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Pastore, A., Tarpanov, D., Davesne, D., & Navarro, J. (2015). Spurious finite-size instabilities in nuclear energy density functionals: Spin channel. Phys. Rev. C, 92(2), 024305–9pp.
Abstract: Background: It has been recently shown that some Skyrme functionals can lead to nonconverging results in the calculation of some properties of atomic nuclei. A previous study has pointed out a possible link between these convergence problems and the appearance of finite-size instabilities in symmetric nuclear matter (SNM) around saturation density. Purpose: We show that the finite-size instabilities not only affect the ground-state properties of atomic nuclei, but they can also influence the calculations of vibrational excited states in finite nuclei. Method: We perform systematic fully-self consistent random phase approximation (RPA) calculations in spherical doubly magic nuclei. We employ several Skyrme functionals and vary the isoscalar and isovector coupling constants of the time-odd term s . Delta s. We determine critical values of these coupling constants beyond which the RPA calculations do not converge because the RPA stability matrix becomes nonpositive. Results: By comparing the RPA calculations of atomic nuclei with those performed for SNM we establish a correspondence between the critical densities in the infinite system and the critical coupling constants for which the RPA calculations do not converge. Conclusions: We find a quantitative stability criterion to detect finite-size instabilities related to the spin s . Delta s term of a functional. This criterion could be easily implemented in the standard fitting protocols to fix the coupling constants of the Skyrme functional.
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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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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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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. (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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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. (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. (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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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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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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