Variations on a theme by Skyrme: A systematic study of adjustments of model parameters

Abstract

We present a survey of the phenomenological adjustment of the parameters of the Skyrme-Hartree-Fock (SHF) model for a self-consistent description of nuclear structure and low-energy excitations. A large sample of reliable input data from nuclear bulk properties (energy, radii, surface thickness) is selected guided by the criterion that ground-state correlations should remain small. Least-squares fitting techniques are used to determine the SHF parameters that accommodate best the given input data. The question of the predictive value of the adjustment is scrutinized by performing systematic variations with respect to chosen nuclear matter properties (incompressibility, effective mass, symmetry energy, and sum-rule enhancement factor). We find that the ground-state data, although representing a large sample, leave a broad range of choices, i.e., a broad range of nuclear matter properties. Information from giant resonances is added to pin down more precisely the open features. We then apply the set of newly adjusted parametrizations to several more detailed observables such as neutron skin, isotope shifts, and super-heavy elements. The techniques of least-squares fitting provide safe estimates for the uncertainties of such extrapolations. The systematic variation of forces allows to disentangle the various influences on a given observable and to estimate the predictive value of the SHF model. The results depend very much on the observable under consideration.

Fission barriers and probabilities of spontaneous fission for elements with Z≥ 100

“…Strategies for such adjustment have much developed over the decades. Present standard are least-squares (χ 2 ) fits started in [108] and steadily extended to include more and more data, for recent examples see, e.g., [100,109]. The least-squares (χ 2 ) fits and subsequent analysis of extrapolation errors as well as correlations are a standard technique and well documented at several places [92,110,111].…”

“…For the fit observables entering the χ 2 , we consider here the same set as it was used in the survey [100]: binding energies, key parameters of the charge form factor (r.m.s. radius, diffraction radius, surface thickness), odd-even staggering of binding energies, spin-orbit splittings in semi-magic nuclei selected to be well described by a pure mean-field model.…”

“…Thus we will also consider parametrisations which are fitted as SV-min, but with an additional constraint on NMP. There is, for example, the parametrisation SV-bas which was fitted while freezing K, m * /m, a sym , and κ TRK at values such that one obtains additionally also a good description of giant resonance excitations [100]. The difference between SV-bas and SV-min is one indicator for the influence the these four NMP.…”

“…We will consider here the four NMP which characterise the response properties of nuclear matter: incompressibility K, isoscalar effective mass m * /m, symmetry energy a sym , and TRK sum-rule enhancement κ TRK (for a detailed definition see e.g., [100]). These NMP have been used since long as benchmarks in various nuclear models and thus they have developed an intuitive meaning.…”

“…The trends seen in such variations are the robust against the detailed choice of reference energy and integration limits. The basic citations for the models and parametrisation are: Gogny [94],SkM * [49], SkP [95], SkT6 [96], SLy6 [97], SkI3 [98], BSk1 [99], SV-min [100], UNEDF2 [101], NL-Z2 [102], DD-PC and DD-ME [103].…”