Uncertainty quantification and propagation in nuclear density functional theory

  • N. Schunck
  • J. D. McDonnell
  • D. Higdon
  • J. Sarich
  • S. M. Wild
Review
Part of the following topical collections:
  1. Perspectives on Nuclear Data for the Next Decade

Abstract.

Nuclear density functional theory (DFT) is one of the main theoretical tools used to study the properties of heavy and superheavy elements, or to describe the structure of nuclei far from stability. While on-going efforts seek to better root nuclear DFT in the theory of nuclear forces (see Duguet et al., this Topical Issue), energy functionals remain semi-phenomenological constructions that depend on a set of parameters adjusted to experimental data in finite nuclei. In this paper, we review recent efforts to quantify the related uncertainties, and propagate them to model predictions. In particular, we cover the topics of parameter estimation for inverse problems, statistical analysis of model uncertainties and Bayesian inference methods. Illustrative examples are taken from the literature.

References

  1. 1.
    Karl-Heinz Schmidt, Beatriz Jurado, Charlotte Amouroux, General description of fission observables, Technical Report NEA/DB/DOC(2014)1, Organisation for Economic Co-Operation and Development, Nuclear Energy Agency-OECD/NEA, Le Seine Saint-Germain, 12 boulevard des Iles, F-92130 Issy-les-Moulineaux (France) (2014)Google Scholar
  2. 2.
    Jochen Erler, Noah Birge, Markus Kortelainen, Witold Nazarewicz, Erik Olsen, Alexander M. Perhac, Mario Stoitsov, Nature 486, 509 (2012)ADSCrossRefGoogle Scholar
  3. 3.
    Scott Bogner, Aurel Bulgac, J. Carlson, Jonathan Engel, George Fann, Richard J. Furnstahl, Stefano Gandolfi, Gaute Hagen, Mihai Horoi, C. Johnson, Comput. Phys. Commun. 184, 2235 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    S. Goriely, N. Chamel, J.M. Pearson, Phys. Rev. C 88, 061302 (2013)ADSCrossRefGoogle Scholar
  5. 5.
    S. Goriely, S. Hilaire, M. Girod, S. Péru, Phys. Rev. Lett. 102, 242501 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    J.E. Drut, R.J. Furnstahl, L. Platter, Prog. Part. Nucl. Phys. 64, 120 (2010)ADSCrossRefGoogle Scholar
  7. 7.
    M. Stoitsov, M. Kortelainen, S.K. Bogner, T. Duguet, R.J. Furnstahl, B. Gebremariam, N. Schunck, Phys. Rev. C 82, 054307 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    B.G. Carlsson, J. Dobaczewski, J. Toivanen, P. Veselý, Comput. Phys. Commun. 181, 1641 (2010)ADSCrossRefMATHGoogle Scholar
  9. 9.
    T. Duguet, J. Phys. G: Nucl. Part. Phys. 42, 025107 (2015)ADSCrossRefGoogle Scholar
  10. 10.
    P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)ADSMathSciNetCrossRefGoogle Scholar
  11. 11.
    W. Kohn, L.J. Sham, Phys. Rev. 140, A1133 (1965)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    R.G. Parr, W. Yang, Density Functional Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989)Google Scholar
  13. 13.
    R.M. Dreizler, E.K.U Gross, Density Functional Theory: An Approach to the Quantum Many-Body Problem (Springer-Verlag, 1990)Google Scholar
  14. 14.
    R. Eschrig, Fundamentals of Density Functional Theory (Teubner, Leipzig, 1996)Google Scholar
  15. 15.
    Michael Bender, Paul-Henri Heenen, Paul-Gerhard Reinhard, Rev. Mod. Phys. 75, 121 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, 2000)Google Scholar
  17. 17.
    T. Duguet, The nuclear energy density functional formalism, in The Euroschool on Exotic Beams, Vol. IV, edited by Christoph Scheidenberger, Marek Pfützner, Vol. 879 (Springer Berlin Heidelberg, Berlin, Heidelberg, 2014) pp. 293--350Google Scholar
  18. 18.
