44 research outputs found
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
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
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 -body
() 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
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 W ion
Spectra of the W 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 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 transitions, while
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