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The No Core Shell Model

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Extensions to the No-Core Shell Model

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Abstract

As has been discussed in the introduction, the No-Core Shell Model (NCSM), is one of the recently developed ab-initio many-body techniques, for solving bound state properties of light nuclei (\(A \le 20)\)[13].

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Notes

  1. 1.

    The Weinberg power counting scheme is known to be inconsistent. As there is no other viable EFT alternative for the many-body community presently, it is often used in calculations without regard to the issues of renormalization-group invariance.

References

  1. P. Navrátil, S. Quaglioni, I. Stetcu, B.R. Barrett, Recent developments in no-core shell-model calculations. J. Phys. G: Nucl. Part. Phys. 36(8), 083101 (2009)

    Google Scholar 

  2. P. Navrátil, B.R. Barrett, Shell-model calculations for the three-nucleon system. Phys. Rev. C 57, 562–568 (1998)

    Article  ADS  Google Scholar 

  3. P. Navrátil, J.P. Vary, B.R. Barrett, Properties of \({}^{12}c\) in the Ab Initio nuclear shell model. Phys. Rev. Lett. 84, 5728–5731 (2000)

    Article  ADS  Google Scholar 

  4. P. Navrátil, V.G. Gueorguiev, J.P. Vary, W.E. Ormand, A. Nogga, Structure of \(a=10\breve{}13\) nuclei with two- plus three-nucleon interactions from chiral effective field theory. Phys. Rev. Lett. 99, 042501 (2007)

    Google Scholar 

  5. B. Alex Brown, W.A. Richter, New “USD” hamiltonians for the \(\mathit{sd}\) shell. Phys. Rev. C 74, 034315 (2006)

    Article  ADS  Google Scholar 

  6. 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)

    Article  ADS  Google Scholar 

  7. Hideki Yukawa, On the interaction of elementary particles. i \(^{*}\). Prog. Theoret. Phys. Suppl. 1, 1–10 (1955)

    Article  ADS  Google Scholar 

  8. R. Machleidt, High-precision, charge-dependent bonn nucleon-nucleon potential. Phys. Rev. C 63, 024001 (2001)

    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, 38–51 (1995)

    Article  ADS  Google Scholar 

  10. P. Doleschall, Influence of the short range nonlocal nucleon–nucleon interaction on the elastic \(n-d\) scattering: below 30 MeV. Phys. Rev. C 69, 054001 (2004)

    Google Scholar 

  11. P. Doleschall, I. Borbély, Z. Papp, W. Plessas, Nonlocality in the nucleon-nucleon interaction and three-nucleon bound states. Phys. Rev. C 67, 064005 (2003)

    Article  ADS  Google Scholar 

  12. J. Gasser, H. Leutwyler, Chiral perturbation theory to one loop. Ann. Phys. 158(1), 142–210 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  13. J. Gasser, H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark. Nucl. Phys. B 250(1–4), 465–516 (1985)

    Article  ADS  Google Scholar 

  14. S. Weinberg, Phenomenological lagrangians. Physica A 96(12), 327–340 (1979)

    Article  ADS  Google Scholar 

  15. S. Weinberg, Nuclear forces from chiral lagrangians. Phys. Lett. B 251(2), 288–292 (1990)

    Article  ADS  Google Scholar 

  16. S. Weinberg, Effective chiral lagrangians for nucleon-pion interactions and nuclear forces. Nucl. Phys. B 363(1), 3–18 (1991)

    Article  ADS  Google Scholar 

  17. U. van Kolck, Few-nucleon forces from chiral lagrangians. Phys. Rev. C 49, 2932–2941 (1994)

    Article  ADS  Google Scholar 

  18. C. Ordóñez, L. Ray, U. van Kolck, Nucleon-nucleon potential from an effective chiral lagrangian. Phys. Rev. Lett. 72, 1982–1985 (1994)

    Article  ADS  Google Scholar 

  19. C. Ordóñez, L. Ray, U. van Kolck, Two-nucleon potential from chiral lagrangians. Phys. Rev. C 53, 2086–2105 (1996)

    Article  ADS  Google Scholar 

  20. D. Gazit, S. Quaglioni, P. Navrátil, Three-nucleon low-energy constants from the consistency of interactions and currents in chiral effective field theory. Phys. Rev. Lett. 103, 102502 (2009)

