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]).
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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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