Abstract.
Starting from successful self-consistent mean-field models, this paper discusses why and how to go beyond the mean field approximation. To include long-range correlations from fluctuations in collective degrees of freedom, one has to consider symmetry restoration and configuration mixing, which give access to ground-state correlations and spectroscopy.
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M. Bender, P.-H. Heenen, P.-G. Reinhard, Rev. Mod. Phys. 75, 121 (2003)
D. Vretenar, Eur. Phys. J. Special Topics 156, 37 (2008)
W. Kohn, Rev. Mod. Phys. 71, 1253 (1998)
A Primer in Density Functional Theory, edited by C. Fiolhais, F. Nogueira, M. Marques, Lecture Notes Phys. 620 (Springer-Verlag, Berlin, Heidelberg, 2003)
P.-G. Reinhard, E.W. Otten, Nucl. Phys. A 420, 173 (1984)
W. Nazarewicz, Prog. Part. Nucl. Phys. 28, 307 (1992)
W. Nazarewicz, Nucl. Phys. A 574, 27 (1994)
E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves, A.P. Zuker, Rev. Mod. Phys. 77, 427 (2005)
W. Satuła, R. Wyss, Rep. Prog. Phys. 68, 131 (2005)
N. Paar, D. Vretenar, E. Khan, G. Colò, Rep. Prog. Phys. 70, 691 (2007)
H.J. Mang, Phys. Rep. 18, 327 (1975)
P. Ring, P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, Heidelberg, 1980), p. 438
B.F. Bayman, Nucl. Phys. 15, 33 (1960)
V.N. Fomenko, J. Phys. A 3, 8 (1970)
H. Flocard, N. Onishi, Ann. Phys. (NY) 254, 275 (1997)
C.Y. Wong, Phys. Rep. 15, 283 (1975)
F. Grümmer, K.W. Schmid, A. Faessler, Nucl. Phys. A 306, 134 (1978)
J.A. Sheikh, P. Ring, Nucl. Phys. A 665, 71 (2001)
J.L. Egido, L.M. Robledo, Nucl. Phys. A 524, 65 (1991)
M. Anguiano, J.L. Egido, L.M. Robledo, Nucl. Phys. A 696, 467 (2001)
M.V. Stoitsov, J. Dobaczewski, R. Kirchner, W. Nazarewicz, J. Terasaki, Phys. Rev. C 76, 014308 (2007)
K.W. Schmid, F. Grümmer, Rep. Prog. Phys. 50, 731 (1987)
K.W. Schmid, Prog. Part. Nucl. Phys. 52, 565 (2004)
D. Baye, P.-H. Heenen, Phys. Rev. C 29, 1056 (1984)
H. Zduńczuk, W. Satuła, J. Dobaczewski, M. Kosmulski, Phys. Rev. C 76, 044304 (2007)
D.L. Hill, J.A. Wheeler, Phys. Rev. 89, 1106 (1953); J.J. Griffin, J.A. Wheeler, Phys. Rev. 108, 311 (1957)
P. Bonche, J. Dobaczewski, H. Flocard, P.-H. Heenen, J. Meyer, Nucl. Phys. A 510, 466 (1990)
P.-H. Heenen, P. Bonche, J. Dobaczewski, H. Flocard, Nucl. Phys. A 561, 367 (1993)
R.R. Rodriguez-Guzman, J.L. Egido, L.M. Robledo, Phys. Rev. C 62, 054319 (2002)
F. Dönau, J.-y. Zhang, L.L. Riedinger, Nucl. Phys. A 496, 333 (1989)
P.-H. Heenen, A. Valor, M. Bender, P. Bonche, H. Flocard, Eur. Phys. J. A 11, 393 (2001)
J. Meyer, P. Bonche, M.S. Weiss, J. Dobaczewski, H. Flocard, P.-H. Heenen, Nucl. Phys. A 588, 597 (1995)
A. Valor, P.-H. Heenen, P. Bonche, Nucl. Phys. A 671, 145 (2000)
M. Bender, H. Flocard, P.-H. Heenen, Phys. Rev. C 68, 044321 (2003)
R.R. Rodriguez-Guzman, J.L. Egido, L.M. Robledo, Nucl. Phys. A 709, 201 (2002)
