Accurate computations of bound state properties in three- and four-electron atomic systems in the basis of multi-dimensional gaussoids

Results of accurate computations of bound states in three- and four-electron atomic systems are discussed. Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state are determined from the results of accurate, variational computations. We also consider a closely related problem of accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry.Comment: arXiv admin note: substantial text overlap with arXiv:1411.113

Three-particle integrals with the Bessel functions

Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas obtained in such an analysis allow us to consider three-particle integrals of more complicated functions of relative/perimetric coordinates. In many actual problems such three-particle integrals can be found in matrix elements of the Hamiltonian and other operators

Secondary electrons emitted during nuclear β−\beta^{-} decay in few-electron atoms

`Additional' ionization of light atoms and ions during nuclear $\beta^{-}$ decay is investigated. The procedure which can be used to determine the corresponding transition probabilities and the velocity/energy spectrum of secondary electrons is developed. Emission of very fast secondary electrons ($\delta-$electrons) from $\beta^{-}$-decaying atoms is also briefly discussed

On the classical theory of molecular optical activity

The basic principles of classical and semi-classical theories of molecular optical activity are discussed. These theories are valid for dilute solutions of optically active organic molecules. It is shown that all phenomena known in the classical theory of molecular optical activity can be described with the use of one pseudo-scalar which is a uniform function of the incident light frequency $\omega$. The relation between optical rotation and circular dichroism is derived from the basic Kramers-Kronig relations. In our discussion of the general theory of molecular optical activity we introduce the tensor of molecular optical activity. It is shown that to evaluate the optical rotation and circular dichroism at arbitrary frequencies one needs to know only nine (3 + 6) molecular tensors. The quantum (or semi-classical) theory of molecular optical activity is also briefly discussed. We also raise the possibility of measuring the optical rotation and circular dichroism at wavelengths which correspond to the vacuum ultraviolet region, i.e. for $\lambda \le 150$ $nm$

On contribution of the electron-electron correlations into bremsstrahlung from few-electron ions

A new approach is developed to evaluate contribution of the electron-electron correlations into bremsstrahlung from few-electron ions and atoms. Our approach is based on the explicit formula for the electron density distribution in such systems. We derive the closed analytical formula for the matrix elements which are needed for highly accurate computations of atomic form-factors of two-electron atoms and ions. We also discuss the energy loss due to bremsstrahlung in a plasma which contains multi-charged ions and free electrons. Bremsstrahlung from a high-temperature plasma is considered as well as its role in the high-temperature burn-up of deuterium plasma

On bound state computations in three- and four-electron atomic systems

A variational approach is developed for bound state calculations in three- and four-electron atomic systems. This approach can be applied to determine, in principle, an arbitrary bound state in three- and four-electron ions and atoms. Our variational wave functions are constructed from four- and five-body gaussoids which depend upon the six ($r_{12}, r_{13}, r_{14}, r_{23}, r_{24}, r_{34}$) and ten ($r_{12}, r_{13}, r_{14}, r_{15}, r_{23}, r_{24}, r_{25}, r_{34}, r_{35}$ and $r_{45}$) relative coordinates, respectively. The approach allows one to operate with the different number of electron spin functions. In particular, the trial wave functions for the ${}^1S$-states in four-electron atomic systems include the two independent spin functions $\chi_1 = \alpha \beta \alpha \beta + \beta \alpha \beta \alpha - \beta \alpha \alpha \beta - \alpha \beta \beta \alpha$ and $\chi_2 = 2 \alpha \alpha \beta \beta + 2 \beta \beta \alpha \alpha - \beta \alpha \alpha \beta - \alpha \beta \beta \alpha - \beta \alpha \beta \alpha - \alpha \beta \alpha \beta$. We also discuss the construction of variational wave functions for the excited $2^3S$-states in four-electron atomic systems.Comment: This paper was published in ZhETPh (JETP), v.137, 1 - 11 (2010). In this version only a few corrections have been made in formula

Optical activity tensor for radiating atomic and molecular systems

The optical activity tensor (OAT) is explicitly derived. It is shown that to evaluate a large number of effects related to optical activity of some atomic/molecular system at arbitrary frequency $\omega$ of the incident light, one needs to know only four optical activity tensors which have twelve irreducible (tensor) components. An additional amplification factor contains one $3 \times 3$ tensor of light scattering with three irreducible components. The explicit dependence of all irreducible components of OAT upon $\omega$ and some molecular parameters is derived and discussed. We apply OAT to explain the dispersion of optical rotation in dilute solutions of organic molecules. This study opens a new avenue in application of methods of modern Quantum Electrodynamics to the optical activity

Bound state spectra and properties of the doublet states in three-electron atomic systems

The bound state spectra of the doublet states in three-electron atomic systems are investigated. By using different variational expansions we determine various bound state properties in these systems. Such properties include the electron-nucleus and electron-electron delta-functions and cusp values. The general structure of the bound state spectra in several three-electron atomic systems (Li, Be+, C3+ and F6+) is investigated with the use of the Hylleraas-Configuration Interaction and the Configuration Interaction wave functions. The advantage of our Configuration Interaction based procedure is that it provides high numerical accuracy for all rotationally excited states, including the bound states with L >= 7.Comment: 27 pages, 4 figures, 5 tables and 33 reference

Compact variational wave functions for bound states in three-electron atomic systems

The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional gaussoids written in the relative four-body coordinates $r_{12}, r_{13}, r_{23}, r_{14}, r_{24}$ and $r_{34}$. The non-linear parameters in each basis function have been optimized carefully. By using these variational wave functions we have determined the energies and other bound state properties are determined for the ground $1^2S$-states in a number of three-electron atoms and ions. The three-electron atomic systems considered in this work include the neutral Li atom and nine positively charged lithium-like ions: Be$^+$, B$^{2+}$, C$^{3+}, ...$Na$^{8+}$ and Mg$^{9+}$. Our variational wave functions are used to determine the hyperfine structure splitting and field shifts for some lithium-like ions. The explicit formulas of the $Q^{-1}$ expansion are derived for the total energies of these three-electron systems

Properties of negatively charged lithium ions and evaluation of the half-life of 7{}^{7}Be atom(s)

Bound state properties of the four-electron lithium ion Li$^{-}$ in its ground $2^{2}S-$state and isotope-subsistuted ${}^{6}$Li$^{-}$ and ${}^{7}$Li$^{-}$ ions in their ground $2^1S-$state(s) are determined from the results of accurate, variational computations. Another closely related problem discussed in this study is accurate numerical evaluation of the half-life of the beryllium-7 isotope. This problem is of paramount importance for modern radiochemistry