Importance Truncated No Core Shell Model

Chapter
First Online:
Part of the Springer Theses book series (Springer Theses)

Abstract

The NCSM has been very successful at describing light nuclei (\(A \le 6\)), and in some cases, has also been able to describe nuclei in the middle of the p-shell (see [1] for an extensive list of results). However, NCSM calculations in the middle or in the upper part of the p-shell (\(A \ge 10\)) become very difficult to perform. Currently, interesting nuclei such as the Carbon or Oxygen isotopes are beyond the capabilities of the NCSM. To extend our calculations to the start of the sd-shell, is an even more challenging task. It is possible to do some exploratory calculations for the start of the sd-shell, in which \(N_\mathrm{max}\le 4\), but fully converged results will be out of reach for many years. We remind the reader that by fully converged results, we mean calculations which are free of the two NCSM parameters (\(N_\mathrm{max}\) and \(\hbar \Omega \)).

Keywords

Reference State Basis Space Configuration Interaction Importance Measure Slater Determinant 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

References

  1. 1.
    P. Navrátil, S. Quaglioni, I. Stetcu, and B.R. Barrett, Recent developments in no-core shell-model calculations. J. Phys. G: Nucl. Part. Phys. 36(8), 083101 (2009)Google Scholar
  2. 2.
    R. Roth, P. Navrátil, Ab Initio study of \(^{40}{\rm {Ca}}\) with an importance-truncated no-core shell model. Phys. Rev. Lett. 99, 092501 (2007)ADSCrossRefGoogle Scholar
  3. 3.
    R. Roth, Importance truncation for large-scale configuration interaction approaches. Phys. Rev. C 79, 064324 (2009)Google Scholar
  4. 4.
    P. Navrátil, R. Roth, S. Quaglioni, Ab initio many-body calculations of nucleon scattering on \(^{4}{\rm {He}}\), \(^{7}{\rm {Li}}\), \(^{7}{\rm {Be}}\), \(^{12}{\rm {C}}\), and \(^{16}{\rm {O}}\). Phys. Rev. C 82, 034609 (2010)Google Scholar
  5. 5.
    R. Roth, J. Langhammer, A. Calci, S. Binder, P. Navrátil, Similarity-transformed chiral \(nn+3n\) interactions for the Ab Initio description of \(^{12}{\\\mathbf{C}}\) and \(^{16}{\\\mathbf{O}}\). Phys. Rev. Lett. 107, 072501 (2011)Google Scholar
  6. 6.
    D.J. Dean, G. Hagen, M. Hjorth-Jensen, T. Papenbrock, A. Schwenk, Comment on “Ab initio study of \(^{40}{\rm {Ca}}\) with an importance-truncated no-core shell model”. Phys. Rev. Lett. 101, 119201 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    R. Roth, P. Navrátil, Roth and Navrátil reply. Phys. Rev. Lett. 101, 119202 (2008)Google Scholar
  8. 8.
    J. Goldstone, Derivation of the brueckner many-body theory. Proc. R. Soc. Lond. Ser. A. Math. Phys. Sci. 239(1217), 267–279 (1957)MathSciNetADSCrossRefMATHGoogle Scholar
  9. 9.
    J.R. Bartlett, M. Musiał, Coupled-cluster theory in quantum chemistry. Rev. Mod. Phys. 79, 291–352 (2007)Google Scholar
  10. 10.
    C.D. Sherrill, H.F. Schaefer III, The configuration interaction method: advances in highly correlated approaches, in Advances in Quantum Chemistry, volume 34 of Advances in Quantum Chemistry, ed. by M.C. Zerner Per-Olov Lowdin, J.R. Sabin, E. Brandas (Academic Press, New York, 1999), pp. 143–269Google Scholar
  11. 11.
    P.R. Surján, Z. Rolik, A. Szabados, D. Köhalmi, Partitioning in multiconfiguration perturbation theory. Annalen der Physik 13(4), 223–231 (2004)MathSciNetADSCrossRefMATHGoogle Scholar
  12. 12.
    Z. Rolik, Á. Szabados, P.R. Surján, On the perturbation of multiconfiguration wave functions. J. Chem. Phys. 119(4), 1922–1928 (2003)Google Scholar
  13. 13.
    P. Navrátil. No core slater determinant code (unpublished, 1995)Google Scholar
  14. 14.
