Statistical Model Of Atom Research Articles

On a simple method of calculating atomic one-electron eigenfunctions

Starting from a statistical atom model in which electrons are grouped in shells according to the principal quantum number, a method is developed to calculate atomic one-electron eigenfunctions in a simple way.

Statistical Model of Atoms with Correlation and Angular Momentum

within the semi-classical frame work, to include the correlation energy of the electron gas. The equations for the model are derived by means of a variational principle and are solved approximately by a perturbation method. As an application of the model, the approximate solution is used to compute values of the orbital magnetic hyper-fine structure parameter for five different elements. Also, the previously reported values of the same quantity for the case of no-correlation are recalculated by using revised values of the TF and TFD functions. The results are presented graphically. The effect of correlation on the orbital magnetic hyper-fine structure is shown to be quite large.

Solutions of the Thomas—Fermi—Dirac Statistical Model of Atoms

Numerical integration of the zero-temperature Thomas—Fermi—Dirac equation has been carried out on the IBM 701 for atomic numbers Z = 1 to 100. Compressed, expanded, and isolated atoms were treated, the latter using the boundary condition suggested by Jensen. Physical properties of interest for compressed and expanded atoms are presented graphically and, in the case of isolated atoms, tabularly as well.

Foundations for a Treatment of the Scattering of Light by the Hydrodynamical and Statistical Atom Model

A study has been made on the scattering of light by the hydrodynamical and statistical atom model. Bloch's treatment of the hydrodynamical equations of motion for this model is supplemented here by inclusion of the interaction with the electromagnetic field. We limited attention to oscillations of small amplitude. By correspondence principle arguments, general expressions were derived for the cross sections for absorption, coherent and incoherent scattering. The energy can be expressed—following Bloch—as the energy of a Thomas-Fermi atom plus a Hamiltonian which is associated with departures from the Thomas-Fermi distribution. Using Bloch's quantization of this Hamiltonian and applying the method of quantum field theory, we rederived the correspondence principle results for elementary cross sections. Then applying the correspondence theoretical argument to the matrix element, we rederived Heisenberg's result for the total intensity of the Compton scattering. We also apply the method of stationary phase to the hydrodynamical treatment and show that this method gives the same result as does the linear term in the momentum transfer in Heisenberg's expression, except for a numerical factor 3½/2—a point that was discussed by Bloch many years ago. Application of the general formulas given here for angular distribution of Rayleigh and Compton scattering will require electronic machine calculations of higher modes of oscillation of the gas model of the atom analogous to those made by Wheeler and Fireman for l=1.

Über die Breite und Intensitätsverteilung der Compton-Linie

The calculations of A. Konya for the electron distribution in the narrow Compton band are applied to the Gombas statistical atomic model expanded by kinetic energy corrections and to the statistical model in which the electrons are grouped according to the principal quantum number. The values obtained for neon agree with the experimental results. ( J.S.R.)

The Impact of Large Meteorites.

Abstract : The impact of large meteorites on the moon or earth is discussed, on the basis of a one-dimensional idealization of the flow problem in which a plane shock wave in both meteorite and impact surface is considered. Conditions are discussed under which such a model can yield physically valid estimates of pressure and temperature generated on explosive impact of meteorites. Computations are carried out for an equation of state and internal energy from the statistical Thomas-Fermi atom model; departures from complete degeneracy are taken into account by means of results of a first-order perturbation with respect to temperature.

Exchange Potential in the Statistical Model of Atoms

Exchange Potential in the Statistical Model of Atoms

A calculation of internal kinetic energy and polarizability of compressed argon from the statistical atom model

Synopsis From Jensen's and Gombas' modification of the statistical Thomas-Fermi atom model, a theory for compressed atoms is developed by changing the boundary conditions. Internal kinetic energy and polarizability of argon are calculated as functions of pressure. At 1000 atm. an internal kinetic energy of about 5.2 kcal/mole is found; the polarizability is about 2.9% less than that at zero pressure. The change with pressure of these quantities is in rough agreement with experimental results at high densities.

On the dynamics of the RbI crystal

The lattice constant, the compressibility and the infra-red wave-lenght of theRb I crystal are calculated by a statistical atomic model improved by Gombás. The results show, that this model which includes the correlation effect is much more adaptable to problems, where the outer parts of the atoms or ions are of the greatest importance. Estimations are made for the lattice energy and for the ideal tensile strength of theRbI crystal on the same basis. All these calculations are made without any empirical or semi-empirical parameter.

On the Dynamics of the RbI Crystal

The lattice constant, the compressibility and the infra-red wave-lenght of theRb I crystal are calculated by a statistical atomic model improved by Gombas. The results show, that this model which includes the correlation effect is much more adaptable to problems, where the outer parts of the atoms or ions are of the greatest importance. Estimations are made for the lattice energy and for the ideal tensile strength of theRbI crystal on the same basis. All these calculations are made without any empirical or semi-empirical parameter.