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Davesne, D., Pastore, A., & Navarro, J. (2021). Linear response theory with finite-range interactions. Prog. Part. Nucl. Phys., 120, 103870–55pp.
Abstract: This review focuses on the calculation of infinite nuclear matter response functions using phenomenological finite-range interactions, equipped or not with tensor terms. These include Gogny and Nakada families, which are commonly used in the literature. Because of the finite-range, the main technical difficulty stems from the exchange terms of the particle-hole interaction. We first present results based on the so-called Landau and Landau-like approximations of the particle-hole interaction. Then, we review two methods which in principle provide numerically exact response functions. The first one is based on a multipolar expansion of both the particle-hole interaction and the particle-hole propagator and the second one consists in a continued fraction expansion of the response function. The numerical precision can be pushed to any degree of accuracy, but it is actually shown that two or three terms suffice to get converged results. Finally, we apply the formalism to the determination of possible finite-size instabilities induced by a finite-range interaction.
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Becker, P., Davesne, D., Meyer, J., Pastore, A., & Navarro, J. (2015). Tools for incorporating a D-wave contribution in Skyrme energy density functionals. J. Phys. G, 42(3), 034001–19pp.
Abstract: The possibility of adding a D-wave term to the standard Skyrme effective interaction has been widely considered in the past. Such a term has been shown to appear in the next-to-next-to-leading order of the Skyrme pseudo-potential. The aim of the present article is to provide the necessary tools to incorporate this term in a fitting procedure: first, a mean-field equation written in spherical symmetry in order to describe spherical nuclei and second, the response function to detect unphysical instabilities. With these tools it will be possible to build a new fitting procedure to determine the coupling constants of the new functional.
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Davesne, D., Pastore, A., & Navarro, J. (2014). Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms. Phys. Rev. C, 89(4), 044302–14pp.
Abstract: The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry, and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.
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Davesne, D., Pastore, A., & Navarro, J. (2013). Skyrme effective pseudopotential up to the next-to-next-to-leading order. J. Phys. G, 40(9), 095104–8pp.
Abstract: The explicit form of the next-to-next-to-leading order ((NLO)-L-2) of the Skyrme effective pseudopotential compatible with all required symmetries and especially with gauge invariance is presented in a Cartesian basis. It is shown in particular that for such a pseudopotential there is no spin-orbit contribution and that the D-wave term suggested in the original Skyrme formulation does not satisfy the invariance properties. The six new (NLO)-L-2 terms contribute to both the equation of state and the Landau parameters. These contributions to symmetric nuclear matter are given explicitly and discussed.
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Pastore, A., Martini, M., Davesne, D., Navarro, J., Goriely, S., & Chamel, N. (2014). Linear response theory and neutrino mean free path using Brussels-Montreal Skyrme functionals. Phys. Rev. C, 90(2), 025804–11pp.
Abstract: The Brussels-Montreal Skyrme functionals have been successful in describing properties of both finite nuclei and infinite homogeneous nuclear matter. In their latest version, these functionals have been equipped with two extra density-dependent terms in order to reproduce simultaneously ground state properties of nuclei and infinite nuclear matter properties while avoiding at the same time the arising of ferromagnetic instabilities. In the present article, we extend our previous results of the linear response theory to include such extra terms at both zero and finite temperature in pure neutron matter. The resulting formalism is then applied to derive the neutrino mean free path. The predictions from the Brussels-Montreal Skyrme functionals are compared with ab initio methods.
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Davesne, D., Navarro, J., Meyer, J., Bennaceur, K., & Pastore, A. (2018). Two-body contributions to the effective mass in nuclear effective interactions. Phys. Rev. C, 97(4), 044304–7pp.
Abstract: Starting from general expressions of well-chosen symmetric nuclear matter quantities derived for both zero-and finite-range effective theories, we derive some universal relations between them. We first showthat, independently of the range, the two-body contribution is enough to describe correctly the saturation mechanism but gives an effective mass value around m(*)/m similar or equal to 0.4 when the other properties of the saturation point are set near their generally accepted values. Then, we show that a more elaborated interaction (for instance, an effective two-body density-dependent term on top of the pure two-body term) is needed to reach the accepted value m(*)/m similar or equal to 0.7-0.8.
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Pastore, A., Davesne, D., & Navarro, J. (2015). Linear response of homogeneous nuclear matter with energy density functionals. Phys. Rep., 563, 1–67.
Abstract: Response functions of infinite nuclear matter with arbitrary isospin asymmetry are studied in the framework of the random phase approximation. The residual interaction is derived from a general nuclear Skyrme energy density functional. Besides the usual central, spin-orbit and tensor terms it could also include other components as new density-dependent terms or three-body terms. Algebraic expressions for the response functions are obtained from the Bethe-Salpeter equation for the particle-hole propagator. Applications to symmetric nuclear matter, pure neutron matter and asymmetric nuclear matter are presented and discussed. Spin-isospin strength functions are analyzed for varying conditions of density, momentum transfer, isospin asymmetry, and temperature for some representative Skyrme functionals. Particular attention is paid to the discussion of instabilities, either real or unphysical, which could manifest in finite nuclei.
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Davesne, D., Pastore, A., & Navarro, J. (2014). Fitting (NLO)-L-3 pseudo-potentials through central plus tensor Landau parameters. J. Phys. G, 41(6), 065104–12pp.
Abstract: Landau parameters determined from phenomenological finite-range interactions are used to get an estimation of next-to-next-to-next-to-leading order ((NLO)-L-3) pseudo-potentials parameters. The parameter sets obtained in this way are shown to lead to consistent results concerning saturation properties. The uniqueness of this procedure is discussed, and an estimate of the error induced by the truncation at (NLO)-L-3 is given.
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Davesne, D., Pastore, A., & Navarro, J. (2023). Hartree-Fock Calculations in Semi-Infinite Matter with Gogny Interactions. Universe, 9(9), 398–11pp.
Abstract: Hartree-Fock equations in semi-infinite nuclear matter for finite range Gogny interactions are presented together with a detailed numerical scheme to solve them. The value of the surface energy is then extracted and given for standard Gogny interactions.
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Davesne, D., Meyer, J., Pastore, A., & Navarro, J. (2015). Partial wave decomposition of the N3LO equation of state. Phys. Scr., 90(11), 114002–6pp.
Abstract: By means of a partial wave decomposition, we separate their contributions to the equation of state (EoS) of symmetric nuclear matter for the N3LO pseudo-potential. In particular, we show that although both the tensor and the spin-orbit terms do not contribute to the EoS, they give a non-vanishing contribution to the separate (JLS) channels.
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