    J.-P. Blaizot, G. Ripka, Quantum Theory of Finite Systems (The MIT Press, Cambridge, 1985)Google Scholar
  19. 19.
    D.M. Brink, R.A. Broglia (Editors), Nuclear Superfluidity -- Pairing in Finite Systems (Cambridge University Press, 2005)Google Scholar
  20. 20.
    J.G. Valatin, Phys. Rev. 122, 1012 (1961)ADSMathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Hans-Jörg Mang, Phys. Rep. 18, 325 (1975)ADSCrossRefGoogle Scholar
  22. 22.
    J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 131, 164 (2000)ADSCrossRefMATHGoogle Scholar
  23. 23.
    J. Dobaczewski, J. Dudek, S.G. Rohoziński, T.R. Werner, Phys. Rev. C 62, 014310 (2000)ADSCrossRefGoogle Scholar
  24. 24.
    S.G. Rohoziński, J. Dobaczewski, W. Nazarewicz, Phys. Rev. C 81, 014313 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    Andrzej Baran, Aurel Bulgac, Michael Forbes, Gaute Hagen, Witold Nazarewicz, Nicolas Schunck, Mario Stoitsov, Phys. Rev. C 78, 014318 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    T.H.R. Skyrme, Nucl. Phys. 9, 615 (1959)CrossRefMATHGoogle Scholar
  27. 27.
    D. Vautherin, D.M. Brink, Phys. Rev. C 5, 626 (1972)ADSCrossRefGoogle Scholar
  28. 28.
    J. Dechargé, D. Gogny, Phys. Rev. C 21, 1568 (1980)ADSCrossRefGoogle Scholar
  29. 29.
    J.R. Stone, P.-G. Reinhard, Prog. Part. Nucl. Phys. 58, 587 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    J. Erler, P. Klüpfel, P.-G. Reinhard, J. Phys. G: Nucl. Part. Phys. 37, 064001 (2010)ADSCrossRefGoogle Scholar
  31. 31.
    M. Kortelainen, T. Lesinski, J. Moré, W. Nazarewicz, J. Sarich, N. Schunck, M.V. Stoitsov, S. Wild, Phys. Rev. C 82, 024313 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    M. Kortelainen, J. McDonnell, W. Nazarewicz, P.-G. Reinhard, J. Sarich, N. Schunck, M.V. Stoitsov, S.M. Wild, Phys. Rev. C 85, 024304 (2012)ADSCrossRefGoogle Scholar
  33. 33.
    M. Kortelainen, J. McDonnell, W. Nazarewicz, E. Olsen, P.-G. Reinhard, J. Sarich, N. Schunck, S.M. Wild, D. Davesne, J. Erler, A. Pastore, Phys. Rev. C 89, 054314 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    M. Anguiano, J.L. Egido, L.M. Robledo, Nucl. Phys. A 683, 227 (2001)ADSCrossRefMATHGoogle Scholar
  35. 35.
    M.V. Stoitsov, J. Dobaczewski, R. Kirchner, W. Nazarewicz, J. Terasaki, Phys. Rev. C 76, 014308 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    M. Bender, K. Bennaceur, T. Duguet, P.-H. Heenen, T. Lesinski, J. Meyer, Phys. Rev. C 80, 064302 (2009)ADSCrossRefGoogle Scholar
  37. 37.
    T. Duguet, T. Lesinski, Non-Empirical Nuclear Energy Functionals, Pairing Gaps and Odd-Even Mass Differences (AIP, 2009) p. 243Google Scholar
  38. 38.
    D. Lacroix, T. Duguet, M. Bender, Phys. Rev. C 79, 044318 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    F. Raimondi, K. Bennaceur, J. Dobaczewski, J. Phys. G: Nucl. Part. Phys. 41, 055112 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    J. Sadoudi, T. Duguet, J. Meyer, M. Bender, Phys. Rev. C 88, 064326 (2013)ADSCrossRefGoogle Scholar
  41. 41.
    J. Sadoudi, M. Bender, K. Bennaceur, D. Davesne, R. Jodon, T. Duguet, Phys. Scr. T154, 014013 (2013)ADSCrossRefGoogle Scholar
  42. 42.
