Gamow-Teller strength and the spin-isospin coupling constants of the Skyrme energy functional

Abstract

We investigate the effects of the spin-isospin channel of the Skyrme energy functional on predictions for Gamow-Teller distributions and superdeformed rotational bands. We use the generalized Skyrme interaction SkO' to describe even-even ground states and then analyze the effects of time-odd spinisospin couplings, first term by term and then together via linear regression. Some terms affect the strength and energy of the Gamow-Teller resonance in finite nuclei without altering the Landau parameter g ′ 0 that to leading order determines spin-isospin properties of nuclear matter. Though the existing data are not sufficient to uniquely determine all the spin-isospin couplings, we are able to fit them locally. Altering these coupling constants does not change the quality with which the Skyrme functional describes rotational bands.

Tensor part of the Skyrme energy density functional. III. Time-odd terms at high spin

“…This confirms and extends a conclusion of Bender et al [40]. These authors have shown in a similar manner and for another Skyrme parametrization SkO' that the dynamical moment of inertia J (2) of the SD band of 152 Dy depends mainly on the spin-isospin Landau parameter g ′ 0 and not so much on the actual values of the individual coupling constants C s 1 and C T 1 .…”

“…This choice is not unique. Other groups use SLy4 in their cranked HFB or QRPA calculations by setting just C T t = 0, keeping C s t and C ∆s t at their Skyrme-force values [21,28,40].…”

“…[31,89] and in Ref. [40] the effect of the spin-isopin coupling constants of the Skyrme EDFs on predictions for Gamow-Teller distributions is investigated. In the latter study, a local fit of the C s…”

Isospin-breaking corrections to superallowed Fermiβdecay in isospin- and angular-momentum-projected nuclear density functional theory

“…Nilsson levels in the vicinity of the Fermi surface for nearly spherical nuclei, there appears another type of ambiguity in choosing the Slater determinants representing the anti-aligned configurations. Within the set of nuclei studied in this work, this ambiguity manifests itself particularly strongly in 42 Sc, where we deal with four possible anti-aligned MF configurations built on the Nilsson orbits originating from 0.5 the spherical νf 7/2 and πf 7/2 sub-shells. These configurations can be labeled in terms of the quantum number K as |νK ⊗ πK with K = 1/2, 3/2, 5/2, and 7/2.…”

“…This is an intriguing result, which indicates that an increase of the bulk symmetry energy -that tends to restore the isospin symmetry -is partly compensated by other effects. The most likely origin of this compensation mechanism is due to the time-odd spin-isospin mean fields, which are poorly constrained by the standard fitting protocols of Skyrme EDFs [41][42][43]. For instance, if one compares the Landau-Migdal parameters characterizing the spin-isospin time-odd channels [41][42][43] To illustrate the compensation mechanism related to the bulk symmetry energy and g 0 , in Fig.…”