arXiv subjects

G. Gaigalas

Publications and source records attributed to G. Gaigalas.

At least 37 records · Page 2Linked to original sources

arXiv2011

Tensorial form and matrix elements of the relativistic nuclear recoil operator

Within the lowest-order relativistic approximation ($\sim v^2/c^2$) and to first order in $m_e/M$, the tensorial form of the relativistic corrections of the nuclear recoil Hamiltonian is derived, opening interesting perspectives for calculating isotope shifts in the multiconfiguration Dirac-Hartree-Fock framework. Their calculation is illustrated for selected Li-, B- and C-like ions. The present work underlines the fact that the relativistic corrections to the nuclear recoil are definitively necessary for getting reliable isotope shift values.

physics.atom-ph↗

arXiv2009

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations.

physics.atom-ph↗

arXiv2009

Multiconfiguration electron density function for the ATSP2K-package

A new ATSP2K module is presented for evaluating the electron density function of any multiconfiguration Hartree-Fock or configuration interaction wave function in the non relativistic or relativistic Breit-Pauli approximation. It is first stressed that the density function is not a priori spherically symmetric in the general open shell case. Ways of building it as a spherical symmetric function are discussed, from which the radial electron density function emerges. This function is written in second quantized coupled tensorial form for exploring the atomic spherical symmetry. The calculation of its expectation value is performed using the angular momentum theory in orbital, spin, and quasispin spaces, adopting a generalized graphical technique. The natural orbitals are evaluated from the diagonalization of the density matrix.

physics.atom-ph↗

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

Spectroscopic LSJ notation for atomic levels obtained from relativistic calculations

Today, relativistic calculations are known to provide a very successful means in the study of open-shell atoms and ions. But although accurate atomic data are obtained from these computations, they are traditionally carried out in jj-coupling and, hence, do often not allow for a simple LSJ classification of the atomic levels as needed by experiment. In fact, this lack of providing a proper spectroscopic notation from relativistic structure calculations has recently hampered not only the spectroscopy of medium and heavy elements, but also the interpretation and analysis of inner-shell processes, for which the occurrence of additional vacancies usually leads to a very detailed fine structure. Therefore, in order to facilitate the classification of atomic levels from such computations, here we present a program (within the Ratip environment) which help transform the atomic wave functions from jj-coupled multiconfiguration Dirac-Fock computations into a LS-coupled representation. Beside of a proper LSJ assignment to the atomic levels, the program also supports the full transformation of the wave functions if required for (nonrelativistic) computations.

physics.atom-ph↗

arXiv2004

Extension of the HF program to partially filled f-subshells

A new version of a Hartree-Fock program is presented that includes extensions for partially filled f-subshells. The program allows the calculation of term dependent Hartree-Fock orbitals and energies in LS coupling for configurations with no more than two open subshells, including f-subshells.

physics.atom-ph↗

arXiv2004

Pure spin-angular momentum coefficients for non-scalar one-particle operators in jj-coupling

A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version of the Anco program now provides these coefficients for both, scalar as well as non-scalar one-particle operators as they arise frequently in the study of transition probabilities, photoionization and electron capture processes, the alignment transfer through excited atomic states, collision strengths, and in many other investigations. The program is based on a recently developed formalism [G.Gaigalas, Z.Rudzikas, and C.F.Fischer, J. Phys. B 30 (1997) 3747], which combines techniques from second quantization in coupled tensorial form, the theory of quasispin, and the use of reduced coefficients of fractional parentage, in order to derive the spin-angular coefficients for complex atomic shell structures more efficiently. By making this approach now available also for non-scalar interactions, therefore, studies on a whole field of new properties and processes are likely to become possible even for atoms and ions with a complex structure.

physics.atom-ph↗

arXiv2004

Maple procedures for the coupling of angular momenta. VI. LS-jj transformations

Transformation matrices between different coupling schemes are required, if a reliable classification of the level structure is to be obtained for open-shell atoms and ions. While, for instance, relativistic computations are traditionally carried out in jj-coupling, a LSJ coupling notation often occurs much more appropriate for classifying the valence-shell structure of atoms. Apart from the (known) transformation of single open shells, however, further demand on proper transformation coefficients has recently arose from the study of open d- and f-shell elements, the analysis of multiple--excited levels, or the investigation on inner-shell phenomena. Therefore, in order to facilitate a simple access to LS <-> jj transformation matrices, here we present an extension to the Racah program for the set-up and the transformation of symmetry-adapted functions. A flexible notation is introduced for defining and for manipulating open-shell configurations at different level of complexity which can be extended also to other coupling schemes and, hence, may help determine an optimum classification of atomic levels and processes in the future.

physics.atom-ph↗

arXiv2004

Calculation of reduced coefficients and matrix elements in jj-coupling

A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the coefficients of fractional parentage, the reduced coefficients of fractional parentage, the reduced matrix elements of the unit operator T^{(k)} as well as the completely reduced matrix elements of the operator W^{(k_jk_q)} in jj-coupling. These quantities are now available for all subshells (nj) with j \leq 9/2 including partially filled 9/2-shells. Our program is based on a recently developed new approach on the spin-angular integration which combines second quantization and quasispin methods with the theory of angular momentum in order to obtain a more efficient evaluation of many-electron matrix elements. An underlying Fortran 90/95 module can directly be used also in (other) atomic structure codes to accelerate the computation for open-shell atoms and ions.

physics.atom-ph↗

arXiv2004

Program to calculate pure angular momentum coefficients in jj-coupling

A program for computing pure angular momentum coefficients in relativistic atomic structure for any scalar one- and two-particle operator is presented. The program, written in Fortran 90/95 and based on techniques of second quantization, irreducible tensorial operators, quasispin and the theory of angular momentum, is intended to replace existing angular coefficient modules from GRASP92. The new module uses a different decomposition of the coefficients as sums of products of pure angular momentum coefficients, which depend only on the tensor rank of the interaction but not on its details, with effective interaction strengths of specific interactions. This saves memory and reduces the computational cost of big calculations signficantly.

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

Integration over spin-angular variables in atomic physics

A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given. These methods are compared in various aspects, and the advantages or shortcomings of each particular method are discussed. Efficient method to find the abovementioned quantities in LS coupling is presented, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), second quantization in coupled tensorial form, graphical technique and Wick's theorem. This allows to efficiently account for correlation effects practically for any atom and ion of periodical table.

physics.atom-ph↗

arXiv2004

Some new simplifications for general form of the orbit-orbit interaction operator

The general tensorial form of the orbit-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 with respect to configurations, in a uniform way. Some special cases are shown for which the orbit-orbit interaction operator reduces to simple form. The importance of different contributions to the Breit-Pauli hamiltonian is investigated in ground states and ionization potentials for Li isoelectronic sequency in the systematic way.

physics.atom-ph↗

arXiv2004

The library of subroutines for calculating standard quantities in atomic structure theory

This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage, the reduced coefficients of fractional parentage as well as reduced and completely reduced matrix elements for several operators. So the library is assigned for any computational scheme. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), and the graphical technique of angular momentum. This implementation extends applications in atomic theory capabilities to partially filled f-- shells and has lead to faster execution of angular integration codes.

physics.atom-ph↗

arXiv2004

The library of subroutines for calculation of matrix elements of two-particle operators for many-electron atoms

In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum theory in 3 spaces (orbital, spin and quasispin), and the graphical technique of angular momentum. This implementation extends applications of the relevant methodology to open f- shells and leads to faster execution of angular integration codes. The possibility of using some library routines for solving various angular momentum problems in atomic physics is also discussed.

physics.atom-ph↗