    Article  ADS  Google Scholar 

  21. W. Gloeckle, E. Epelbaum, U.G. Meissner, A. Nogga, H. Kamada, et al., Nuclear forces and few nucleon studies based on chiral perturbation theory (2003)

    Google Scholar 

  22. D.R. Entem, R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory. Phys. Rev. C 68, 041001 (2003)

    Article  ADS  Google Scholar 

  23. E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, Ulf-G. Meißner, H. Witała, Three-nucleon forces from chiral effective field theory. Phys. Rev. C 66, 064001 (2002)

    Google Scholar 

  24. S.K. Bogner, T.T.S. Kuo, A. Schwenk, Model-independent low momentum nucleon interaction from phase shift equivalence. Phys. Rep. 386(1), 1–27 (2003)

    Article  ADS  Google Scholar 

  25. S.D. Głazek, K.G. Wilson, Renormalization of hamiltonians. Phys. Rev. D 48, 5863–5872 (1993)

    Article  ADS  Google Scholar 

  26. S.D. Glazek, K.G. Wilson, Perturbative renormalization group for hamiltonians. Phys. Rev. D 49, 4214–4218 (1994)

    Article  MathSciNet  ADS  Google Scholar 

  27. F.J. Wegner. Flow equations for hamiltonians. Phys. Rep. 348(1–2), 77–89 (2001) [Renormalization group theory in the new millennium. II]

    Google Scholar 

  28. F. Wegner, Flow-equations for hamiltonians. Ann. Phys. 506(2), 77–91 (1994)

    Article  Google Scholar 

  29. S.K. Bogner, R.J. Furnstahl, R.J. Perry, Similarity renormalization group for nucleon-nucleon interactions. Phys. Rev. C 75, 061001 (2007)

    Article  ADS  Google Scholar 

  30. S.K. Bogner, R.J. Furnstahl, R.J. Perry, A. Schwenk, Are low-energy nuclear observables sensitive to high-energy phase shifts? Phys. Lett. B 649(5–6), 488–493 (2007)

    Article  ADS  Google Scholar 

  31. E.D. Jurgenson, Applications of the similarity renormalization group to the nuclear interaction. Ph.D. Thesis (Advisor: R.J. Furnstahl) (2009)

    Google Scholar 

  32. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Evolution of nuclear many-body forces with the similarity renormalization group. Phys. Rev. Lett. 103, 082501 (2009)

    Article  ADS  Google Scholar 

  33. S. Ôkubo, Diagonalization of hamiltonian and tamm-dancoff equation. Progress Theoret. Phys. 12(5), 603–622 (1954)

    Article  ADS  MATH  Google Scholar 

  34. K. Suzuki, S.Y. Lee, Convergent theory for effective interaction in nuclei. Progress Theoret. Phys. 64(6), 2091–2106 (1980)

    Google Scholar 

  35. H. Kamada, A. Nogga, W. Glöckle, E. Hiyama, M. Kamimura, K. Varga, Y. Suzuki, M. Viviani, A. Kievsky, S. Rosati, J. Carlson, S.C. Pieper, R.B. Wiringa, P. Navrátil, B.R. Barrett, N. Barnea, W. Leidemann, G. Orlandini, Benchmark test calculation of a four-nucleon bound state. Phys. Rev. C 64, 044001 (2001)

    Google Scholar 

  36. E.D. Jurgenson, P. Navrátil, R.J. Furnstahl, Evolving nuclear many-body forces with the similarity renormalization group. Phys. Rev. C 83, 034301 (2011)

    Article  ADS  Google Scholar 

  37. A.F. Lisetskiy, B.R. Barrett, M.K.G. Kruse, P. Navratil, I. Stetcu, J.P. Vary, Ab-initio shell model with a core. Phys. Rev. C 78, 044302 (2008)

    Article  ADS  Google Scholar 

  38. M. Moshinsky, Transformation brackets for harmonic oscillator functions. Nucl. Phys. 13(1), 104–116 (1959)

    Article  MathSciNet  MATH  Google Scholar 

  39. P. Navrátil, G.P. Kamuntavičius, B.R. Barrett, Few-nucleon systems in a translationally invariant harmonic oscillator basis. Phys. Rev. C 61, 044001 (2000)

    Article  ADS  Google Scholar 

  40. P. Navrátil, B.R. Barrett, Four-nucleon shell-model calculations in a faddeev-like approach. Phys. Rev. C 59, 1906–1918 (1999)

