Calculation of the Critical Distances in a System of Two Colliding Nuclei Beyond the Monopole Approximation

A method for calculating electronic levels in compact superheavy nuclear quasimolecules based on solving the Dirac equation in spherical coordinates using a multipole expansion of a two-center potential is developed. It is shown that, for internuclear distances up to ∼100 fm, such a technique enables fast convergence, which allows one to calculate the electronic energy levels with an accuracy better than 10−6. Moreover, all the multipole moments can be calculated analytically. The critical distances between the similar colliding nuclei have been calculated in the range Z ∼ 87–100 for bottom electronic levels: even 1σg and odd 1σu, respectively.     

Multipole contributions to atom-surface scattering potential

We calculate multipole corrections to the standard van der Waals (dipole) potential in atom-surface scattering. The quadru- and octupoles give at most a 15% deeper potential at relevant physisorption distances, and the degree of metal screening is shown to have very little effect on this conclusion.     

Calculation of Electric Mult ipole Moment Integrals Using Translation Formulas for Slater-Type Orbitals

Using translation formulas for Slater-type orbitals the infinite series through the overlap integrals are derived for the electric multipole moment integrals. By the use of the derived expressions the electric multipole moment integrals, and therefore, the electric properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of for 10^-5 the computer results is obtained for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

Expansion of the Madelung parameter in terms of multipole moments and as a function of the ratio of two lattice parameters

A method is derived to expand the Madelung parameters of non-cubic crystals as a function of the ratio of two lattice parameters and in terms of multipole moments. Only one expansion of this kind is necessary to evaluate the Madelung constants for a series of compounds of one type of structure either containing polyatomic ions or spherical ions at positions slightly varying from one compound to the other. This method also allows the minimisation of the lattice energy with respect to one particular lattice parameter, leaving invariant all internal distances in the polyatomic ions.     

A galactic model II: The gravitationally radiated angular and linear momenta fluxes

Using the linearised theory of general relativity the gravitationally radiated angular and linear momenta from a galactic model ofN gravitational radiators is calculated. The results are presented in terms of the lowest order contributing multipole moments (quadrupole), the orientations of the radiators about a common reference frame, the distances between pairs of radiators and the frequency of each radiator. This work is a continuation of an earlier work in which the galactic model was first proposed and its gravitationally radiated energy flux was computed.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.