    S.A. Fayans, S.V. Tolokonnikov, E.L. Trykov, D. Zawischa, Phys. Lett. B 338, 1 (1994)ADSCrossRefGoogle Scholar
  43. 43.
    E. Krömer, S.V. Tolokonnikov, S.A. Fayans, D. Zawischa, Phys. Lett. B 363, 12 (1995)ADSCrossRefGoogle Scholar
  44. 44.
    S.A. Fayans, S.V. Tolokonnikov, E.L. Trykov, D. Zawischa, Nucl. Phys. A 676, 49 (2000)ADSCrossRefGoogle Scholar
  45. 45.
    M. Baldo, P. Schuck, X. Viñas, Phys. Lett. B 663, 390 (2008)ADSCrossRefGoogle Scholar
  46. 46.
    M. Baldo, L.M. Robledo, P. Schuck, X. Viñas, Phys. Rev. C 87, 064305 (2013)ADSCrossRefGoogle Scholar
  47. 47.
    Guillaume Hupin, Denis Lacroix, Phys. Rev. C 83, 024317 (2011)ADSCrossRefGoogle Scholar
  48. 48.
    Guillaume Hupin, Denis Lacroix, Michael Bender, Phys. Rev. C 84, 014309 (2011)ADSCrossRefGoogle Scholar
  49. 49.
    Guillaume Hupin, Denis Lacroix, Phys. Rev. C 86, 024309 (2012)ADSCrossRefGoogle Scholar
  50. 50.
    Thomas Lesinski, Phys. Rev. C 89, 044305 (2014)CrossRefGoogle Scholar
  51. 51.
    Jacek Dobaczewski, J. Phys. G: Nucl. Part. Phys. 36, 105105 (2009)ADSCrossRefGoogle Scholar
  52. 52.
    X.B. Wang, J. Dobaczewski, M. Kortelainen, L.F. Yu, M.V. Stoitsov, Phys. Rev. C 90, 014312 (2014)ADSCrossRefGoogle Scholar
  53. 53.
    J. Engel, Phys. Rev. C 75, 014306 (2007)ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    Jérémie Messud, Michael Bender, Eric Suraud, Phys. Rev. C 80, 054314 (2009)ADSCrossRefGoogle Scholar
  55. 55.
    J. Dobaczewski, W. Nazarewicz, M.V. Stoitsov, Contact pairing interaction for the Hartree-Fock-Bogoliubov calculations, in The Nuclear Many-Body Problem 2001 (Springer, 2002)Google Scholar
  56. 56.
    Yuan Tian, Zhong-yu Ma, Peter Ring, Phys. Rev. C 79, 064301 (2009)ADSCrossRefGoogle Scholar
  57. 57.
    Yuan Tian, Zhong-yu Ma, P. Ring, Phys. Rev. C 80, 024313 (2009)ADSCrossRefGoogle Scholar
  58. 58.
    S.K. Bogner, R.J. Furnstahl, H. Hergert, M. Kortelainen, P. Maris, M. Stoitsov, J.P. Vary, Phys. Rev. C 84, 044306 (2011)ADSCrossRefGoogle Scholar
  59. 59.
    S. Gandolfi, J. Carlson, Steven C. Pieper, Phys. Rev. Lett. 106, 012501 (2011)ADSCrossRefGoogle Scholar
  60. 60.
    W.J. Metzger, Statistical methods in data analysis, Technical report, Katholieke Universiteit Nijmegen (2002)Google Scholar
  61. 61.
    Siegmund Brandt, Data Analysis - Statistical and Computational Methods for Scientists and Engineers (Springer, 2014)Google Scholar
  62. 62.
    S. Goriely, M. Samyn, J. Pearson, Phys. Rev. C 75, 064312 (2007)ADSCrossRefGoogle Scholar
  63. 63.
    P. Klüpfel, P.-G. Reinhard, T.J. Bürvenich, J.A. Maruhn, Phys. Rev. C 79, 034310 (2009)ADSCrossRefGoogle Scholar
  64. 64.
