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The European Physical Journal A

, Volume 39, Issue 2, pp 219–241 | Cite as

Density matrix expansion for low-momentum interactions

  • S. K. Bogner
  • R. J. Furnstahl
  • L. PlatterEmail author
Regular Article - Theoretical Physics

Abstract

A first step toward a universal nuclear energy density functional based on low-momentum interactions is taken using the density matrix expansion (DME) of Negele and Vautherin. The DME is adapted for non-local momentum space potentials and generalized to include local three-body interactions. Different prescriptions for the three-body DME are compared. Exploratory results are given at the Hartree-Fock level, along with a roadmap for systematic improvements within an effective action framework for the Kohn-Sham density functional theory.

PACS

21.10.Dr Binding energy and masses 21.60.Jz Nuclear Density Functional Theory and extensions (includes Hartree-Fock and random-phase approximations) 21.65.-f Nuclear matter 

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References

  1. 1.
    J.A. Carlson, G. Ortiz (Editors), Recent Progress in Many-body Theories: Proceedings of the 12th International Conference (World Scientific, Singapore, 2006)Google Scholar
  2. 2.
    M.W. Ahmed, H. Gao, H.R. Weller, B. Holstein (Editors), Chiral Dynamics 2006 (World Scientific, Singapore, 2007).Google Scholar
  3. 3.
    R.J. Furnstahl, G. Rupak, T. Schäfer, Ann. Phys. Nucl. Part. Sci. 58, 1 (2008) [arXiv:0801.0729].Google Scholar
  4. 4.
    E. Epelbaum, H.W. Hammer, U.-G. Meißner, arXiv:0811.1338 [nucl-th].Google Scholar
  5. 5.
    E. Epelbaum, W. Glöckle, U.-G. Meißner, Phys. Lett. B 439, 1 (1998).Google Scholar
  6. 6.
    S.K. Bogner, T.T.S. Kuo, A. Schwenk, D.R. Entem, R. Machleidt, Phys. Lett. B 576, 265 (2003).Google Scholar
  7. 7.
    S.K. Bogner, T.T.S. Kuo, A. Schwenk, Phys. Rep. 386, 1 (2003).Google Scholar
  8. 8.
    S.K. Bogner, A. Schwenk, T.T.S. Kuo, G.E. Brown, arXiv:nucl-th/0111042, unpublished.Google Scholar
  9. 9.
    A. Nogga, S.K. Bogner, A. Schwenk, Phys. Rev. C 70, 061002(R) (2004).Google Scholar
  10. 10.
    S.K. Bogner, A. Schwenk, R.J. Furnstahl, A. Nogga, Nucl. Phys. A 763, 59 (2005).Google Scholar
  11. 11.
    S.K. Bogner, R.J. Furnstahl, S. Ramanan, A. Schwenk, Nucl. Phys. A 773, 203 (2006).Google Scholar
  12. 12.
    S.K. Bogner, R.J. Furnstahl, R.J. Perry, Phys. Rev. C 75, 061001(R) (2007).Google Scholar
  13. 13.
    S.K. Bogner, R.J. Furnstahl, R.J. Perry, A. Schwenk, Phys. Lett. B 649, 488 (2007).Google Scholar
  14. 14.
    S.K. Bogner, R.J. Furnstahl, R.J. Perry, Ann. Phys. (N.Y.) 323, 1478 (2008).Google Scholar
  15. 15.
    R. Roth, H. Hergert, P. Papakonstantinou, T. Neff, H. Feldmeier, Phys. Rev. C 72, 034002 (2005) and references therein.Google Scholar
  16. 16.
    R. Roth, P. Papakonstantinou, N. Paar, H. Hergert, T. Neff, H. Feldmeier, Phys. Rev. C 73, 044312 (2006)Google Scholar
  17. 17.
    G.F. Bertsch, D.J. Dean, W. Nazarewicz, SciDAC Rev. 6, 42 (2007).Google Scholar
  18. 18.
