Showing papers on "Thomas–Fermi model published in 2022"

Coulomb corrections to Fermi beta decay in nuclei

Abstract: We study the influence of the Coulomb force on the Fermi beta-decays in nuclei. This work is composed of two main parts. In the first part, we calculate the Coulomb corrections to super-allowed beta decay. We use the notion of the isovector monopole state and the self-consistent charge-exchange Random Phase Approximation to compute the correction. In the second part of this work, we examine the influence of the anti-analog state on isospin mixing in the isobaric analog state and the correction to the beta-decay Fermi transition.

Subbarrier fusion and elastic scattering cross-sections based on modified Thomas-Fermi method potentials

Abstract: The nucleon density distributions and nucleus-nucleus interaction potentials for the reactions 16O+92Zr and 16O+116Sn were calculated using the modified Thomas-Fermi method, taking into account all terms up to members of the second order by ħ in the quasiclassical decomposition of the kinetic energy. As a nucleon-nucleon interaction, density depended Skyrme forces were used. Based on the obtained potentials, the cross-sections of subbarrier fusion and elastic scattering were calculated. It is shown that the obtained cross-sections of the reactions agree well with the latest experimental data.

Thomas–Fermi profile of a fast rotating Bose–Einstein condensate

Abstract: Abstract. We study the minimizers of a magnetic 2D non-linear Schrödinger energy functional in a quadratic trapping potential, describing a rotating Bose–Einstein condensate. We derive an effective Thomas–Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement, and available states are restricted to the lowest Landau level. The coupling constant of the effective Thomas–Fermi functional is to linked the emergence of vortex lattices (the Abrikosov problem). We define it via a low density expansion of the energy of the corresponding homogeneous gas in the thermodynamic limit.

Born–Oppenheimer Potential Energy Surfaces for Kohn–Sham Models in the Local Density Approximation

Abstract: We show that the Born–Oppenheimer potential energy surface in Kohn–Sham theory behaves like the corresponding one in Thomas–Fermi theory up to $$o(R^{-7})$$ for small nuclear separation R. We also prove that if a minimizing configuration exists, then the minimal distance of nuclei is larger than some constant which is independent of the nuclear charges.

Constructing nonlocal density functionals for kinetic energy

Abstract: A new method is proposed for constructing energy density functionals, which include a nonlocal dependence on the density gradients. This method is used to construct functionals for kinetic energy, which is a nonlocal generalization of the Thomas-Fermi-Kirzhnits functional.

Lieb's most useful contribution to density functional theory?

Abstract: The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which functionals become local, implies that there exist well-defined leading functional corrections to local approximations that become relatively exact for the error in local approximations in this limit. It is argued that this principle might be used to greatly improve the accuracy of the thousand or so DFT calculations that are now published each week. A key question is how to find the leading corrections to any local density approximation as this limit is approached. These corrections have been explicitly derived in ridiculously simple model systems to ridiculously high order, yielding ridiculously accurate energies. Much analytic work is needed to use this principle to improve realistic calculations of molecules and solids.

Lieb’s most useful contribution to density functional theory?

Abstract: The importance of the Lieb–Simon proof of the relative exactness of Thomas–Fermi theory in the large-$Z$ limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which functionals become local, implies that there exist well-defined leading functional corrections to local approximations that become relatively exact for the error in local approximations in this limit. It is argued that this principle might be used to greatly improve the accuracy of the thousand or so DFT calculations that are now published each week. A key question is how to find the leading corrections to any local density approximation as this limit is approached. These corrections have been explicitly derived in ridiculously simple model systems to ridiculously high order, yielding ridiculously accurate energies. Much analytic work is needed to use this principle to improve realistic calculations of molecules and solids.

Van der Waals equation of state for asymmetric nuclear matter

Abstract: The application of van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting from the Thomas--Fermi entropy expression which ensures the fulfilment of Nernst theorem. The derived corrections account for the effective nucleon mass and neutron-proton isotopic asymmetry. The parameters of van der Waals equation of state are deduced taking the experimental value of critical temperature for symmetric nuclear matter and testing the model of van der Waals with statistics corrections included against the theory of Skyrme energy density functional. Critical line in pressure-temperature-composition space is considered. Incompressibility coefficient is determined along the critical line as a function of nuclear matter composition. Jump in the value of specific heat upon crossing critical line is discussed.

