Existence and uniqueness of positive solutions of semilinear elliptic equations with Coulomb potentials on ℝ3

We study the positive solutions of a semilinear equation with a Coulomb potential on ?³. We give a new uniqueness theorem for the positive radial solutions of such an equation and we apply these results to the Thomas-Fermi-Dirac-von Weizsäcker equation without electrostatic repulsion.     

Effective Schrödinger equation for nuclear fluid dynamics

The equations of motion for a nuclear fluid are transformed into an effective single-particle Schrödinger equation with self-interactions. This transformation is particularly useful for numerical applications, because the Weizsäcker corrections, which cause numerical instabilities in computationswithin the fluid-dynamical picture, are absorbed in the kinetic energy term of the effective Schrödinger equation. In applications to the motion and collision of nuclear slabs the numerical treatment of the nuclear fluid by the effective Schrödinger equation is proven to be stable and accurate.     

Charge oscillations and photoabsorption of the Thomas-Fermi-Dirac-Weizsäcker atom

Following the work of Bloch and Ball et al. the theory of linear response of a hydrodynamic Thomas-Fermi model is extended to a general density dependent energy functional. The theory is applied to the Thomas-Fermi-Dirac-Weizsäcker atom. Normal mode solutions and the atomic photoabsorption cross section are calculated.     

Nonexistence in Thomas-Fermi-Dirac-von Weizsäcker Theory with Small Nuclear Charges

We study the ionization problem in the Thomas-Fermi-Dirac-von Weizsäcker theory for atoms and molecules. We prove the nonexistence of minimizers for the energy functional when the number of electrons is large and the total nuclear charge is small. This nonexistence result also applies to external potentials decaying faster than the Coulomb potential. In the case of arbitrary nuclear charges, we obtain the nonexistence of stable minimizers and radial minimizers.     

Kinetic energy functionals for molecular calculations

The orbitals and eigenvalues of a Kohn-Sham density functional theory calculation can be used to determine the kinetic potential, the functional derivative of the non-interacting kinetic energy. Thus, approproximate kinetic energy functionals can be systematically parameterized to improve their functional derivatives. Fitting procedures have been applied to various functional forms and the quality of the resulting functionals investigated using variationally optimized densities. The best functionals include the full correction of Weizsäcker and a modulation of the Thomas-Fermi p^5/3 term by a function of the distance from the nucleus. These atom-specific functionals predict virtually exact shell structure, and may be combined readily into a functional which supports molecular binding.     

The Thomas-Fermi-von Weizsäcker theory of atoms and molecules

We place the Thomas-Fermi-von Weizsäcker model of atoms on a firm mathematical footing. We prove existence and uniqueness of solutions of the Thomas-Fermi-von Weizsäcker equation as well as the fact that they minimize the Thomas-Fermi-von Weizsäcker energy functional. Moreover, we prove the existence of binding for two very dissimilar atoms in the frame of this model.on leave from Universidad de Chile, Santiago, ChileResearch supported by U. S. National Science Foundation under Grants MCS78-20455 (R. B.), PHY-7825390 A 01 (H. B. and E. L.), and Army Research Grant DAH 29-78-6-0127 (H. B.)     

Thomas-Fermi approach to diatomic quasimolecules: Correlation diagrams for neutral,heteronuclear systems

Correlation diagrams for the heteronuclear systems C-Ar, O-Ar, C-Ne, Al-F, and I-Cl are calculated with an effective Hartree-Fock-Slater potential constructed from Thomas-Fermi-Dirac-Weizsäcker densities.     

Accurate solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for the case of neutral atoms and positive ions

The numerical solution of the Thomas-Fermi-Dirac-Weizsäcker variational equations for atomic many electron systems is discussed in terms of a spline representation. Accurate values for groundstate energies are obtained for the full range of the central charge and all degrees of ionisation.     

A geometric model of space-time and matter

A geometric model of a spin one-half charged particle based on a modified version of Weyl's unified model of electromagnetism and gravity is presented. The model predicts a short-range force which we identify with the strong force. A nuclear mass formula similar to the Weizsäcker mass formula provides experimental verification of the geometric approach.     

Variation of single-particle occupations and the uncertainty principle

A relation between a temporal variation of the occupation of a single-particle state and the uncertainty of a single-particle energy is derived. The analogous space-momentum uncertainty principle provides a lower bound for the kinetic energy density. The bound has the form of the von Weizsäcker correction to the ground-state Thomas-Fermi energy density.     

