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

Abstract

Background 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.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 doublymagic nuclei. We employ several Skyrme functionals and vary the isoscalar and isovector coupling constants of the time-odd term s · ∆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.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 · ∆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.

Solution of Hartree-Fock-Bogoliubov equations and fitting procedure using the N2LO Skyrme pseudopotential in spherical symmetry

“…We observe no finite-size instabilities, apart from the physical spinodal one [77], around saturation density. This means that our interaction is well stable in all spin-isospin channels [10,11]. This results confirm our preliminary findings in Ref.…”

Impact of the surface energy coefficient on the deformation properties of atomic nuclei as predicted by Skyrme energy density functionals

“…The coupling constants of the other terms in the time-odd part of the EDF can be linked to those of the time-even part (2) by calculating the entire Skyrme EDF as the expectation value of a density-dependent zero-range two-body interaction for a Slater determinant [21,23]. This, however, is not always done, in particular because the term containing the Laplacian of the spin density ∆s t (r) can be the source of a non-physical finite-size instability in the spin channels [21,[24][25][26] when keeping its coupling constant at the Skyrme-force value. Adding the constraint proposed in Ref.…”

Skyrme pseudopotentials at next-to-next-to-leading order Construction of local densities and first symmetry-breaking calculations

“…As representative examples, we will discuss deformation properties of eveneven krypton and neodymium isotopes, the fission barrier of 240 Pu, and the superdeformed rotational band of 194 Hg. The latter also serves as a verification that time-reversal breaking calculations using the SN2LO1 parametrization are stable with respect to unphysical finite-size instabilities that plague many older Skyrme functionals at NLO [11,35].…”

“…For many Skyrme NLO parametrizations, however, making such a choice is impossible in practice, as they exhibit finitesize instabilities with respect to spin polarization which show up in situations when time-reversal symmetry is broken. Examples are calculations with brokenpair blocked quasiparticles [62], self-consistent cranked calculations [11], QRPA calculations [35], or timedependent calculations [63]. When working with NLO parametrizations that exhibit such instability, one and/or the other of the coupling constants of the A (2,1)…”