    E. Caurier, F. Nowacki, Present status of shell model techniques. Acta Phys. Pol. B 30(3), 705 (1999)ADSGoogle Scholar
  15. 15.
    R. Roth, H. Hergert, P. Papakonstantinou, T. Neff, H. Feldmeier, Matrix elements and few-body calculations within the unitary correlation operator method. Phys. Rev. C 72, 034002 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    D.R. Entem, R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001 (2003)ADSCrossRefGoogle Scholar
  17. 17.
    P. Navrátil, E. Caurier, Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: application to \(^{6}{\rm {Li}}\) and \(^{10}{\rm {B}}\). Phys. Rev. C 69, 014311 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    P. Navrátil, S. Quaglioni, Ab initio many-body calculations of deuteron-\(^{4}{\rm {He}}\) scattering and \(^{6}{\rm {Li}}\) states. Phys. Rev. C 83, 044609 (2011)Google Scholar
  19. 19.
    E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Evolving nuclear many-body forces with the similarity renormalization group. Phys. Rev. C 83, 034301 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    R. Roth, J.R. Gour, P. Piecuch, Center-of-mass problem in truncated configuration interaction and coupled-cluster calculations. Phys. Lett. B 679(4), 334–339 (2009)Google Scholar
  21. 21.
    M. Thoresen, P. Navrátil, B.R. Barrett, Comparison of techniques for computing shell-model effective operators. Phys. Rev. C 57, 3108–3118 (1998)Google Scholar
  22. 22.
    E. Caurier, P. Navrátil, Proton radii of \(^{4,6,8}{\rm {He}}\) isotopes from high-precision nucleon-nucleon interactions. Phys. Rev. C 73, 021302 (2006)ADSCrossRefGoogle Scholar
  23. 23.
    A.F. Lisetskiy, M.K.G. Kruse, B.R. Barrett, P. Navratil, I. Stetcu, J.P. Vary, Effective operators from exact many-body renormalization. Phys. Rev. C 80, 024315 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    C. Forssén, E. Caurier, P. Navrátil, Charge radii and electromagnetic moments of li and be isotopes from the ab initio no-core shell model. Phys. Rev. C 79, 021303 (2009)ADSCrossRefGoogle Scholar
  25. 25.
    C. Cockrell, J.P. Vary, P. Maris, Lithium isotopes within the ab intio no-core full configuration approach. Phys. Rev. C 86, 034325 (2012)Google Scholar
  26. 26.
    W.N. Polyzou, Nucleon-nucleon interactions and observables. Phys. Rev. C 58, 91–95 (1998)Google Scholar
  27. 27.
    G. Hagen, T. Papenbrock, D.J. Dean, M. Hjorth-Jensen, Medium-mass nuclei from chiral nucleon-nucleon interactions. Phys. Rev. Lett. 101, 092502 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    W. Duch, G.H.F. Diercksen, Size-extensivity corrections in configuration interaction methods. J. Chem. Phys. 101(4), 3018–3030 (1994)Google Scholar
  29. 29.
    K.A. Brueckner, Two-body forces and nuclear saturation. iii. details of the structure of the nucleus. Phys. Rev. 97, 1353–1366 (1955)ADSCrossRefMATHGoogle Scholar
  30. 30.
    R.J. Bartlett, G.D. Purvis, Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitations for the correlation problem. Int. J. Quantum Chem. 14(5), 561–581 (1978)Google Scholar
  31. 31.
    G. Hagen, D.J. Dean, M. Hjorth-Jensen, T. Papenbrock, A. Schwenk, Benchmark calculations for \(^{3}{\rm {H}}\), \(^{4}{\rm {He}}\), \(^{16}{\rm {O}}\), and \(^{40}{\rm {Ca}}\) with ab initio coupled-cluster theory. Phys. Rev. C 76, 044305 (2007)ADSCrossRefGoogle Scholar
  32. 32.
    G.R. Jansen, M. Hjorth-Jensen, G. Hagen, T. Papenbrock, Toward open-shell nuclei with coupled-cluster theory. Phys. Rev. C 83, 054306 (2011)ADSCrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.Lawrence Livermore National LaboratoryLivermoreUSA

Personalised recommendations