Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · nucl-th/9808066

B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations

W. Poeschl
View original source ↗Read source document ↗Export metadata ↓

Abstract

A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.

Explore related subjects

nucl-thphysics.comp-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

W. Poeschl. 1998-08-26. B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations. https://doi.org/10.1016/s0010-4655(98)00003-4

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

KEEP EXPLORING

Related papers

arXiv2026

A Halo: The Trigger to a New Era of Nuclear Correlations

In this contribution to the Halo-40 Proceedings, we discuss two topics regarding halo phenomena: The first is the pairing anti-halo effect on the neutron radius of halo nuclei and its restoration due to the coupling to the continuum; the second is the soft dipole excitation of deformed halo nuclei. We demonstrate the importance of Hartree-Fock-Bogoliubov and the relativistic Hartree-Bogoliubov theory in continuum for properly taking into account the halo nature of extended wave functions in calculations of neutron radii, as well as the soft dipole excitations of halo nuclei. It was shown that the anti-halo effect is very sensitive to the continuum coupling induced by Bogoliubov-type quasi-particles, which largely cancels the anti-halo effect on the neutron radius. The soft dipole excitations of deformed halo nuclei Ne-31 and Mg-37 are discussed within the deformed Woods-Saxon model. We point out that the sharp peak just above the threshold in the dipole response is created by the halo effect, and its strength can be used to identify the magnitude of deformation and the halo configuration in the Nilsson level scheme.

nucl-th↗
arXiv2026

Exploring the short-range correlations in $^{16}$O+$^{16}$O collisions at the LHC

Short-range correlations (SRCs) dominate the nuclear force at short distances, including the repulsive core and intermediate-range attraction, and are one of the most fascinating aspects of the nucleon-nucleon (NN) interaction. In this work, we investigate the effects of SRCs on the final-state observables in $^{16}$O+$^{16}$O collisions at $\sqrt{s_{NN}}=5.36$~TeV, using the iEBE-VISHNU hybrid model with {T\raisebox{-0.5ex}{R}ENTo} initial conditions. We embed the nucleon configurations of $^{16}$O generated from variational Monte Carlo (VMC) simulations with realistic SRCs in the initial stage, along with uncorrelated VMC samples and Woods--Saxon distributions implementing a hard repulsive core or short-range attraction as comparison runs. We find that SRCs reduce both $v_2\{2\}$ and $v_2\{4\}$ in the most central collisions, with the decrease of $v_2\{4\}$ being more pronounced due to the event-by-event flow fluctuations. Meanwhile, SRCs noticeably enhance the correlation between the elliptic flow and the mean transverse momentum, $ρ_2(v_2^2,[p_T])$. These effects are mainly attributed to the strong repulsive core of the SRCs, which suppresses the probability of finding nucleon pairs at short relative distances and renders the initial geometry more uniform. This interpretation is supported by the calculations based on Woods--Saxon distributions with a hard repulsive core, which reproduce similar results, while the contribution from a pure intermediate-range attraction is negligible. Our results demonstrate that relativistic nuclear collisions provide a complementary probe of the short-range structure of the nuclear force, beyond the traditional nuclear experiments at low energies.

nucl-th↗
arXiv2026

Shell structure and spontaneous decay of superheavy $Z=124$ isotopes with the deformed relativistic Hartree-Bogoliubov theory in continuum

Shell structure and spontaneous decay of $Z = 124$ isotopes are systematically investigated using the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with the PC-PK1 density functional. By accounting for deformation and continuum effects, the neutron drip line is predicted to be located at $N = 320$, and eight potential multi-neutron emitters beyond the neutron drip line are identified. The results, compared with the spherically constrained case, highlight the critical role of deformation effects in determining the ground-state properties of superheavy nuclei. In addition, potential neutron shell closures emerge at $N = 258$ and $350$, alongside subshell closures at $N = 232$ and $320$. The results disfavor $Z = 124$ as a possible proton magic number and suggest $Z = 120$ and $138$ as more favorable candidates for proton shell closures in the superheavy region. Finally, the competition between $α$ decay, $β$ decay, and spontaneous fission is analyzed by calculating half-lives within various semi-empirical formulas. The results indicate that $α$ decay is the predominant mode on the proton-rich side, whereas spontaneous fission and $β^-$ decay gradually become dominant with increasing neutron number.

nucl-th↗