Agency, 2000), chap. The Similarity renormalization group, pp. 59–81
R. Roth, A. Calci, J. Langhammer, S. Binder, Phys. Rev. C 90, 024325 (2014)
R. Roth, S. Binder, K. Vobig, A. Calci, J. Langhammer, P. Navratil, Phys. Rev. Lett. 109, 052501 (2012)
I. Talmi, Helv. Phys. Acta 25, 185 (1952)
M. Moshinsky, Nucl. Phys. 13, 104 (1959)
M. Moshinsky, Y.F. Smirnov, The Harmonic Oscillator in Modern Physics (Harwood Academic Publishers, Amsterdam, 1996)
G.P. Kamuntavicius, R.K. Kalinauskas, B.R. Barrett, S. Mickevicius, D. Germanas, Nucl. Phys. A 695, 191 (2001)
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980)
J. Suhonen, From Nucleons to Nucleus: Concepts of Microscopic Nuclear Theory. Theoretical and Mathematical Physics (Springer, Berlin, Germany, 2007)
R. Roth, P. Papakonstantinou, N. Paar, H. Hergert, T. Neff, H. Feldmeier, Phys. Rev. C 73, 044312 (2006)
C. Constantinou, M.A. Caprio, J.P. Vary, P. Maris, Nucl. Sci. Tech. 28, 179 (2017)
A. Tichai, J. Müller, K. Vobig, R. Roth, Phys. Rev. C 99, 034321 (2019)
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)
S. Binder, J. Langhammer, A. Calci, P. Navratil, R. Roth, Phys. Rev. C 87, 021303 (2013)
S. Binder, J. Langhammer, A. Calci, R. Roth, Phys. Lett. B 736, 119 (2014)
W. Kutzelnigg, D. Mukherjee, J. Chem. Phys. 107, 432 (1997)
D. Mukherjee, Chem. Phys. Lett. 274, 561 (1997)
L. Kong, M. Nooijen, D. Mukherjee, J. Chem. Phys. 132, 234107 (2010)
E. Gebrerufael, A. Calci, R. Roth, Phys. Rev. C 93, 031301 (2016)
B.R. Barrett, P. Navratil, J.P. Vary, Prog. Part. Nucl. Phys. 69, 131 (2013)
P. Navratil, S. Quaglioni, I. Stetcu, B.R. Barrett, J. Phys. G 36, 083101 (2009)
R. Roth, P. Navratil, Phys. Rev. Lett. 99, 092501 (2007)
R. Roth, Phys. Rev. C 79, 064324 (2009)
C. Stumpf, J. Braun, R. Roth, Phys. Rev. C 93, 021301 (2016)
P. Navratil, G.P. Kamuntavicius, B.R. Barrett, Phys. Rev. C 61, 044001 (2000)
C. Forssén, B.D. Carlsson, H.T. Johansson, D. Sääf, A. Bansal, G. Hagen, T. Papenbrock, Phys. Rev. C 97, 034328 (2018)
M. Shao, H.M. Aktulga, C. Yang, E.G. Ng, P. Maris, J.P. Vary, Comput. Phys. Commun. 222, 1 (2018)
K. Tsukiyama, S.K. Bogner, A. Schwenk, Phys. Rev. Lett. 106, 222502 (2011)
H. Hergert, S.K. Bogner, S. Binder, A. Calci, J. Langhammer, R. Roth, A. Schwenk, Phys. Rev. C 87, 034307 (2013)
H. Hergert, S.K. Bogner, T.D. Morris, A. Schwenk, K. Tsukiyama, Phys. Rept. 621, 165 (2016)
H. Hergert, S.K. Bogner, J.G. Lietz, T.D. Morris, S. Novario, N.M. Parzuchowski, F. Yuan, Lect. Notes Phys. 936, 477 (2017)
H. Hergert, Phys. Scripta 92, 023002 (2017)
K. Tsukiyama, S.K. Bogner, A. Schwenk, Phys. Rev. C 85, 061304 (2012)
S.R. Stroberg, A. Calci, H. Hergert, J.D. Holt, S.K. Bogner, R. Roth, A. Schwenk, Phys. Rev. Lett. 118, 032502 (2017)
H. Hergert, S. Binder, A. Calci, J. Langhammer, R. Roth, Phys. Rev. Lett. 110, 242501 (2013)
H. Hergert, S.K. Bogner, T.D. Morris, S. Binder, A. Calci, J. Langhammer, R. Roth, Phys. Rev. C 90, 041302 (2014)
E. Gebrerufael, K. Vobig, H. Hergert, R. Roth, Phys. Rev. Lett. 118, 152503 (2017)
G. Hagen, T. Papenbrock, M. Hjorth-Jensen, D.J. Dean, Rept. Prog. Phys. 77, 096302 (2014)
V. Somà, Front. in Phys. 8, 340 (2020)
A. Tichai, R. Roth, T. Duguet, Front. in Phys. 8, 164 (2020)
S. Gandolfi, D. Lonardoni, A. Lovato, M. Piarulli, Front. Phys. 8, 117 (2020)
T.A. Lähde, U.G. Meißner, Nuclear Lattice Effective Field Theory: An Introduction, vol. 957 (Springer, Berlin, 2019)
H. Hergert, Front. Phys. 8, 379 (2020)
E. Epelbaum, et al., Phys. Rev. C 99, 024313 (2019)
P. Maris, et al., Phys. Rev. C 103, 054001 (2021)
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
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
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
DOI: https://doi.org/10.1007/978-3-031-10751-1_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-10750-4
Online ISBN: 978-3-031-10751-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)