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Register a new userNonlocal energy density functionals for low-energy nuclear structure
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We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order (N$^3$LO) and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of the nonlocal EDF, for both finite nuclei and infinite nuclear matter, are expressed through the parameters of the pseudopotential. All central, spin-orbit, and tensor terms of the pseudopotential are derived both in the spherical-tensor and Cartesian representation. At next-to-leading order (NLO), we also derive relations between the nonlocal EDF expressed in the spherical-tensor and Cartesian formalism. Finally, a simplified version of the finite-range pseudopotential is considered, which generates the EDF identical to that generated by a local potential.
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Machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density functional for nuclei is established. Self-consistent calculations that bypass the Kohn-Sham equations provide the ground-state densities, total energies, and root-mean-square radii with a high accuracy in comparison with the Kohn-Sham solutions. No existing orbital-free density functional theory comes close to this performance for nuclei. Therefore, it provides a new promising way for future developments of nuclear energy density functionals for the whole nuclear chart.
We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle-hole and particle-particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order (NLO) and next-to-next-to-leading order (N2LO), which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.
We address the question of how to improve the agreement between theoretical nuclear single-particle energies (SPEs) and experiment. Empirically, in doubly magic nuclei, the SPEs can be deduced from spectroscopic properties of odd nuclei that have one more, or one less neutron or proton. Theoretically, bare SPEs, before being confronted with experiment, must be corrected for the effects of the particle-vibration-coupling (PVC). In the present work, we determine the PVC corrections in a fully self-consistent way. Then, we adjust the SPEs, with PVC corrections included, to empirical data. In this way, the agreement with experiment, on average, improves; nevertheless, large discrepancies still remain. We conclude that the main source of disagreement is still in the underlying mean fields, and not in including or neglecting the PVC corrections.
It is known that some well-established parametrizations of the EDF do not always provide converged results for nuclei and a qualitative link between this finding and the appearance of finite-size instabilities of SNM near saturation density when computed within the RPA has been pointed out. We seek for a quantitative and systematic connection between the impossibility to converge self-consistent calculations of nuclei and the occurrence of finite-size instabilities in SNM for the example of scalar-isovector (S=0, T=1) instabilities of the standard Skyrme EDF. We aim to establish a stability criterion based on computationally-friendly RPA calculations of SNM that is independent on the functional form of the EDF and that can be utilized during the adjustment of its coupling constants. Tuning the coupling constant $C^{rho Deltarho}_{1}$ of the gradient term that triggers scalar-isovector instabilities of the standard Skyrme EDF, we find that the occurrence of instabilities in finite nuclei depends strongly on the numerical scheme used to solve the self-consistent mean-field equations. The link to instabilities of SNM is made by extracting the lowest density $rho_{text{crit}}$ at which a pole appears at zero energy in the RPA response function when employing the critical value of the coupling constant $C^{rho Deltarho}_{1}$ extracted in nuclei. Our analysis suggests a two-fold stability criterion to avoid scalar-isovector instabilities: (i) The density $rho_{text{min}}$ corresponding to the lowest pole in the RPA response function should be larger than about 1.2 times the saturation density; (ii) one needs to verify that $rho_{p}(q_{text{pq}})$ exhibits a distinct global minimum and is not a decreasing function for large transferred momenta.
We present the simplest nuclear energy density functional (NEDF) to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizsacker mass formula, while also describing density structures (charge radii, neutron skins etc.) and time-dependent phenomena (induced fission, giant resonances, low energy nuclear collisions, etc.). The 4 significant parameters are necessary to describe bulk nuclear properties (binding energies and charge radii); an additional 2 to 3 parameters have little influence on the bulk nuclear properties, but allow independent control of the density dependence of the symmetry energy and isovector excitations, in particular the Thomas-Reiche-Kuhn sum rule. This Hohenberg-Kohn-style of density functional theory successfully realizes Weizsackers ideas and provides a computationally tractable model for a variety of static nuclear properties and dynamics, from finite nuclei to neutron stars, where it will also provide a new insight into the physics of the r-process, nucleosynthesis, and neutron star crust structure. This new NEDF clearly separates the bulk geometric properties - volume, surface, symmetry, and Coulomb energies which amount to 8MeV per nucleon or up to 2000MeV per nucleus for heavy nuclei - from finer details related to shell effects, pairing, isospin breaking, etc. which contribute at most a few MeV for the entire nucleus. Thus it provides a systematic framework for organizing various contributions to the NEDF. Measured and calculated physical observables - symmetry and saturation properties, the neutron matter equation of state, and the frequency of giant dipole resonances - lead directly to new terms not considered in current NEDF parameterizations.
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