J.L. Egido, L.M. Robledo, in Extended Density Functionals in Nuclear Physics, edited by G.A. Lalazissis, P. Ring, D. Vretenar, Lecture Notes Phys. 641 (Springer, Berlin, 2004), p. 269
T. Nikšić, D. Vretenar, P. Ring, Phys. Rev. C 73, 034308 (2006); Phys. Rev. C 74, 064309 (2006)
T. Nikšić, Eur. Phys. J. Special Topics 156, 175 (2008)
M. Girod, K. Kumar, B. Grammaticos, P. Aguer, Phys. Rev. Lett. 41, 1765 (1978)
J. Libert, M. Girod, J.-P. Delaroche, Phys. Rev. C 60, 054301 (1999)
L. Prochniak, P. Quentin, D. Samsœn, J. Libert, Nucl. Phys. A 730, 59 (2004)
P. Fleischer, P. Klüpfel, P.-G. Reinhard, J.A. Maruhn, Phys. Rev. C 70, 054321 (2004)
M. Bender, P.-H. Heenen, Nucl. Phys. A 713, 390 (2003)
M. Bender, P. Bonche, P.-H. Heenen, Phys. Rev. C 74, 024312 (2006)
T. Duguet, M. Bender, P. Bonche, P.-H. Heenen, Phys. Lett. B 559, 201 (2003)
M. Bender, P. Bonche, T. Duguet, P.-H. Heenen, Phys. Rev. C 69, 064303 (2004)
M. Bender, P.-H. Heenen, P. Bonche, Phys. Rev. C 70, 054304 (2004)
R. Julin, K. Helariutta, M. Muikki, J. Phys. G 27, R109 (2001)
T. Grahn et al., Phys. Rev. Lett. 97, 062501 (2006)
F. Tondeur, S. Goriely, J.M. Pearson, M. Onsi, Phys. Rev. 62, 024308 (2000)
M. Samyn, S. Goriely, P.-H. Heenen, J.M. Pearson, F. Tondeur, Nucl. Phys. A 700, 142 (2002)
S. Goriely, M. Samyn, M. Bender, J.M. Pearson, Phys. Rev. C 68, 054325 (2003)
M. Samyn, S. Goriely, M. Bender, J.M. Pearson, Phys. Rev. C 70, 044309 (2004)
M. Bender, G.F. Bertsch, P.-H. Heenen, Phys. Rev. Lett. 94, 102503 (2006); Phys. Rev. C 73, 034322 (2006)
M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, S. Pittel, D.J. Dean, Phys. Rev. C 68, 054312 (2003)
G.F. Bertsch, B. Sabbey, M. Uusnäkki, Phys. Rev. C 71, 054311 (2005)
P. Fleischer P. Klüpfel, T. Cornelius, T.J. Bürvenich, S. Schramm, J.A. Maruhn, P.-G. Reinhard, Eur. Phys. J. A 22, 363 (2004)
R. Balian, E. Brézin, Il Nuovo Cimento, B 64, 37 (1969)
L.M. Robledo, Int. J. Mod. Phys. E 16, 337 (2007)
J. Dobaczewski, M.V. Stoitsov, W. Nazarewicz, P.-G. Reinhard, Phys. Rev. C 76, 054315 (2007)
D. Lacroix, T. Duguet, M. Bender (unpublished)
M. Bender, T. Duguet, D. Lacroix (unpublished)
W. Satuła, R. Wyss, Phys. Rev. Lett. 87, 052504 (2001)
Hsi-Tseng Chen, H. Müther, A. Faessler, Nucl. Phys. A 297, 445 (1978)
S. Marcos, H. Flocard, P.-H. Heenen, Phys. Lett. B 134, 287 (1984)
R.R. Rodriguez-Guzman, K.W. Schmid, Eur. Phys. J. A 19, 45 (2004); Eur. Phys. J. A 19, 61 (2004)
K.W. Schmid, Eur. Phys. J. A 12, 29 (2001)
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Bender, M. Going beyond the self-consistent mean-field with the symmetry-restored generator coordinate method. Eur. Phys. J. Spec. Top. 156, 217–228 (2008). https://doi.org/10.1140/epjst/e2008-00619-9
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DOI: https://doi.org/10.1140/epjst/e2008-00619-9