## 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·Δs. 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·Δs term of a functional. This criterion could be easily implemented in the standard fitting protocols to fix the coupling constants of the Skyrme functional.

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·Δs. 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·Δs term of a functional. This criterion could be easily implemented in the standard fitting protocols to fix the coupling constants of the Skyrme functional.

Original language | English |
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Pages (from-to) | 1-9 |

Number of pages | 9 |

Journal | Physical Review C (Nuclear Physics) |

Volume | 92 |

DOIs | |

Publication status | Published - 3 Aug 2015 |