    J. Bartel, Ph Quentin, Matthias Brack, C. Guet, H.-B. Håkansson, Nucl. Phys. A 386, 79 (1982)ADSCrossRefGoogle Scholar
  65. 65.
    J.F. Berger, M. Girod, D. Gogny, Comput. Phys. Commun. 63, 365 (1991)ADSCrossRefMATHGoogle Scholar
  66. 66.
    G. Audi, A.H. Wapstra, C. Thibault, Nucl. Phys. A 729, 337 (2003)ADSCrossRefGoogle Scholar
  67. 67.
    W. Satuła, J. Dobaczewski, W. Nazarewicz, Phys. Rev. Lett. 81, 3599 (1998)ADSCrossRefGoogle Scholar
  68. 68.
    K. Rutz, M. Bender, P.-G. Reinhard, J.A. Maruhn, Phys. Lett. B 468, 1 (1999)ADSCrossRefGoogle Scholar
  69. 69.
    J. Dobaczewski, W. Nazarewicz, P.-G. Reinhard, Nucl. Phys. A 693, 361 (2001)ADSCrossRefGoogle Scholar
  70. 70.
    T. Duguet, P. Bonche, P.-H. Heenen, J. Meyer, Phys. Rev. C 65, 014311 (2001)ADSCrossRefGoogle Scholar
  71. 71.
    G. Bertsch, C. Bertulani, W. Nazarewicz, N. Schunck, M. Stoitsov, Phys. Rev. C 79, 034306 (2009)ADSCrossRefGoogle Scholar
  72. 72.
    F. Tondeur, S. Goriely, J.M. Pearson, M. Onsi, Phys. Rev. C 62, 024308 (2000)ADSCrossRefGoogle Scholar
  73. 73.
    Stefan M. Wild, Jason Sarich, Nicolas Schunck, J. Phys. G: Nucl. Part. Phys. 42, 034031 (2015)ADSCrossRefGoogle Scholar
  74. 74.
    T. Munson, J. Sarich, Stefan M. Wild, S. Benson, L. Curfman McInnes, TAO 2.0 users manual, Tech. Memo. ANL/MCS-TM-322, Argonne National Laboratory, Argonne, IL, 2012Google Scholar
  75. 75.
    Stefan M. Wild, Solving derivative-free nonlinear least squares with POUNDERS, Preprint ANL/MCS-P5120-0414, Argonne, April 2014Google Scholar
  76. 76.
    A. Ekström, G. Baardsen, C. Forssén, G. Hagen, M. Hjorth-Jensen, G.R. Jansen, R. Machleidt, W. Nazarewicz, T. Papenbrock, J. Sarich, S.M. Wild, Phys. Rev. Lett. 110, 192502 (2013)ADSCrossRefGoogle Scholar
  77. 77.
    M. Bertolli, T. Papenbrock, S.M. Wild, Phys. Rev. C 85, 014322 (2012)ADSCrossRefGoogle Scholar
  78. 78.
    J. Dobaczewski, W. Nazarewicz, P.-G. Reinhard, J. Phys. G: Nucl. Part. Phys. 41, 074001 (2014)ADSCrossRefGoogle Scholar
  79. 79.
    N. Schunck, D. Duke, H. Carr, Phys. Rev. C 91, 034327 (2015)ADSCrossRefGoogle Scholar
  80. 80.
    E. Chabanat, P. Bonche, P. Haensel, J. Meyer, R. Schaeffer, Nucl. Phys. A 627, 710 (1997)ADSCrossRefGoogle Scholar
  81. 81.
    J. Toivanen, J. Dobaczewski, M. Kortelainen, K. Mizuyama, Phys. Rev. C 78, 034306 (2008)ADSCrossRefGoogle Scholar
  82. 82.
    M. Kortelainen, J. Dobaczewski, K. Mizuyama, J. Toivanen, Phys. Rev. C 77, 064307 (2008)ADSCrossRefGoogle Scholar
  83. 83.
