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Register a new userMirror and triplet displacement energies within nuclear DFT: numerical stability
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Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.
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Background: Small asymmetry between neutrons and protons, caused by the differences in masses and charges of the up and down constituent quarks leads to the isospin symmetry breaking. The isospin non-conservation affects broad range of observables from superallowed Fermi weak interaction to isospin-forbidden electromagnetic rates. Its most profound and cleanest manifestation are systematic shifts in masses and excitation energies of mirror atomic nuclei. Purpose: Recently, we constructed the charge-dependent DFT that includes class II and III local interactions and demonstrated that the model allows for very accurate reproduction of Mirror and Triplet Displacement energies in a very broad range of masses. The aim of this work is to further test the charge-dependent functional by studying Mirror Energy Differences (MEDs) in function of angular momentum $I$. Methods: To compute MEDs we use DFT-rooted no core configuration interaction model. This post mean-field method restores rotational symmetry and takes into account configuration mixing within a space that includes relevant (multi)particle-(multi)hole Slater determinants. Results: We applied the model to $f_{7/2}$-shell mirror pairs of $A=43$, $45$, $47$, and $49$ focusing on MEDs in low-spin part (below band crossing) what allowed us to limit the model space to seniority one and three (one broken pair) configurations. Conclusions: We demonstrate that, for spins $Ileq 15/2$ being subject of the present study, our model reproduces well experimental MEDs which vary strongly in function of $I$ and $A$. The quality of models predictions is comparable to the nuclear shell-model results by Bentley et al. Phys. Rev. C 92, 024310 (2015).
We investigate the properties of 3He, 4He, 6He, 7Li and 16O nuclei in nuclear matter of finite temperature and density. A Dyson expansion of the many-body Green function leads to few-body equations that are solved using the ntegro-Differential Equation Approach (IDEA) and the Antisymmetrized Molecular Dynamics (AMD) methods. The use of the latter method allows us to trace the individual movement of the wave packet for each nucleon and the formation and disintegration of quasi-nuclei in a changing thermodynamical nuclear matter environment.
We developed new parameterizations of local regularized finite-range pseudopotentials up to next-to-next-to-next-to-leading order (N3LO), used as generators of nuclear density functionals. When supplemented with zero-range spin-orbit and density-dependent terms, they provide a correct single-reference description of binding energies and radii of spherical and deformed nuclei. We compared the obtained results to experimental data and discussed benchmarks against the standard well-established Gogny D1S functional.
We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.
We consider a chiral baryon-meson model for nucleons and their parity partners in mirror assignment interacting with pions, sigma and omega mesons to describe the liquid-gas transition of nuclear matter together with chiral symmetry restoration in the high density phase. Within the mean-field approximation the model is known to provide a phenomenologically successful description of the nuclear-matter transition. Here, we go beyond this approximation and include mesonic fluctuations by means of the functional renormalization group. While these fluctuations do not lead to major qualitative changes in the phase diagram of the model, beyond mean-field, one is no-longer free to adjust the parameters so as to reproduce the binding energy per nucleon, the nuclear saturation density, and the nucleon sigma term all at the same time. However, the prediction of a clear first-order chiral transition at low temperatures inside the high baryon-density phase appears to be robust.
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