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Register a new userSpurious finite-size instabilities in nuclear energy density functionals
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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.
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Recently, a new parameterization of the Gogny interaction suitable for astrophysical applications, named D1M*, has been presented. We investigate the possible existence of spurious finite-size instabilities of this new Gogny force by repeating a study that we have already performed for the most commonly used parameterizations (D1, D1S, D1N, D1M) of the Gogny force. This study is based on a fully-antisymmetrized random phase approximation (RPA) calculation of the nuclear matter response functions employing the continued fraction technique. It turns out that this new Gogny interaction is affected by spurious finite-size instabilities in the scalar isovector channel; hence, unphysical results are expected in the calculation of properties of nuclei, like neutron and proton densities, if this D1M* force is used. The conclusions from this study are then, for the first time, tested against mean-field calculations in a coordinate representation for several nuclei. Unphysical results for several nuclei are also obtained with the D1N parameterization of the Gogny force. These observations strongly advocate for the use of the linear response formalism to detect and avoid finite-size instabilities during the fit of the parameters of Gogny interactions as it is already done for some Skyrme forces.
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 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.
We discuss the construction of a nuclear Energy Density Functional (EDF) from ab initio calculations, and we advocate the need of a methodical approach that is free from ad hoc assumptions. The equations of state (EoS) of symmetric nuclear and pure neutron matter are computed using the chiral NNLO$_{rm sat}$ and the phenomenological AV4$^prime$+UIX$_{c}$ Hamiltonians as inputs in the Self-consistent Greens Function (SCGF) and Auxiliary Field Diffusion Monte Carlo (AFDMC) methods, respectively. We propose a convenient parametrization of the EoS as a function of the Fermi momentum and fit it on the SCGF and AFDMC calculations. We apply the ab initio-based EDF to carry out an analysis of the binding energies and charge radii of different nuclei in the local density approximation. The NNLO$_{rm sat}$-based EDF produces encouraging results, whereas the AV4$^prime$+UIX$_{c}$-based one is farther from experiment. Possible explanations of these different behaviors are suggested, and the importance of gradient and spin-orbit terms is analyzed. Our work paves the way for a practical and systematic way to merge ab initio nuclear theory and DFT, while at the same time it sheds light on some of the critical aspects of this procedure.
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.
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