Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach
Reinhard PG, Nazarewicz W (2016)
Publication Type: Journal article
Publication year: 2016
Journal
Book Volume: 93
Article Number: 051303
Journal Issue: 5
DOI: 10.1103/PhysRevC.93.051303
Abstract
Background: Radii of charge and neutron distributions are fundamental nuclear properties. They depend on both nuclear interaction parameters related to the equation of state of infinite nuclear matter and on quantal shell effects, which are strongly impacted by the presence of nuclear surface. Purpose: In this work, by studying the correlation of charge and neutron radii, and neutron skin, with nuclear matter parameters, we assess different mechanisms that drive nuclear sizes. Method: We apply nuclear density functional theory using a family of Skyrme functionals obtained by means of optimization protocols, which do not include any radius information. By performing the Monte Carlo sampling of reasonable functionals around the optimal parametrization, we scan all correlations between nuclear matter properties and observables characterizing charge and neutron distributions of spherical closed-shell nuclei Ca48,Pb208, and Fl298. Results: By considering the influence of various nuclear matter properties on charge and neutron radii in a multidimensional parameter space of Skyrme functionals, we demonstrate the existence of two strong relationships: (i) between the nuclear charge radii and the saturation density of symmetric nuclear matter ρ0, and (ii) between the neutron skins and the slope of the symmetry energy L. The impact of other nuclear matter properties on nuclear radii is weak or nonexistent. For functionals optimized to experimental binding energies only, proton and neutron radii are found to be weakly correlated due to canceling trends from different nuclear matter characteristics. Conclusion: The existence of only two strong relations connecting nuclear radii with nuclear matter properties has important consequences. First, by requiring that the nuclear functional reproduces the empirical saturation point of symmetric nuclear matter practically fixes the charge (or proton) radii, and vice versa. This explains the recent results of ab initio calculations with two-nucleon and three-nucleon forces optimized simultaneously to binding energies and radii of selected nuclei. Second, since the neutron skin uncertainty primarily depends on the slope of the symmetry energy, imposing constraints on both ρ0 and L practically determines the nuclear size, modulo small variations due to shell effects.
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APA:
Reinhard, P.-G., & Nazarewicz, W. (2016). Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach. Physical Review C - Nuclear Physics, 93(5). https://doi.org/10.1103/PhysRevC.93.051303
MLA:
Reinhard, Paul-Gerhard, and W. Nazarewicz. "Nuclear charge and neutron radii and nuclear matter: Trend analysis in Skyrme density-functional-theory approach." Physical Review C - Nuclear Physics 93.5 (2016).
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