Zenonas Rudzikas

An efficient approach for spin-angular integrations in atomic structure calculations

A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional parentage nor unit tensors. It is based on the combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. The latter allows us to graphically calculate the irreducible tensorial products of the second-quantization operators and their commutators, and to formulate additional rules for operations with diagrams. The additional rules allow us to graphically find the normal form of the complicated tensorial products of the operators. All matrix elements (diagonal and non-diagonal with respect to configurations) differ only by the values of the projections of the quasispin momenta of separate shells and are expressed in terms of completely reduced matrix elements (in all three spaces) of the second-quantization operators. As a result, it allows us to use standard quantities uniformly for both diagonal and off-diagonal matrix elements.

LS–jj transformation matrices for a shell of equivalent electrons

Abstract The general method of accounting for relativistic effects, starting with relativistic wave functions (which implies the use of jj-coupling) and afterwords transforming the relevant weights of the eigenfunctions to LS-coupling, is considered. The properties and some special cases of the relevant transformation matrices from jj- to LS-coupling schemes for the case of a shell of equivalent electrons lN are discussed. The complete numerical tables of these above-mentioned transformation matrices are presented for l N (l=1,2,3) .

On the secondly quantized theory of the many-electron atom

The traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. The calculation of spin-angular coefficients of radial integrals appearing in the expressions of matrix elements of arbitrary physical operators of atomic quantities has two main disadvantages: (i) the numerical codes for the calculation of spin-angular coefficients are usually very time consuming; (ii) f-shells are often omitted from programs for matrix element calculations since the tables for their coefficients of fractional parentage are very extensive. The authors assume that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements can be avoided by using this secondly quantized methodology, based on angular momentum theory, on the concept of the irreducible tensorial sets, on a generalized graphical method, on quasispin and on the reduced coefficients of fractional parentage.

Spin-other-orbit Operator in the Tensorial Form of Second Quantization

The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin), and a generalized graphical technique. One of the basic features of this approach is the use of tables of standard quantities, without which the process of obtaining matrix elements of spin-other-orbit interaction operator between any electron configurations is much more complicated. Some special cases are shown for which the tensorial structure of the spin-other-orbit interaction operator reduces to an unusually simple form.

Hyperfine structure operator in the tensorial form of second quantization

The general tensorial form of the hyperfine interaction operator in the formalism of second quantization is presented. Both diagonal and off-diagnonal matrix elements of the above-mentioned operator are found using an approach based on a combination of second quantization in the coupled tensorial form, angular momentum theory in three spaces (orbital, spin and quasispin) and a generalised graphical technique. This methodology allows us to account for correlation effects efficiently and, therefore, to study the hyperfine interactions in complex many-electron atoms, those with openf-shells included, in a practical manner. All this will lead us to design an efficient program for large scale calculations of hyperfine structure and isotope shift.

Pecularities of spectroscopic properties of W{sup 24+}

We aim at demonstrating the feasibility of accurate theoretical studies of atoms and ions having complex electronic configurations, open f shell included, by combining the second quantization method in coupled tensorial form with a quasispin technique, leading to triple tensors (in orbital, spin, and quasispin spaces). The large-scale nonrelativistic and relativistic calculations of the 977 lowest energy levels of W{sup 24+}, accounting for correlation, relativistic, and quantum electrodynamics effects, demonstrate the high efficacy of the methods used. The accuracy of the LS- and jj-coupling schemes is discussed as well. The wavelengths of electric dipole transitions, their line strengths and transition probabilities, as well as the lifetimes of some lowest excited levels are also calculated. The authors hope that the success in theoretical studies of such complex ions will stimulate relevant experimental research, encouraging yet further progress in the theory.

Challenges of Theoretical Spectroscopy of Heavy and Superheavy Atoms and Ions

A review of methods of efficient accounting for correlation and relativistic effects is presented. A considerable part of efforts for these approaches must be devoted to coping with integrations over spin‐angular variables, occurring in the matrix elements of the operators under consideration. Efficient methods to find the abovementioned quantities are described, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), on second quantization in coupled tensorial form, and on graphical technique. This allows to study and to generate fairly accurate their spectroscopic data practically for any atom and ion of periodical table.

Symmetries and Spectra of Many-Electron Atoms and Ions

The role of tensorial and symmetry properties of the quantities of theoretical atomic spectroscopy, increasing the efficiency of the relevant mathematical apparatus, is discussed. The main attention is paid to the progress of research in this field carried out by Adolfas Jucys scientific school of theoretical physicists in Lithuania, particularly to the second quantization in a coupled tensorial form as well as to the role of quasispin in the new version of Racah algebra. The role of Professor Indrek Martinson in strengthening the scientific cooperation between the atomic physicists of a Lund University and theoretical physicists from Lithuania will be emphasized.

Progress in Physics of Highly Charged Ions: Synopsis of the 12th International Conference on the Physics of Highly Charged Ions

The 12th International Conference on the Physics of Highly Charged Ions was held in Vilnius (Lithuania) 6–11 September 2004. The papers presented at this conference are analysed and commented upon. The following thematic topics were discussed at the conference: fundamental aspects of the physics of multiply charged atoms, structure and spectroscopy, interactions with photons, plasmas and related processes in strong fields, collisions with electrons, ions, atoms and molecules, interaction with clusters, surfaces and solids, production of highly charged ions, experimental developments and applications. The trends in the development of this field of physics are discussed as well.