Abstract
We review the general theory of the Hartree-Fock-Bogoliubov method in the context of the nuclear many-body problem. We examine the response of the Hartree-Fock-Bogoliubov solutions to a one-body external field and derive the formalism needed to impose multiple constraints on the calculations. Finally, a pedagogical example is given to illustrate the Hartree-Fock-Bogoliubov method using a schematic model of the nucleus.
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Notes
- 1.
In an alternate formulation, Eq. (1.6) can be symmetrized so that it depends explicitly on both ρ and ρ ∗, as in [5]. In that case, the density and its complex conjugate are treated as independent variables when minimizing the energy, and Eq. (1.10) must be modified by a factor of 2 on the right-hand side, as in Eq. (2) of [5].
- 2.
Note that the expression for δ 2E does not explicitly account for any dependence of the potential on the density for the sake of simplicity, but the extension is relatively straightforward (see, e.g., [6]).
References
Ring, P., Schuck, P.: The Nuclear Many-Body Problem. Springer, Heidelberg (1980)
Berger, J.-F.: Approches de champ moyen et au-delà. Ecole Joliot-Curie, Maubuisson, 10ème session (1991)
Greiner, W., Maruhn, J., Bromley, D.A.: Nuclear Models. Springer, Heidelberg (1997)
Blaizot, J.-P., Ripka, G.: Quantum Theory of Finite Systems. MIT Press, Cambridge (1986)
Dechargé, J., Gogny, D.: Phys. Rev. C 21, 1568 (1980)
Péru, S., Martini, M.: Eur. Phys. J. A 50, 88 (2014)
Mizobuchi, Y.: Prog. Theor. Phys. 65, 1450 (1981)
Matsuyanagi, K.: Prog. Theor. Phys. 67, 1441 (1982)
Suzuki, T., Mizobuchi, Y.: Prog. Theor. Phys. 79, 480 (1988)
Fukui, T., Matsuo, M., Matsuyanagi, K.: Prog. Theor. Phys. 85, 281 (1991)
Nakatsukasa, T., Walet, N.R.: Phys. Rev. C 58, 3397 (1998)
Kobayasi, M., Nakatsukasa, T., Matsuo, M., Matsuyanagi, K.: Prog. Theor. Phys. 110, 65 (2003)
Akaike, H., Tsue, Y., Nishiyama, S.: Prog. Theor. Phys. 112, 583 (2004)
Hinohara, N., Nakatsuakasa, T., Matsuo, M., Matsuyanagi, K.: Prog. Theor. Phys. 115, 567 (2006)
Baranger, M., Kumar, K.: Nucl. Phys. 62, 113 (1965)
Nikšić, T., Kralj, N., Tutiš, T., Vretenar, D., Ring, P.: Phys. Rev. C 88, 044327 (2013)
Younes, W., Gogny, D.: Phys. Rev. C 80, 054313 (2009)
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This chapter was prepared by a contractor of the U.S. Government under contract number DE-AC52-06NA27344. Accordingly, the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for U.S. Government purposes.
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Younes, W., Gogny, D.M., Berger, JF. (2019). Hartree-Fock-Bogoliubov Theory. In: A Microscopic Theory of Fission Dynamics Based on the Generator Coordinate Method. Lecture Notes in Physics, vol 950. Springer, Cham. https://doi.org/10.1007/978-3-030-04424-4_1
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DOI: https://doi.org/10.1007/978-3-030-04424-4_1
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