The History and Impact of the CNO Cycles in Nuclear Astrophysics

The carbon cycle, or Bethe-Weizsäcker cycle, plays an important role in astrophysics as one of the most important energy sources for quiescent and explosive hydrogen burning in stars. This paper presents the intellectual and historical background of the idea of the correlation between stellar energy production and the synthesis of the chemical elements in stars on the example of this cycle. In particular, it addresses the contributions of Carl Friedrich von Weizsäcker and Hans Bethe, who provided the first predictions of the carbon cycle. Further, the experimental verification of the predicted process as it developed over the following decades is discussed, as well as the extension of the initial carbon cycle to the carbon-nitrogen-oxygen (CNO) multi-cycles and the hot CNO cycles. This development emerged from the detailed experimental studies of the associated nuclear reactions over more than seven decades. Finally, the impact of the experimental and theoretical results on our present understanding of hydrogen burning in different stellar environments is presented, as well as the impact on our understanding of the chemical evolution of our universe.     

A quantitative approach to ionic adsorption

Binding properties of multi-atomic systems with ionic bonds are calculated by using a recently developed method based on the density functional formalism. The charge density is obtained from a superposition of the respective atomic densities where the charge transfer between these atoms is chosen such that the total energy attains a minimum. The kinetic energy of the electrons can to a very good approximation be calculated by means of a modified Thomas-Fermi-v. Weizsäcker expression. The molecules NaCl and NaW and a NaW₄ cluster have been treated as model systems for ionic interaction. Moreover, we have computed the binding properties of a Na atom adsorbed on a W(100) surface. This particular problem is the primary subject of the present study. The calculations yield binding energies, binding distances, vibrational frequencies, and induced dipole moments.     

Color Conductivity at High Resolution: A New Phenomenon of Nuclear Physics

In this paper we discuss in detail the hyothesis that nuclei show extended quark and gluon modes when explored with a high resolution probe. We call this color conductivity at high resolution. We relate color conductivity to the behaviour of proton-proton total and elastic cross sections at high energies. For deep inelastic muon-nucleon scattering we discuss in detail the nuclear evolution equation following from color conductivity and introduced by us previously. The EMC Fe/d data are well described by our theory if due allowance is made for the quoted systematic error. We predict striking effects from color conductivity in the final state of deep inelastic lepton-nucleus scattering. The possibility of making fundamental tests of quantum chromodynamics in leptonnucleus scattering is emphasized. We connect the shadowing phenomenon to the volume and surface terms in the Bethe-Weizsäcker formula for the nuclear binding energy. Finally we point out that deep inelastic scattering on deformed nuclei may be crucial to distinguish between different theories of the EMC effect.     

Two-photon production of leptons at hadron colliders in semielastic and elastic cases

The mechanism of two-photon dilepton production is studied in the equivalent-photon (Weizsäcker–Williams) approximation. This approximation is shown to describe well experimental data from hadron accelerators. The respective total and differential cross sections were obtained for the LHC and for the Tevatron collider at various energies of colliding hadrons. The differential cross sections were studied versus the dilepton invariant mass, transverse momentum, and emission angle in the reference frame comoving with the center of mass of colliding hadrons. The cases of semielastic and inelastic collisions were examined.     

Mass formula based on SU(4)

The quality of the fit of experimental masses by a mass formula based on the two-body Casimir operator of SU(4) is tested and found to be at least as good as that of the Weizsäcker mass formulae, in spite of the fact that this formula is inherently less flexible. The physical basis for, and some ramifications of, this formula are discussed. A simple form for the shell corrections is then added in the formulae, leading to improved fits without modification of the above conclusions.     

A nuclear mass formula based onSU(4) symmetry

It is argued that mass anomalies at the N≈Z line are associated with SU(4) isospin-spin symmetry. Drawing on these arguments, a Weizsäcker-type nuclear mass formula is investigated which has the eigenvalue of the quadratic Casimir operator of SU(4) as a Wigner term. This SU(4)-based mass formula yields a better agreement than the one with the usual Wigner term |N—Z|/A. In addition, the SU(4) eigenvalue expression adequately replaces the usual pairing term of the Weizsäcker formula giving a lower overall rms deviation than the latter.     

Fragmentation of light nuclei by intermediate energy photons

New data on the fragmentation of carbon nuclei by photons with energies from 800 to 1500 MeV, obtained in the collaboration GRAAL, are presented. These data include the yields of heavier fragments than nucleons. Comparison of new results with literature data, obtained with real and virtual photons in reactions with electrons and relativistic ions (Coulomb dissociation) is done using a general approach in frame of the Weizsäcker–Williams model. Possible reasons for the observed differences between them are discussed.     

Zur isotropen Turbulenz

On Isotropic Turbulence We demonstrate for the example of isotropic turbulence according to the statistical approaches by A. N. Komolgoroff and by W. Heisenberg and C. F. v. Weizsäcker that the mathematical “chaos” is a state with a high degree of order. This isotropic “chaos” vanishes in a finite time by energy dissipation (J. R. Mayer's fundamental experiment). According Einstein's formula for stochastic motions “chaos” becomes a static fluid with a higher temperature.