    D.C. Montgomery, G.C. Runger (Editors), Applied Statistics and Probability for Engineers (John Wiley & Sons, Inc., 2002)Google Scholar
  84. 84.
    J. Dudek, B. Szpak, M.-G. Porquet, B. Fornal, J. Phys.: Conf. Ser. 267, 012062 (2011)ADSGoogle Scholar
  85. 85.
    B. Szpak, J. Dudek, M.-G. Porquet, B. Fornal, J. Phys.: Conf. Ser. 267, 012063 (2011)ADSGoogle Scholar
  86. 86.
    F.H. Fröhner, Evaluation and analysis of nuclear resonance data, Technical Report 18, OECD Nuclear Energy Agency, Paris, 2000Google Scholar
  87. 87.
    H. Leeb, D. Neudecker, Th. Srdinko, Nucl. Data Sheets 109, 2762 (2008)ADSCrossRefGoogle Scholar
  88. 88.
    Roberto Capote, Donald L. Smith, Nucl. Data Sheets 109, 2768 (2008)ADSCrossRefGoogle Scholar
  89. 89.
    M. Herman, A. Koning, Covariance data in the fast neutron region. Technical Report 24, Technical report NEA/ WPEC-24, OECD Nuclear Energy Agency, Paris, 2011Google Scholar
  90. 90.
    Patrick Talou, Toshihiko Kawano, Mark B. Chadwick, Denise Neudecker, Michael E. Rising, J. Phys. G: Nucl. Part. Phys. 42, 034025 (2015)ADSCrossRefGoogle Scholar
  91. 91.
    M.R. Schindler, D.R. Phillips, Ann. Phys. 324, 682 (2009)ADSCrossRefMATHGoogle Scholar
  92. 92.
    R.J. Furnstahl, D.R. Phillips, S. Wesolowski, J. Phys. G: Nucl. Part. Phys. 42, 034028 (2015)ADSCrossRefGoogle Scholar
  93. 93.
    J.J. Mortensen, K. Kaasbjerg, S.L. Frederiksen, J.K. Nørskov, J.P. Sethna, K.W. Jacobsen, Phys. Rev. Lett. 95, 216401 (2005)ADSCrossRefGoogle Scholar
  94. 94.
    Albert Tarantola, Inverse problem theory and methods for model parameter estimation (Society for Industrial and Applied Mathematics, Philadelphia, 2005)Google Scholar
  95. 95.
    D. Gamerman, H.F. Lopes, Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference (Chapman & Hall/CRC, 2006)Google Scholar
  96. 96.
    Marc C. Kennedy, Anthony O’Hagan, J. R. Stat. Soc. 63, 425 (2001)CrossRefMATHGoogle Scholar
  97. 97.
    Dave Higdon, James Gattiker, Brian Williams, Maria Rightley, J. Am. Stat. Assoc. 103, 570 (2008)CrossRefMATHGoogle Scholar
  98. 98.
    Ilias Bilionis, Nicholas Zabaras, Bledar A. Konomi, Guang Lin, J. Comput. Phys. 241, 212 (2013)ADSCrossRefGoogle Scholar
  99. 99.
    Nicolas Schunck, Jordan D. McDonnell, Jason Sarich, Stefan M. Wild, Dave Higdon, J. Phys. G: Nucl. Part. Phys. 42, 034024 (2015)ADSCrossRefGoogle Scholar
  100. 100.
    S. Goriely, R. Capote, Phys. Rev. C 89, 054318 (2014)ADSCrossRefGoogle Scholar
  101. 101.
    J.D. McDonnell, N. Schunck, D. Higdon, J. Sarich, S.M. Wild, W. Nazarewicz, Phys. Rev. Lett. 114, 122501 (2015)ADSCrossRefGoogle Scholar
  102. 102.
    J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102, 166 (1997)ADSCrossRefGoogle Scholar
  103. 103.
    J. Dobaczewski, J. Dudek, Comput. Phys. Commun. 102, 183 (1997)ADSCrossRefGoogle Scholar
  104. 104.
    J. Dobaczewski, P. Olbratowski, Comput. Phys. Commun. 158, 158 (2004)ADSCrossRefGoogle Scholar
  105. 105.
