Irreducible tensor form of three-particle operator for open-shell atoms

The three-particle operator in a second quantized form is studied. The operator is transformed into irreducible tensor form. Possible coupling schemes, distinguished by the classes of symmetric group \mathrm{S_{6}}, are presented. Recoupling coefficients, which allow one to transform given scheme into another, are produced by using the angular momentum theory, combined with quasispin formalism. The classification of three-particle operator, which acts on n=1,2,...,6 open shells of equivalent electrons of atom, is considered. The procedure to construct three-particle matrix elements are examined

Development of algebraic techniques for the atomic open-shell MBPT(3)

The atomic third-order open-shell many-body perturbation theory is developed. Special attention is paid to the generation and algebraic analysis of terms of the wave operator and the effective Hamiltonian as well. Making use of occupation-number representation and intermediate normalization, the third-order deviations are worked out by employing a computational software program that embodies the generalized Bloch equation. We prove that in the most general case, the terms of effective interaction operator on the proposed complete model space are generated by not more than eight types of the $n$-body ($n\geq2$) parts of the wave operator. To compose the effective Hamiltonian matrix elements handily, the operators are written in irreducible tensor form. We present the reduction scheme in a versatile disposition form, thus it is suited for the coupled-cluster approach

Contribution of high-nl shells to electron-impact ionization processes

The contribution to electron-impact ionization cross sections from excitations to high-nl shells and a consequent autoionization is investigated. We perform relativistic subconfiguration-average and detailed level-to-level calculations for this process. Ionization cross sections for the W27+ ion are presented to illustrate the large influence of the high shells (n >= 9) and orbitals (l >= 4) in the excitation-autoionization process. The obtained results show that the excitations to the high shells (n >= 9) increase cross sections of the indirect ionization process by a factor of 2 compared to the excitations to the lower shells (n <= 8). The excitations to the shells with orbital quantum number l = 4 give the largest contribution comparedwith the other orbital quantum numbers l. Radiative damping reduces the cross sections of the indirect process approximately twofold in the case of the level-to-level calculations. Determined data show that the excitation-autoionization process contributes approximately 40% to the total ionization cross sections.Comment: 18 pages including 6 figures and 2 table

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

General expression for the dielectronic recombination cross section of polarized ions with polarized electrons

A general expression for the differential cross section of dielectronic recombination (DR) of polarized electrons and polarized ions is derived by using usual atomic theory methods and is represented in the form of multiple expansions over spherical tensors. The ways of the application of the general expressions suitable for the specific experimental conditions are outlined by deriving asymmetry parameters of angular distribution of DR radiation in the case of nonpolarized and polarized ions and electrons.Comment: 4 page

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

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