Coupled tensorial form for atomic relativistic two-particle operator given in second quantization representation

General formulas of the two-electron operator representing either atomic or effective interactions are given in a coupled tensorial form in relativistic approximation. The alternatives of using uncoupled, coupled and antisymmetric two-electron wave functions in constructing coupled tensorial form of the operator are studied. The second quantization technique is used. The considered operator acts in the space of states of open-subshell atoms

Cascade emission in electron beam ion trap plasma of W25+^{25+} ion

Spectra of the W$^{25+}$ ion are studied using the collisional-radiative model (CRM) with an ensuing cascade emission. It is determined that the cascade emission boosts intensities only of a few lines in the $10 - 3$ nm range. The cascade emission is responsible for the disappearance of structure of lines at about 6 nm in the electron beam ion trap plasma. Emission band at 4.5 to 5.3 nm is also affected by the cascade emission. The strongest lines in the CRM spectrum correspond to $4d^{9} 4f^{4} \rightarrow 4f^{3}$ transitions, while $4f^{2} 5d \rightarrow 4f^{3}$ transitions arise after the cascade emission is taken into account.Comment: 16 pages including 4 figures and 3 table

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

The transformation of irreducible tensor operators under spherical functions

The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the spherical coordinates of vector in the fixed and rotated coordinate systems are determined. A new way of calculation of the irreducible coupled tensor product matrix elements is suggested. As an example, the proposed technique is applied for the matrix element construction for two electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy

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

CHIANTI - An Atomic Database for Emission Lines. XII. Version 7 of the Database

The CHIANTI spectral code consists of an atomic database and a suite of computer programs to calculate the optically thin spectrum of astrophysical objects and carry out spectroscopic plasma diagnostics. The database includes atomic energy levels, wavelengths, radiative transition probabilities, collision excitation rate coefficients, and ionization and recombination rate coefficients, as well as data to calculate free-free, free-bound, and two-photon continuum emission. Version 7 has been released, which includes several new ions, significant updates to existing ions, as well as Chianti-Py, the implementation of CHIANTI software in the Python programming language. All data and programs are freely available at http://www.chiantidatabase.org, while the Python interface to CHIANTI can be found at http://chiantipy.sourceforge.net.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98606/1/0004-637X_744_2_99.pd

Biases in abundance derivations for metal-rich nebulae

Using ab-initio photoionization models of giant HII regions, we test methods for abundance determinations based on a direct measurement of the electron temperature, now possible even for moderate to high-metallicity objects. We find that, for metallicities larger than solar, the computed abundances deviate systematically from the real ones, generally by larger amounts for more metal-rich HII regions. We discuss the reasons for this, and present diagrams allowing the reader to better understand the various factors coming into play. We briefly discuss less classical methods to derive abundances in metal-rich HII regions. In particular, we comment on the interest of the oxygen and carbon recombination lines. We also show that, contrary to the case of giant HII regions, the physical conditions in bright extragalactic planetary nebulae are such that their chemical composition can be accurately derived even at high metallicities. Thus, extragalactic planetary nebulae are promising potential probes of the metallicity of the interstellar medium in the internal parts of spiral galaxies as well as in metal-rich elliptical galaxies.Comment: 15 pages, 13 figures, Accepted for publication in A&