    Article  ADS  Google Scholar 

  41. P. Navrátil, B.R. Barrett, W. Glöckle, Spurious states in the faddeev formalism for few-body systems. Phys. Rev. C 59, 611–616 (1999)

    Article  ADS  Google Scholar 

  42. L. Trlifaj, Simple formula for the general oscillator brackets. Phys. Rev. C 5, 1534–1539 (1972)

    Article  ADS  Google Scholar 

  43. B.J. Cole, R.R. Whitehead, A. Watt, I. Morrison, Computationa methods for shell-model calculations. Adv. Nucl. Phys. 9, 123–176 (1977)

    Google Scholar 

  44. P.K. Rath, A. Faessler, H. Muther, A. Watt, A practical solution to the problem of spurious states in shell-model calculations. J. Phys. G Nucl. Part. Phys. 16(2), 245 (1990)

    Article  ADS  Google Scholar 

  45. D.H. Gloeckner, R.D. Lawson, Spurious center-of-mass motion. Phys. Lett. B 53(4), 313–318 (1974)

    Article  ADS  Google Scholar 

  46. C. Forssén, J.P. Vary, E. Caurier, P. Navrátil, Converging sequences in the ab initio no-core shell model. Phys. Rev. C 77, 024301 (2008)

    Article  ADS  Google Scholar 

  47. P. Navrátil, E. Caurier, Nuclear structure with accurate chiral perturbation theory nucleon-nucleon potential: application to \(^{6}\)Li and \(^{10}\)B. Phys. Rev. C 69, 014311 (2004)

    Google Scholar 

  48. P. Maris, J.P. Vary, A.M. Shirokov, Ab initio no-core full configuration calculations of light nuclei. Phys. Rev. C 79, 014308 (2009)

    Article  ADS  Google Scholar 

  49. P. Navrátil. No core slater determinant code. Unpublished (1995)

    Google Scholar 

  50. J.P. Vary, D.C. Zheng, The many-fermion-dynamics shell-model code. Unpublished (1994)

    Google Scholar 

  51. J.P. Vary, The many-fermion-dynamics shell-model code. Iowa State University, Unpublished (1992)

    Google Scholar 

  52. P. Navrátil, Manyeff code. Unpublished (1998)

    Google Scholar 

  53. E. Caurier, F. Nowacki, Present status of shell model techniques. Acta Phys. Pol. B 30(3), 705 (1999)

    ADS  Google Scholar 

  54. E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, The shell model as a unified view of nuclear structure. Rev. Mod. Phys. 77, 427–488 (2005)

    Article  ADS  Google Scholar 

  55. P. Maris, M. Sosonkina, J.P. Vary, E. Ng, C. Yang, Scaling of ab-initio nuclear physics calculations on multicore computer architectures. Procedia Comput. Sci. 1(1), 97–106 (2010)

    Article  Google Scholar 

  56. P. Sternberg, E.G. Ng, C. Yang, P. Maris, J.P. Vary, M. Sosonkina, H.V. Le, Accelerating configuration interaction calculations for nuclear structure, in Proceedings of the 2008 ACM/IEEE conference on Supercomputing, SC ’08, Piscataway, NJ, USA (IEEE Press, 2008), pp. 15:1–15:12

    Google Scholar 

  57. P. Maris, A.M. Shirokov, J.P. Vary, Ab initio nuclear structure simulations: the speculative \(^{14}\)F nucleus. Phys. Rev. C 81, 021301 (2010)

    Google Scholar 

  58. P. Maris, J.P. Vary, P. Navrátil, W.E. Ormand, H. Nam, D.J. Dean, Origin of the anomalous long lifetime of \(^{14}\)C. Phys. Rev. Lett. 106, 202502 (2011)

    Google Scholar 

  59. V.Z. Goldberg, B.T. Roeder, G.V. Rogachev, G.G. Chubarian, E.D. Johnson, C. Fu, A.A. Alharbi, M.L. Avila, A. Banu, M. McCleskey, J.P. Mitchell, E. Simmons, G. Tabacaru, L. Trache, R.E. Tribble, First observation of 14f. Phys. Lett. B 692(5), 307–311 (2010)

    Article  ADS  Google Scholar 

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Correspondence to Michael Karl Gerhard Kruse .

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Kruse, M.K.G. (2013). The No Core Shell Model. In: Extensions to the No-Core Shell Model. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01393-0_2

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