    J. Dobaczewski, P. Olbratowski, Comput. Phys. Commun. 167, 214 (2005)ADSCrossRefGoogle Scholar
  106. 106.
    M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167, 43 (2005)ADSCrossRefGoogle Scholar
  107. 107.
    N. Schunck, J. Dobaczewski, J. McDonnell, W. Satuła, J.A. Sheikh, A. Staszczak, M. Stoitsov, P. Toivanen, Comput. Phys. Commun. 183, 166 (2012)ADSMathSciNetCrossRefGoogle Scholar
  108. 108.
    M.V. Stoitsov, N. Schunck, M. Kortelainen, N. Michel, H. Nam, E. Olsen, J. Sarich, S. Wild, Comput. Phys. Commun. 184, 1592 (2013)ADSCrossRefGoogle Scholar
  109. 109.
    Nicolas Schunck, J. Phys.: Conf. Ser. 436, 012058 (2013)Google Scholar
  110. 110.
    K. Bennaceur, J. Dobaczewski, Comput. Phys. Commun. 168, 96 (2005)ADSCrossRefGoogle Scholar
  111. 111.
    J. Dobaczewski, H. Flocard, J. Treiner, Nucl. Phys. A 422, 103 (1984)ADSCrossRefGoogle Scholar
  112. 112.
    J. Pei, M. Stoitsov, G. Fann, W. Nazarewicz, N. Schunck, F. Xu, Phys. Rev. C 78, 064306 (2008)ADSCrossRefGoogle Scholar
  113. 113.
    A. Bohr, B.R. Mottelson, Nuclear Structure, Vol. II (Benjamin, New-York, 1975)Google Scholar
  114. 114.
    P. Bonche, H. Flocard, P.H. Heenen, Comput. Phys. Commun. 171, 49 (2005)ADSCrossRefGoogle Scholar
  115. 115.
    W. Ryssens, V. Hellemans, M. Bender, P.-H. Heenen, Comput. Phys. Commun. 187, 175 (2015)ADSCrossRefGoogle Scholar
  116. 116.
    W. Pöschl, D. Vretenar, A. Rummel, P. Ring, Comput. Phys. Commun. 101, 75 (1997)ADSCrossRefMATHGoogle Scholar
  117. 117.
    W. Pöschl, D. Vretenar, P. Ring, Comput. Phys. Commun. 103, 217 (1997)ADSCrossRefGoogle Scholar
  118. 118.
    J.C. Pei, G.I. Fann, R.J. Harrison, W. Nazarewicz, Yue Shi, S. Thornton, Phys. Rev. C 90, 024317 (2014)ADSCrossRefGoogle Scholar
  119. 119.
    M. Samyn, S. Goriely, J. Pearson, Phys. Rev. C 72, 044316 (2005)ADSCrossRefGoogle Scholar
  120. 120.
    S. Hilaire, M. Girod, Eur. Phys. J. A 33, 237 (2007)ADSCrossRefGoogle Scholar
  121. 121.
    S.A. Coon, M.I. Avetian, M.K.G. Kruse, U. van Kolck, P. Maris, J.P. Vary, Phys. Rev. C 86, 054002 (2012)ADSCrossRefGoogle Scholar
  122. 122.
    R.J. Furnstahl, G. Hagen, T. Papenbrock, Phys. Rev. C 86, 031301 (2012)ADSCrossRefGoogle Scholar
  123. 123.
    S.N. More, A. Ekström, R.J. Furnstahl, G. Hagen, T. Papenbrock, Phys. Rev. C 87, 044326 (2013)ADSCrossRefGoogle Scholar
  124. 124.
    M. Kortelainen, J. Erler, W. Nazarewicz, N. Birge, Y. Gao, E. Olsen, Phys. Rev. C 88, 031305 (2013)ADSCrossRefGoogle Scholar
  125. 125.
    Y. Gao, J. Dobaczewski, M. Kortelainen, J. Toivanen, D. Tarpanov, Phys. Rev. C 87, 034324 (2013)ADSCrossRefGoogle Scholar
  126. 126.
