11 research outputs found
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 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
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