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., Davesne, D., & Navarro, J. (2014). Nuclear matter response function with a central plus tensor Landau interaction. J. Phys. G, 41(5), 055103–17pp.
Abstract: We present a method to obtain response functions in the random phase approximation (RPA) based on a residual interaction described in terms of Landau parameters with central plus tensor contributions. The response functions keep the explicit momentum dependence of the RPA, in contrast with the traditional Landau approximation. Results for symmetric nuclear matter and pure neutron matter are presented using Landau parameters derived from finite-range interactions, both phenomenological and microscopic. We study the convergence of response functions as the number of Landau parameters is increased.
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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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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. (2016). Extended Skyrme equation of state in asymmetric nuclear matter. Astron. Astrophys., 585, A83–11pp.
Abstract: We present a new equation of state for infinite systems (symmetric, asymmetric, and neutron matter) based on an extended Skyrme functional that has been constrained by microscopic Brueckner-Bethe-Goldstone results. The resulting equation of state reproduces the main features of microscopic calculations very accurately and is compatible with recent measurements of two times Solar-mass neutron stars. We provide all necessary analytical expressions to facilitate a quick numerical implementation of quantities of astrophysical interest.
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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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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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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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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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Davesne, D., Pastore, A., & Navarro, J. (2019). Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms. II. Charge exchange. Phys. Rev. C, 100(6), 064301–10pp.
Abstract: We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry, and temperature. We evaluate the role of statistical errors related to the uncertainties of the coupling constants of the Skyrme functional and thus determine the confidence interval of the resulting response function.
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