Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1606.00407

State-of-the-art of beyond mean field theories with nuclear density functionals

J. Luis Egido
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present an overview of beyond mean field theories (BMFT) based on the generator coordinate method (GCM) and the recovery of symmetries used in nuclear physics with effective forces. After a reminder of the Hartree-Fock-Bogoliubov (HFB) theory a discussion of the shortcomings of any mean field approximation (MFA) is presented. The recovery of the symmetries spontaneously broken in the HFB approach, in particular the angular momentum, is necessary, among others, to describe excited states and transitions. Particle number projection is needed to guarantee the right number of protons and neutrons. Furthermore a projection before the variation prevents the pairing collapse in the weak pairing regime. The lack of fluctuations around the average values of the MFA is a shortcoming of this approach. To build in correlations in BMFT one selects the relevant degrees of freedom: quadrupole, octupole and the pairing vibrations as well as the single particle ones. In the GCM the operators representing these degrees of freedom are used as coordinates to generate a collective subspace. The highly correlated GCM wave function is finally written as a linear combination of a projected basis of this space. The variation of the coefficients of the linear combination leads to the Hill-Wheeler equation. We discuss the classical beta and gamma vibrations by considering the quadrupole operators as coordinates. We present pairing fluctuations by considering the pairing gaps as generator coordinates. Lastly the explicit consideration of the time reversal symmetry breaking in the HFB wave function by the cranking procedure allows the alignment of nucleon pairs opening a new dimension in the BMFT calculations. Abundant calculations with the Gogny force illustrate the state-of-the-art of BMFTs with density functionals. We conclude with a thorough discussion on the potential poles of the theory.

Explore related subjects

nucl-thnucl-ex

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. Luis Egido. 2016-06-01. State-of-the-art of beyond mean field theories with nuclear density functionals. https://doi.org/10.1088/0031-8949%2F91%2F7%2F073003

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Three-dimensional orbital-free density functional theory description of nuclear pasta in the inner crust of neutron stars

Background: In the bottom layer of the inner crust of neutron stars, various crystalline structures are expected to emerge that are collectively called ``nuclear pasta.'' It is desirable to know properties of nuclear pasta in a wide variety of conditions for astrophysical applications. However, three-dimensional fully-microscopic calculations require huge computational effort that makes it still challenging to carry out systematic calculations. Purpose: In this paper, we propose an efficient method to calculate various nuclear pasta configurations in a non-empirical manner, based on three-dimensional orbital-free density functional theory (OF-DFT). We demonstrate the feasibility of the proposed approach by applying it to densities across the inner crust of neutron stars. Methods: As a first application of OF-DFT for nuclear pasta, we employ the second-order extended Thomas-Fermi (ETF) expansion of Skyrme energy density functional (EDF) to construct an EDF that depends only on neutron and proton number densities. Based on the variational principle, we derive Euler-Lagrange equations to determine optimal neutron and proton density distributions and solve them self-consistently. In this work, we call this approach the self-consistent ETF (SC-ETF) method. Results: We perform three-dimensional SC-ETF calculations with various box sizes. We successfully obtain various pasta structures, depending on given average nucleon number densities, consistent with earlier studies. Moreover, we find other exotic structures, such as bending and/or connected rods, slabs with a hole, etc., underlining the advantage of the self-consistent formalism. Conclusions: We demonstrate that the SC-ETF method proposed in this study, which can be regarded as a realization of OF-DFT, is a promising tool that can efficiently describe complex pasta structures without empirical assumptions on geometric shapes.

nucl-th↗
arXiv2026

Microscopic analysis of M1 scissors mode in $^{254}$No

The low-energy $M1$ orbital scissors mode (SM) was recently observed by Oslo group in deformed nucleus $^{254}$No. This is the heaviest nucleus where SM was ever experimentally found. We propose the analysis of SM, together with the spin-flip $M1$ resonance, within fully self-consistent Quasiparticle Random-Phase Approximation (QRPA) with Skyrme forces SG2, SLy4 and SLy5. The impact of "tensor" $J^2$-term, introduced by perturbative (on the base of SG2) and consistent (SLy5) ways, is analyzed and shown to be noticeable but not decisive. The deformation-induced coupling of $M1$ and $E2$ states is inspected. The calculations reasonably describe Oslo's experimental data. The best agreement is obtained for SLy5. A fine structure of SM in $^{254}$No is predicted. A significant constructive interference of the dominant orbital and minor spin-flip contributions to $M1$ strength at SM energy region is found. What is remarkable, our analysis of distributions of the convective nuclear currents challenges the scissors-like flow usually assumed for SM.

nucl-th↗
arXiv2026

Systematic Study of Proton, Two-Proton, Alpha, and Cluster Radioactivity Half-Lives based on the Deformed Gamow-like Model and Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$)

A hybrid framework combining the deformed Gamow-like model ($\mathrm{DGLM}$) with the Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$) is developed to improve half-life predictions for two-proton emission, proton emission, $α$ decay, and cluster radioactivity. A total of 583 radioactive nuclei are investigated, including 17 two-proton emitters, 42 proton emitters, 498 $α$ emitters, and 26 cluster emitters. Among the four considered models, $\mathrm{DGLM}^{b}+\mathrm{TabPFN}$ achieves the best overall performance, with $σ_{\mathrm{RMS}}=0.423$, corresponding to an improvement of approximately $82.2\%$ over $\mathrm{DGLM}^{b}$. The model parameters are optimized for each decay mode using the least-squares method. After introducing $\mathrm{TabPFN}$, the prediction errors for proton emission and $α$ decay are reduced by approximately $80.6\%$ and $87.6\%$, respectively. For $α$ decay, the training, test, and overall RMSEs are 0.208, 0.305, and 0.240, indicating good generalization capability without evident overfitting. The model also reproduces the systematic evolution of $α$-decay half-lives and the shell-closure effect around $N=126$. These results demonstrate that combining $\mathrm{DGLM}$ with $\mathrm{TabPFN}$ significantly improves the accuracy and robustness of radioactive-decay half-life predictions while retaining the physical interpretability of the original model.

nucl-th↗