152 research outputs found
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
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
On the idempotents of Hecke algebras
We give a new construction of primitive idempotents of the Hecke algebras
associated with the symmetric groups. The idempotents are found as evaluated
products of certain rational functions thus providing a new version of the
fusion procedure for the Hecke algebras. We show that the normalization factors
which occur in the procedure are related to the Ocneanu--Markov trace of the
idempotents.Comment: 11 page
Proof of Stanley's conjecture about irreducible character values of the symmetric group
R. Stanley has found a nice combinatorial formula for characters of
irreducible representations of the symmetric group of rectangular shape. Then,
he has given a conjectural generalisation for any shape. Here, we will prove
this formula using shifted Schur functions and Jucys-Murphy elements.Comment: 9 page
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
A mixed hook-length formula for affine Hecke algebras
Consider the affine Hecke algebra corresponding to the group
over a -adic field with the residue field of cardinality . Regard
as an associative algebra over the field . Consider the -module
induced from the tensor product of the evaluation modules over the algebras
and . The module depends on two partitions of and
of , and on two non-zero elements of the field . There is a
canonical operator acting on , it corresponds to the trigonometric
-matrix. The algebra contains the finite dimensional Hecke algebra
of rank as a subalgebra, and the operator commutes with the action of
this subalgebra on . Under this action, decomposes into irreducible
subspaces according to the Littlewood-Richardson rule. We compute the
eigenvalues of , corresponding to certain multiplicity-free irreducible
components of . In particular, we give a formula for the ratio of two
eigenvalues of , corresponding to the ``highest'' and the ``lowest''
components. As an application, we derive the well known -analogue of the
hook-length formula for the number of standard tableaux of shape .Comment: 36 pages, final versio
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
Teksto redaktorių MS Word 2003, MS Word 2007 ir OpenOffice Writer 3.0 naudojamumo palyginimas
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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
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