Lieb's most useful contribution to density functional theory?

Abstract: The importance of the Lieb-Simon proof of the relative exactness of Thomas-Fermi theory in the large-Z limit to modern density functional theory (DFT) is explored. The principle, that there is a specific semiclassical limit in which functionals become local, implies that there exist well-defined leading functional corrections to local approximations that become relatively exact for the error in local approximations in this limit. It is argued that this principle might be used to greatly improve the accuracy of the thousand or so DFT calculations that are now published each week. A key question is how to find the leading corrections to any local density approximation as this limit is approached. These corrections have been explicitly derived in ridiculously simple model systems to ridiculously high order, yielding ridiculously accurate energies. Much analytic work is needed to use this principle to improve realistic calculations of molecules and solids.

Surface energy coefficient of an N2LO Skyrme energy functional: A semiclassical extended Thomas-Fermi approach

Abstract: We generalize to N2LO Skyrme functionals the semiclassical approach of Grammaticos and Voros in order to calculate the extended Thomas-Fermi expressions of the new densities and currents appearing at the N2LO level. Within a one-dimensional model of semi-infinite symmetric nuclear matter and using a simple Fermi-like density profile, we obtain an easy-to-use formula for the surface-energy coefficient including the contributions of the central, density-dependent, and spin-orbit terms up to ${\ensuremath{\hbar}}^{2}$. Such a formula can be easily used as a first attempt to constrain the surface properties of new N2LO Skyrme parametrizations. The N2LO parametrization tested in this paper is shown to exhibit a shift (compared with a full Hartree-Fock calculation) which is quantitatively similar to the one obtained with the traditional Skyrme parametrizations.

Thomas-Fermi profile of a fast rotating Bose-Einstein condensate

Abstract: We study the minimizers of a magnetic 2D non-linear Schr\"odinger energy functional in a quadratic trapping potential, describing a rotating Bose-Einstein condensate. We derive an effective Thomas-Fermi-like model in the rapidly rotating limit where the centrifugal force compensates the confinement, and available states are restricted to the lowest Landau level. The coupling constant of the effective Thomas-Fermi functional is linked to the emergence of vortex lattices (the Abrikosov problem). We define it via a low density expansion of the energy of the corresponding homogeneous gas in the thermodynamic limit.

Derivation of the dimensional thomas-fermi equation for the thomas-fermi atom model

Abstract: This article presents a method for calculating the energies of the values of the set of electron-neutral atoms. In this case, the interaction of electrons other than the Coulomb bond of the nucleus makes an important contribution to energy. Quantitative calculation of the interaction of these interactions with the introduction of the theory of approximation in the framework of the Thomas-Fermi statistical model by the method of self-correction field is particularly inefficient for complex atoms. However, for complex atoms, the method of approximation is shown, and its essence lies in its simplicity. Among the various methods for systems consisting of the same number of particles, the statistical method derived from the Thomas-Fermi statistical model of the atom plays an important role. This method (E. Fermi, L. Thomas, 1927) is based on the fact that in complex atoms with a large number of electrons, most electrons have relatively large quantum numbers. In this case, a semi-classical approximation is used. As a result, the concept of "cells in phase space" can be used for the state of the individual electrons of the atom. This model has been developed by researchers over a long period of time and has led to a consistent, complete doctrine without the defects of previous models, for example, its field of application is wider than the original Thomas-Fermi.

Van der Waals equation of state for asymmetric nuclear matter

Abstract: The application of the van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting from the Thomas - Fermi entropy expression which ensures the fulfilment of the Nernst theorem. The derived corrections account for the effective nucleon mass and neutron-proton isotopic asymmetry. The parameters of the van der Waals equation of state are deduced by taking the experimental value of critical temperature for symmetric nuclear matter and testing the model of van der Waals with statistics corrections included against the theory of Skyrme energy density functional. A critical line in pressure-temperature-composition space is considered. The incompressibility coefficient is determined along the critical line as a function of nuclear matter composition. A jump in the value of specific heat upon crossing a critical line is discussed.