Correlations among symmetry energy elements in Skyrme models

Abstract

Motivated by the interrelationships found between the various symmetry energy elements of the energy density functionals (EDF) based on the Skyrme forces, possible correlations among them are explored. A total of 237 Skyrme EDFs are used for this purpose. As some of these EDFs yield values of a few nuclear observables far off from the present acceptable range, studies are done also with a subset of 162 EDFs that comply with a conservative set of constraints on the values of nuclear matter incompressibility coefficient, effective mass of the nucleon and the isovector splitting of effective nucleon masses to see the enhancement of the correlation strength, if any. The curvature parameter K 0 sym and the skewness parameter Q 0 sym of the symmetry energy are found to be very well correlated with the linear combination of the symmetry energy coefficient and its density derivative L0. The isovector splitting of the effective nucleon mass, however, displays a somewhat meaningful correlation with a linear combination of the symmetry energy, its slope and its curvature parameter.

Constraining nuclear matter parameters from correlation systematics: a mean-field perspective

“…Eq. ( 30) looks very similar to that obtained for the correlations among C 0 2 , L 0 and K 0 sym in Skyrme models [87]. This is not coincidental.…”

“…Mondal et al [87], with a total of 237 Skyrme EDFs also find a correlation between them, but the correlation is not very strong (correlation coefficient r ∼ 0.8); the correlation becomes more robust only when a selected subset of 162 EDFs are chosen (r ∼ 0.91). These 162 Skyrme EDFs are selected by constraining the iso-scalar nucleon effective mass | to less than unity, which more than covers the values from the limited experimental data [88,89,90] and recent theoretical values on it.…”

The Nuclear Matter Density Functional under the Nucleonic Hypothesis

“…Stronger correlations are found among the isovector parameters, which are corr(E sym , L sym ) = 0.67 and corr(L sym , K sym ) = 0.67. The former is found in several works (see References [23,26,65] and references therein for a review), and the latter is also studied in References [66][67][68][69][70][71][72]. Slight correlations between high-order parameters, K sat − Q sat and K sym − Q sym , are also induced due to the narrow EFT energy bands at very low densities.…”

Analysis of the neutron matter equation of state and the symmetry energy up to fourth order of chiral effective field theory

“…Additional studies that have explored these correlations, using a variety of phenomenological and theoretical models, are provided in Refs. [50][51][52][53][54][55]. Constrains on L vary considerably depending on the methods employed [38,56,57].…”