    R.M. Dreizler, E.K.U. Gross, Density Functional Theory (Springer, Berlin, 1990).Google Scholar
  19. 19.
    N. Argaman, G. Makov, Am. J. Phys. 68, 69 (2000).Google Scholar
  20. 20.
    C. Fiolhais, F. Nogueira, M. Marques (Editors), A Primer in Density Functional Theory (Springer, Berlin, 2003).Google Scholar
  21. 21.
    R. Fukuda, T. Kotani, Y. Suzuki, S. Yokojima, Prog. Theor. Phys. 92, 833 (1994).Google Scholar
  22. 22.
    M. Valiev, G.W. Fernando, Phys. Lett. A 227, 265 (1997).Google Scholar
  23. 23.
    M. Valiev, G.W. Fernando, arXiv:cond-mat/9702247 (1997) unpublished.Google Scholar
  24. 24.
    J. Polonyi, K. Sailer, Phys. Rev. B 66, 155113 (2002).Google Scholar
  25. 25.
    S.J. Puglia, A. Bhattacharyya, R.J. Furnstahl, Nucl. Phys. A 723, 145 (2003).Google Scholar
  26. 26.
    A. Bhattacharyya, R.J. Furnstahl, Nucl. Phys. A 747, 268 (2005).Google Scholar
  27. 27.
    A. Bhattacharyya, R.J. Furnstahl, Phys. Lett. B 607, 259 (2005).Google Scholar
  28. 28.
    R.J. Furnstahl, J. Phys. G 31, S1357 (2005).Google Scholar
  29. 29.
    B.D. Day, Rev. Mod. Phys. 39, 719 (1967).Google Scholar
  30. 30.
    M. Baldo (Editor), Nuclear Methods and the Nuclear Equation of State (World Scientific, Singapore, 1999).Google Scholar
  31. 31.
    J. Dobaczewski, W. Nazarewicz, P.G. Reinhard, Nucl. Phys. A 693, 361 (2001).Google Scholar
  32. 32.
    M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003) and references therein.Google Scholar
  33. 33.
    M. Bender, P.H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003).Google Scholar
  34. 34.
    See http://www.scidacreview.org/0704/html/unedf. html for documentation on a large-scale project to build a universal nuclear energy density functional (UNEDF) with an order-of-magnitude improvement over current phenomenological functionals.Google Scholar
  35. 35.
    J.W. Negele, D. Vautherin, Phys. Rev. C 5, 1472 (1972).Google Scholar
  36. 36.
    J.W. Negele, D. Vautherin, Phys. Rev. C 11, 1031 (1975).Google Scholar
  37. 37.
    F. Hofmann, H. Lenske, Phys. Rev. C 57, 2281 (1998).Google Scholar
  38. 38.
    A.K. Kerman, J.P. Svenne, F.M.H. Villars, Phys. Rev. 147, 710 (1966).Google Scholar
  39. 39.
    W.H. Bassichis, A.K. Kerman, J.P. Svenne, Phys. Rev. 160, 746 (1967).Google Scholar
  40. 40.
    M.R. Strayer, W.H. Bassichis, A.K. Kerman, Phys. Rev. C 8, 1269 (1973).Google Scholar
  41. 41.
    B. Gebremariam, S.K. Bogner, T. Duguet, in preparation.Google Scholar
  42. 42.
    R.J. Furnstahl, H.-W. Hammer, S.J. Puglia, Ann. Phys. (N.Y.) 322, 2703 (2007).Google Scholar
  43. 43.
    T. Duguet, T. Lesinski, Eur. Phys. J. ST 156, 207 (2008).Google Scholar
  44. 44.
    J. Engel, Phys. Rev. C 75, 014306 (2007).Google Scholar
  45. 45.
    B.G. Giraud, Phys. Rev. C 77, 014311 (2008).Google Scholar
  46. 46.
    N. Barnea, Phys. Rev. C 76, 067302 (2007).Google Scholar
  47. 47.
    N. Kaiser, S. Fritsch, W. Weise, Nucl. Phys. A 724, 47 (2003).Google Scholar
  48. 48.
    N. Kaiser, Phys. Rev. C 68, 014323 (2003).Google Scholar
  49. 49.
    S. Fritsch, N. Kaiser, W. Weise, Nucl. Phys. A 750, 259 (2005).Google Scholar
