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Spurious finite-size instabilities in nuclear energy density functionals: spin channel

Abstract : It has been recently shown, that some Skyrme functionals can lead to non-converging 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. 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. 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 $\mathbf{s}\cdot \Delta \mathbf{s}$ . We determine critical values of these coupling constants beyond which the RPA calculations do not converge because RPA the stability matrix becomes non-positive.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. We find a quantitative stability criterion to detect finite-size instabilities related to the spin $\mathbf{s}\cdot \Delta \mathbf{s}$ term of a functional. This criterion could be easily implemented into the standard fitting protocols to fix the coupling constants of the Skyrme functional.
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Contributor : Sylvie Flores <>
Submitted on : Wednesday, May 20, 2015 - 7:29:47 AM
Last modification on : Tuesday, November 19, 2019 - 2:46:51 AM

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A. Pastore, D. Tarpanov, D. Davesne, J. Navarro. Spurious finite-size instabilities in nuclear energy density functionals: spin channel. Physical Review C, American Physical Society, 2015, 92, pp.024305. ⟨10.1103/PhysRevC.92.024305⟩. ⟨in2p3-01153566⟩



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