    J. Erler, C.J. Horowitz, W. Nazarewicz, M. Rafalski, P.-G. Reinhard, Phys. Rev. C 87, 044320 (2013)ADSCrossRefGoogle Scholar
  127. 127.
    N. Paar, Ch.C. Moustakidis, T. Marketin, D. Vretenar, G.A. Lalazissis, Phys. Rev. C 90, 011304 (2014)ADSCrossRefGoogle Scholar
  128. 128.
    Wei-Chia Chen, J. Piekarewicz, Phys. Rev. C 90, 044305 (2014)ADSCrossRefGoogle Scholar
  129. 129.
    E. Bauge, P. Dossantos-Uzarralde, J. Kor. Phys. Soc. 59, 1218 (2011)CrossRefGoogle Scholar
  130. 130.
    J. Piekarewicz, B.K. Agrawal, G. Colò, W. Nazarewicz, N. Paar, P.-G. Reinhard, X. Roca-Maza, D. Vretenar, Phys. Rev. C 85, 041302 (2012)ADSCrossRefGoogle Scholar
  131. 131.
    P.-G. Reinhard, J. Piekarewicz, W. Nazarewicz, B.K. Agrawal, N. Paar, X. Roca-Maza, Phys. Rev. C 88, 034325 (2013)ADSCrossRefGoogle Scholar
  132. 132.
    P.-G. Reinhard, W. Nazarewicz, Phys. Rev. C 87, 014324 (2013)ADSCrossRefGoogle Scholar
  133. 133.
    Jørgen Randrup, Peter Möller, Phys. Rev. Lett. 106, 132503 (2011)ADSCrossRefGoogle Scholar
  134. 134.
    J. Randrup, P. Möller, A.J. Sierk, Phys. Rev. C 84, 034613 (2011)ADSCrossRefGoogle Scholar
  135. 135.
    H. Goutte, P. Casoli, J.-F. Berger, Nucl. Phys. A 734, 217 (2004)ADSCrossRefGoogle Scholar
  136. 136.
    W. Younes, D. Gogny, Collective dissipation from saddle to scission in a microscopic approach, Technical Report LLNL-TR-586694, Lawrence Livermore National Laboratory (LLNL) Livermore, CA, 2012Google Scholar
  137. 137.
    D. Regnier, M. Verrière, N. Dubray, N. Schunck, FELIX-1.0: A finite element solver for the time dependent generator coordinate method with the Gaussian overlap approximation, arXiv:1505.02704 (2015)
  138. 138.
    N. Nikolov, N. Schunck, W. Nazarewicz, M. Bender, J. Pei, Phys. Rev. C 83, 034305 (2011)ADSCrossRefGoogle Scholar
  139. 139.
    T.V. Nhan Hao, P. Quentin, L. Bonneau, Phys. Rev. C 86, 064307 (2012)ADSCrossRefGoogle Scholar
  140. 140.
    J.D. McDonnell, W. Nazarewicz, J.A. Sheikh, Phys. Rev. C 87, 054327 (2013)ADSCrossRefGoogle Scholar
  141. 141.
    Samuel A. Giuliani, Luis M. Robledo, Phys. Rev. C 88, 054325 (2013)ADSCrossRefGoogle Scholar
  142. 142.
    N. Schunck, D. Duke, H. Carr, A. Knoll, Phys. Rev. C 90, 054305 (2014)ADSCrossRefGoogle Scholar

Copyright information

© SIF, Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • N. Schunck
    • 1
  • J. D. McDonnell
    • 1
    • 2
  • D. Higdon
    • 3
  • J. Sarich
    • 4
  • S. M. Wild
    • 4
  1. 1.Nuclear and Chemical Science DivisionLawrence Livermore National LaboratoryLivermoreUSA
  2. 2.Department of Physics and AstronomyFrancis Marion UniversityFlorenceUSA
  3. 3.Los Alamos National LaboratoryLos AlamosUSA
  4. 4.Mathematics and Computer Science DivisionArgonne National LaboratoryArgonneUSA

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