  50. 50.
    P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 2000).Google Scholar
  51. 51.
    E. Perlinska, S.G. Rohozinski, J. Dobaczewski, W. Nazarewicz, Phys. Rev. C 69, 014316 (2004).Google Scholar
  52. 52.
    D. Vautherin, D.M. Brink, Phys. Rev. C 5, 626 (1972).Google Scholar
  53. 53.
    J. Dobaczewski, J. Dudek, Phys. Rev. C 52, 1827 (1995), and references therein.Google Scholar
  54. 54.
    J.W. Negele, H. Orland, Quantum Many-Particle Systems (Addison-Wesley, New York, 1988).Google Scholar
  55. 55.
    W. Kutzelnigg, J. Mol. Struct. 768, 163 (2006).Google Scholar
  56. 56.
    R. Rajaraman, H.A. Bethe, Rev. Mod. Phys. 39, 745 (1967).Google Scholar
  57. 57.
    M. Rasamny, M.M. Valiev, G.W. Fernando, Phys. Rev. B 58, 9700 (1998).Google Scholar
  58. 58.
    W. Kohn, J.M. Luttinger, Phys. Rev. 118, 41 (1960).Google Scholar
  59. 59.
    J.M. Luttinger, J.C. Ward, Phys. Rev. 118, 1417 (1960).Google Scholar
  60. 60.
    R.J. Bartlett, V.F. Lotrich, I.V. Schweigert, J. Chem. Phys. 123, 062205 (2005).Google Scholar
  61. 61.
    A. Görling, J. Chem. Phys. 123, 062203 (2005).Google Scholar
  62. 62.
    E.J. Baerends, O.V. Gritsenko, J. Chem. Phys. 123, 062202 (2005).Google Scholar
  63. 63.
    X. Campi, A. Bouyssy, Phys. Lett. B 73, 263 (1978).Google Scholar
  64. 64.
    E.D. Jurgenson, R.J. Furnstahl, arXiv:0809.4199.Google Scholar
  65. 65.
    U. van Kolck, Phys. Rev. C 49, 2932 (1999).Google Scholar
  66. 66.
    E. Epelbaum, A. Nogga, W. Glöckle, H. Kamada, U.-G. Meißner, H. Witala, Phys. Rev. C 66, 064001 (2002).Google Scholar
  67. 67.
    W. Glöckle, The Quantum Mechanical Few-Body Problem (Springer-Verlag, Berlin, 1983).Google Scholar
  68. 68.
    P. Buettiker, U.G. Meissner, Nucl. Phys. A 668, 97 (2000).Google Scholar
  69. 69.
    M.C.M. Rentmeester, R.G.E. Timmermans, J.J. de Swart, Phys. Rev. C 67, 044001 (2003).Google Scholar
  70. 70.
    A. Nogga, S.K. Bogner, A. Schwenk, Phys. Rev. C 70, 061002(R) (2004).Google Scholar
  71. 71.
    E. Epelbaum, W. Glöckle, U.-G. Meißner, Nucl. Phys. A 747, 362 (2005).Google Scholar
  72. 72.
    D.R. Entem, R. Machleidt, Phys. Rev. C 68, 041001(R) (2003).Google Scholar
  73. 73.
    R.B. Wiringa, V.G.J. Stoks, R. Schiavilla, Phys. Rev. C 51, 38 (1995).Google Scholar
  74. 74.
    R.J. Furnstahl, J.C. Hackworth, Phys. Rev. C 56, 2875 (1997).Google Scholar
  75. 75.
    J. Dobaczewski, arXiv:nucl-th/0301069, unpublished.Google Scholar
  76. 76.
    T. Lesinski, M. Bender, K. Bennaceur, T. Duguet, J. Meyer, Phys. Rev. C 76, 014312 (2007).Google Scholar
  77. 77.
    D.M. Brink, Fl. Stancu, Phys. Rev. C 75, 064311 (2007).Google Scholar
  78. 78.
    V. Rotivale, S.K. Bogner, T. Duguet, R.J. Furnstahl, in preparation.Google Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.National Superconducting Cyclotron Laboratory and Department of Physics and AstronomyMichigan State UniversityEast LansingUSA
  2. 2.Department of PhysicsThe Ohio State UniversityColumbusUSA
  3. 3.Department of Physics and AstronomyOhio UniversityAthensUSA

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