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Batail, L., Davesne, D., Peru, S., Becker, P., Pastore, A., & Navarro, J. (2023). A three-ranged Gogny interaction in touch with pion exchange: promising results to improve infinite matter properties. Eur. Phys. J. A, 59(7), 173–11pp.
Abstract: We suggest a new Gogny-type finite-range effective interaction including a third Gaussian in the central term. Based on simple arguments valid for an arbitrary radial form factor, the three ranges are obtained in connection with physical grounds, relating them to one-boson exchange interactions. Moreover, some parameters of the longest range are fixed through the G-matrix elements of the One Pion Exchange Potential. On top of giving a fairly good description of atomic nuclei properties comparable with other existing parametrisations, the resulting interaction leads to a remarkable improvement of some infinite matter properties that are relevant for astrophysical calculations.
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Becker, P., Davesne, D., Meyer, J., Navarro, J., & Pastore, A. (2017). Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry. Phys. Rev. C, 96(4), 044330–17pp.
Abstract: We present the development of the extended Skyrme N2LO pseudopotential in the case of spherical even-even nuclei calculations. The energy density functional is first presented. Then we derive the mean-field equations and discuss the numerical method used to solve the resulting fourth-order differential equation together with the behavior of the solutions at the origin. Finally, a fitting procedure for such an N2LO interaction is discussed and we provide a first parametrization. Typical ground-state observables are calculated and compared against experimental data.
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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., Becker, P., Pastore, A., & Navarro, J. (2016). Infinite matter properties and zero-range limit of non-relativistic finite-range interactions. Ann. Phys., 375, 288–312.
Abstract: We discuss some infinite matter properties of two finite-range interactions widely used for nuclear structure calculations, namely Gogny and M3Y interactions. We show that some useful informations can be deduced for the central, tensor and spin orbit terms from the spin-isospin channels and the partial wave decomposition of the symmetric nuclear matter equation of state. We show in particular that the central part of the Gogny interaction should benefit from the introduction of a third Gaussian and the tensor parameters of both interactions can be deduced from special combinations of partial waves. We also discuss the fact that the spin orbit of the M3Y interaction is not compatible with local gauge invariance. Finally, we show that the zero-range limit of both families of interactions coincides with the specific form of the zero-range Skyrme interaction extended to higher momentum orders and we emphasize from this analogy its benefits.
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Davesne, D., Becker, P., Pastore, A., & Navarro, J. (2016). Partial-wave decomposition of the finite-range effective tensor interaction. Phys. Rev. C, 93(6), 064001–6pp.
Abstract: We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial-wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the next-to-next-to-next-leading-order (N3LO) Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions.
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