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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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