34 research outputs found
Characterization of anomalous Zeeman patterns in complex atomic spectra
The modeling of complex atomic spectra is a difficult task, due to the huge
number of levels and lines involved. In the presence of a magnetic field, the
computation becomes even more difficult. The anomalous Zeeman pattern is a
superposition of many absorption or emission profiles with different Zeeman
relative strengths, shifts, widths, asymmetries and sharpnesses. We propose a
statistical approach to study the effect of a magnetic field on the broadening
of spectral lines and transition arrays in atomic spectra. In this model, the
sigma and pi profiles are described using the moments of the Zeeman components,
which depend on quantum numbers and Land\'{e} factors. A graphical calculation
of these moments, together with a statistical modeling of Zeeman profiles as
expansions in terms of Hermite polynomials are presented. It is shown that the
procedure is more efficient, in terms of convergence and validity range, than
the Taylor-series expansion in powers of the magnetic field which was suggested
in the past. Finally, a simple approximate method to estimate the contribution
of a magnetic field to the width of transition arrays is proposed. It relies on
our recently published recursive technique for the numbering of LS-terms of an
arbitrary configuration.Comment: submitted to Physical Review
Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms
Using a configuration interaction approach we study statistics of the dipole
matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and
21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that
the distribution of the matrix elements is close to Gaussian, although the
width of the Gaussian distribution, i.e. the root-mean-square matrix element,
changes with the excitation energy. The corresponding line strengths are
distributed according to the Porter-Thomas law which describes statistics of
transition strengths between chaotic states in compound nuclei. We also show
how to use a statistical theory to calculate mean squared values of the matrix
elements or transition amplitudes between chaotic many-body states. We draw
some support for our conclusions from the analysis of the 228 experimental line
strengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct
comparison with the calculations is impeded by incompleteness of the
experimental data. Nevertheless, the statistics observed evidence that highly
excited many-electron states in atoms are indeed chaotic.Comment: 16 pages, REVTEX, 4 PostScript figures (submitted to Phys Rev A
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
Additional symmetry for the electronic shell in its ground state and many-electron effects
The additional symmetry for the properties related to the ground state of the atom is considered
taking into account many-electron effects. Calculations of the binding
energies, – system differences and 2p, 3p electron affinities in the second order
of perturbation theory and in the configuration interaction approximation have been performed for the
ground configurations with one open shell. The analysis of separate many-electron corrections for these
quantities and their variation along the sequences of atoms and ions shows that the main corrections
maintain the considered symmetry