arXiv subjects

Z. Rudzikas

Publications and source records attributed to Z. Rudzikas.

8 recordsLinked to original sources

arXiv2004

Studies of Lanthanides 6s Ionization Energy

This work is aimed at the multi-configuration Hartree-Fock calculations of the 6s ionization energies of lanthanides with configurations [Xe]4f^{N}6s^{2}. Authors have used the ATSP MCHF version in which there are new codes for calculation of spin-angular parts of matrix elements of the operators of intraatomic interactions written on the basis of the methodology Gaigalas, Rudzikas and Froese Fischer, based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), graphical technique of spin-angular integrations and reduced coefficients (subcoefficients) of fractional parentage. This methodology allows us to study the configurations with open f-shells without any restrictions, thus providing the possibility to investigate heavy atoms and ions as well as to obtain reasonably accurate values of spectroscopic data for such complex many-electron systems.

physics.atom-ph↗

arXiv2004

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 calculate graphically 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 find graphically 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 diagona and off-diagonal matrix elements.

physics.atom-ph↗

arXiv2004

On the secondly quantized theory of many-electron atom

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. Then 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 calculation since the tables for their coefficients of fractional parentage are very extensive. The authors suppose that a series of difficulties persisting in the traditional approach to the calculation of spin-angular parts of matrix elements could 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.

physics.atom-ph↗

arXiv2004

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.

physics.atom-ph↗

arXiv2004

Optimal classification of HCI spectra

Energy levels of highly charged ions as a rule cannot be classified using LS coupling due to rapid increase of relativistic effects. It is suggested, for optimal classification of energy spectra, to calculate them in LS coupling and to transform the weights of the wave functions, obtained after diagonalization of the energy matrix, to the other coupling schemes. F-like ions are considered as an example.

physics.atom-ph↗

arXiv2004

Secondly quantized multi-configurational approach for atomic databases

General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is based on second quantization in coupled tensorial form, angular momentum theory in orbital, spin and quasispin spaces and generalized graphical technique. All matrix elements (diagonal and non-diagonal with respect to configurations) differ then only by projections of quasispin of separate shells and are expressed via completely reduced (in three spaces) matrix elements of second quantization operator and its products. Thus, all matrix elements are treated uniformly. This approach allows one to generate fairly accurate databases of atomic parameters.

physics.atom-ph↗

arXiv2004

Analytical expressions for special cases of LS-jj transformation matrices for a shell of equivalent electrons

Transformation matrices of the weights of the atomic wave functions in jj coupling to the relevant weights of LS coupling are considered for a shell of equivalent electrons. Their use allows one to preserve main part of relativistic effects but to classify the energy levels of an atom or an ion considered with the help of a set of quantum numbers of LS coupling scheme. Having in mind that the numerical values of the abovementioned transformation matrix (LS-jj) may be generally obtained in a very time consuming recurrent way, the analytical expressions of these matrices for a number of special cases of electronic configurations are presented.

physics.atom-ph↗

arXiv2004

Studies of Er ionization energy

This work is aimed at the multiconfigurational Hartree-Fock calculations of the Er ionization energy. Authors have used the ATSP MCHF version in which there are new codes for calculation of spin-angular parts written on the basis of the methodology Gaigalas, Rudzikas and Froese Fischer, based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin) and graphical technique of spin-angular ntegrations. They allow the study of configurations with open f-shells without any restrictions and lead to fairly accurate values of spectroscopic data.

physics.atom-ph↗