22 research outputs found
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
Spin-other-orbit operator in the tensorial form of second quantization
The tensorial form of the spin-other-orbit interaction operator in the
formalism of second quantization is presented. Such an expression is needed to
calculate both diagonal and off-diagonal matrix elements according to an
approach, based on a combination of second quantization in the coupled
tensorial form, angular momentum theory in three spaces (orbital, spin and
quasispin), and a generalized graphical technique. One of the basic features of
this approach is the use of tables of standard quantities, without which the
process of obtaining matrix elements of spin-other-orbit interaction operator
between any electron configurations is much more complicated. Some special
cases are shown for which the tensorial structure of the spin-other-orbit
interaction operator reduces to an unusually simple form
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
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
Irreducible tensor-form of the relativistic corrections to the M1 transition operator
The relativistic corrections to the magnetic dipole moment operator in the
Pauli approximation were derived originally by Drake (Phys. Rev. A 3(1971)908).
In the present paper, we derive their irreducible tensor-operator form to be
used in atomic structure codes adopting the Fano-Racah-Wigner algebra for
calculating its matrix elements.Comment: 26 page