Gediminas Gaigalas

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.

An MCHF atomic-structure package for large-scale calculations

Abstract An MCHF atomic-structure package is presented based on dynamic memory allocation, sparse matrix methods, and a recently developed angular library. It is meant for large-scale calculations in a basis of orthogonal orbitals for groups of LS terms of arbitrary parity. For Breit–Pauli calculations, all operators—spin–orbit, spin–other orbit, spin–spin, and orbit–orbit—may be included. For transition probabilities the orbitals of the initial and final state need not be orthogonal. A bi-orthogonal transformation is used for the evaluation of matrix elements in such cases. In addition to transition rates of all types, isotope shifts and hyperfine constants can be computed as well as g J factors. New version summary Title of program: atsp 2K Version number: 1.00 Catalogue identifier: ADLY_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADLY_v2_0 Program obtainable from: CPC Program Library, Queens University of Belfast, N. Ireland Computer: Pentium III 500 MHz Installations: Vanderbilt University, Nashville, TN 37235, USA Operating systems under which the present version has been tested: Red Hat 8 Programming language used in the present version: FORTRAN 90 Memory required to execute with typical data: 256 Mbytes words No. of bits in a word: 32 Supplementary material: User manuals for the program atsp 2k and for the Spin-Angular library are available No. of lines in distributed program, including test data, etc.: 209 992 No. of bytes in distributed package, including test data, etc.: 1 740 883 Distribution format: tar.gz CPC Program Library subprograms used: none Does the new version supersede the previous version?: Yes Nature of physical problem: This program determines energy levels and associated wave functions for states of atoms and ions in the MCHF ( LS ) or Breit–Pauli ( LSJ ) approximation. Given the wave function, various atomic properties can be computed such as electric (E k ) and magnetic (M k ) multipole radiative transition probabilities ( k max = 10 ) between LS or LSJ states, isotope shift constants, hyperfine parameters, and g J factors. Method of solution: The new version of the program closely follows the design and structure of the previous one [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635], except that a simultaneous optimization scheme has been introduced. This program uses the angular methodology of [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39] and has been extended to include partially filled f -subshells in wavefunction expansions but assumes all orbitals are orthonormal. The bi-orthogonal transformation method is used to deal with the non-orthogonality of orbitals between initial and final states of an electromagnetic radiative transition. Reasons for new version: The previous version of the MCHF atomic structure package [C. Froese Fischer, Comput. Phys. Comm. 128 (2000) 635] was intended for small calculations, ideal for someone not familiar with the code, producing extensive print-out of intermediate results. The codes for the calculation of spin-angular coefficients were often not the most efficient and could only treat configurations with open f -subshells containing at most two electrons or an almost filled shell with one hole. The present version is designed for large-scale computation using algorithms for angular integration that have been shown to be faster, and include the case of arbitrarily filled f -shells. In addition, the MCHF program has been modified to include optimization on an energy functional that is a weighted average of energy functionals for expansions of wavefunctions for different LS terms or parity, thus facilitating Breit–Pauli calculations for complex atomic systems and for computing targets in collision calculations. Summary of revisions: Programs have been modified to take advantage of the newly developed angular library [G. Gaigalas, Lithuanian J. Phys. 41 (2000) 39], extended to arbitrarily filled f -shells. New programs have been developed for simultaneous optimization and for the efficient calculation of atomic spectra and transition rates for an iso-electronic sequence. All applications now take advantage of dynamic memory allocation and sparse matrix methods. Restrictions on the complexity of the problem: All orbitals in a wave function expansion are assumed to be orthonormal. Configuration states are restricted to at most eight (8) subshells in addition to the closed shells common to all configuration states. The maximum size is limited by the available memory and disk space. Typical running time: Included with the code are scripts for calculating E2 and M1 transitions between levels of 3 s 2 3 p 2 for Si and P + . This calculation has two stages: LS and LSJ . The calculation of the former required 21 minutes for the LS calculation and 36.5 minutes for the Breit–Pauli configuration interaction calculation that determines the mixing of the terms. Unusual features of the program: The programming style is essentially F77 with extensions for the POINTER data type and associated memory allocation. These have been available on workstations for more than a decade but their implementations are compiler dependent. The present serial code has been installed and tested extensively using both the Portland Group, pgf90, compiler and the IBM SP2, xlf90, compiler. The former is compatible also with the Intel Fortran90 compiler. The MPI codes are included for completeness though testing has not been as extensive. Additional comments: Parallel versions (MPI) of the following programs are included in the distribution. Use of these is optional but can speed up the angular integration processing. Serial Parallel nonh nonh_mpi mchf mchf_mpi bp_ang, bp_mat, bp_eiv bp_ang_mpi, bp_mat_ang, bp_eiv_mpi biotr_ang, biotr_tr biotr_ang_mpi, biotr_tr_mpi

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.

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 significantly.

RELCI: A program for relativistic configuration interaction calculations☆

Apparatus for cleaning/deburring manufactured parts, each part having an established axis of rotation, includes a conveyor operable to convey the parts in succession in intermittent step-by-step movement to a cleaning/deburring station and a drying station. At each of the cleaning/deburring and drying stations the part is driven in high speed rotation about its axis by a part rotating device. At the cleaning/deburring station the rotating part is sprayed with high pressure fluid and at the drying station high velocity air is discharged tangentially against the rotating part to strip residual fluid from the part. The spray nozzle assembly can be stationary, or can take the form of a transversing assembly for reciprocating movement along the longitudinal length of the part. Additionally, the transversing assembly can include rotation of the nozzle assembly about an axis as the nozzles are reciprocated longitudinally. Alternatively, the spray nozzle assembly can take the form of a pantograph assembly allowing the spray nozzles to trace the contours of the surface of the part as it rotates at high speed.

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.

Maple procedures for the coupling of angular momenta. III. Standard quantities for evaluating many-particle matrix elements

An extension to the RACAH program 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 within the two most frequently applied coupling schemes, namely LS -a ndjj-coupling, respectively. Values for these quantities are available for all (partially-filled) shells (nl) with l 3i nLS-coupling and for all subshells with j 9/ 2i njj-coupling. Different notations and classification schemes are supported to characterize the antisymmetrized states of partially-filled shells.  2001 Elsevier Science B.V. All rights reserved.

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) .

Electric dipole transitions in ions of the N I isoelectronic sequence

The electric dipole transitions in the nitrogen isoelectronic sequence (Z = 10-30) between the levels of the 1s22s22p3, 1s22s2p4 and 1s22p5 configurations are considered. The stationary second-order many-body perturbation theory (MBPT) is used to account for the electron correlations. Non-local potential is used to calculate the radial part of the effective Hamiltonian. Relativistic corrections were included in the Breit-Pauli approximation. The results include energies, wavelengths, and oscillator strengths for all N-like ions in the interval Z = 10-30.

MBPT CALCULATION OF ENERGY SPECTRA AND E1 TRANSITION PROBABILITIES FOR BORON ISOELECTRONIC SEQUENCE

The energy spectra and the electric dipole transitions in the boron isoelectronic sequence (Z = 8 - 26) between the levels of the 1s22s22p, 1s22s2p2 and 1s22p3 configurations were considered. The stationary second-order many-body perturbation theory (MBPT) was used to account for the electron correlations. The relativistic corrections were included in the Breit-Pauli approximation.