Skyrme Functional Research Articles

Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms. II. Charge exchange

We present the formalism of linear response theory both at zero and finite temperature in the case of asymmetric nuclear matter excited by an isospin flip probe. The particle-hole interaction is derived from a general Skyrme functional that includes spin-orbit and tensor terms. Response functions are obtained by solving a closed algebraic system of equations. Spin strength functions are analyzed for typical values of density, momentum transfer, asymmetry and temperature.

Skyrme Functional with Tensor Terms from ab initio Calculations: Results for the Spin--Orbit Splittings

A new Skyrme functional including tensor terms is presented. The tensor terms have been determined by fitting the results of relativistic Brueckner-Hartree-Fock (RBHF) studies on neutron-proton drops. Unlike all previous studies, where the tensor terms were usually determined by fitting to experimental data of single-particle levels, the pseudodata calculated by RBHF does not contain beyond mean-field effect such as the particle-vibration coupling and, therefore, can provide information on the tensor term without ambiguities. The obtained new functional, named SAMi-T, can describe well ground-state properties such as binding energies, radii, spin-orbit splittings and, at the same time, the excited state properties such as those of the Giant Monopole Resonance (GMR), Giant Dipole Resonance (GDR), Gamow-Teller Resonance (GTR), and Spin-Dipole Resonance (SDR).

Toward a global description of nuclear charge radii: Exploring the Fayans energy density functional

In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain. By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close.

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

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. 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. We perform systematic fully-self consistent Random Phase Approximation (RPA) calculations in spherical doubly-magic nuclei. We employ several Skyrme functionals and vary the isoscalar and isovector coupling constants of the time-odd term $\mathbf{s}\cdot \Delta \mathbf{s}$ . We determine critical values of these coupling constants beyond which the RPA calculations do not converge because RPA the stability matrix becomes non-positive.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. We find a quantitative stability criterion to detect finite-size instabilities related to the spin $\mathbf{s}\cdot \Delta \mathbf{s}$ term of a functional. This criterion could be easily implemented into the standard fitting protocols to fix the coupling constants of the Skyrme functional.

Linear response theory in asymmetric nuclear matter for Skyrme functionals including spin-orbit and tensor terms

The formalism of linear response theory for a Skyrme functional including spin-orbit and tensor terms is generalized to the case of infinite nuclear matter with arbitrary isospin asymmetry. Response functions are obtained by solving an algebraic system of equations, which is explicitly given. Spin-isospin strength functions are analyzed varying the conditions of density, momentum transfer, asymmetry and temperature. The presence of instabilities, including the spinodal one, is studied by means of the static susceptibility.

Hartree-Fock-Bogoliubov nuclear mass model with 0.50 MeV accuracy based on standard forms of Skyrme and pairing functionals

We present a new Hartree-Fock-Bogoliubov nuclear mass model based on standard forms of Skyrme and pairing functionals, which corresponds to the most accurate mass model we ever achieved within the framework of the nuclear energy density functional theory. Our new mass model is characterized by a model standard deviation ${\ensuremath{\sigma}}_{\mathrm{mod}}=0.500$ MeV with respect to essentially all the 2353 available mass data for nuclei with neutron and proton numbers larger than 8. At the same time, the underlying Skyrme functional yields a realistic description of infinite homogeneous nuclear matter properties, as determined by realistic calculations and by experiments; these include in particular the incompressibility coefficient, the pressure in charge-symmetric nuclear matter, the neutron-proton effective mass splitting, the stability against spin and spin-isospin fluctuations, as well as the neutron-matter equation of state.

Fitting Skyrme functionals using linear response theory

It has recently been shown that the linear response theory in symmetric nuclear matter can be used as a tool for detecting finite-size instabilities for different Skyrme functionals. In particular, it has been shown that there is a correlation between the density at which instabilities occur in infinite matter and the instabilities in finite nuclei. In this paper, we present a new fitting protocol that uses this correlation to add a new additional constraint in symmetric infinite nuclear matter in order to ensure the stability of finite nuclei against matter fluctuation in all spin and isospin channels. As an application, we give the parameter set for a new Skyrme functional which includes central and spin–orbit parts and which is free from instabilities by construction.

Testing Skyrme Energy-Density Functionals with the QRPA in Low-lying Vibrational States of Rare-Earth Nuclei

Although nuclear energy density functionals are determined primarily by fitting to ground state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random phase approximation (QRPA). Here we test the Skyrme functionals SkM∗ and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with γ-vibrational states, but our results are not perfect and indicate the presences of multi-particle-hole correlations that are not included in the QRPA. The Skyrme functional SkM∗ performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with “β-vibrational” states than with the γ-vibrational states.

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

Although nuclear energy-density functionals are determined primarily by fitting to ground-state properties, they are often applied in nuclear astrophysics to excited states, usually through the quasiparticle random-phase approximation (QRPA). Here we test the Skyrme functionals SkM${}^{*}$ and SLy4 along with the self-consistent QRPA by calculating properties of low-lying vibrational states in a large number of well-deformed even-even rare-earth nuclei. We reproduce trends in energies and transition probabilities associated with $\ensuremath{\gamma}$-vibrational states, but our results are not perfect and indicate the presence of multiparticle-hole correlations that are not included in the QRPA. The Skyrme functional SkM${}^{*}$ performs noticeably better than SLy4. In a few nuclei, changes in the treatment of the pairing energy functional have a significant effect. The QRPA is less successful with ``$\ensuremath{\beta}$-vibrational'' states than with the $\ensuremath{\gamma}$-vibrational states.