159 research outputs found
The second-order electron self-energy in hydrogen-like ions
A calculation of the simplest part of the second-order electron self-energy
(loop after loop irreducible contribution) for hydrogen-like ions with nuclear
charge numbers is presented. This serves as a test for the
more complicated second-order self-energy parts (loop inside loop and crossed
loop contributions) for heavy one-electron ions. Our results are in strong
disagreement with recent calculations of Mallampalli and Sapirstein for low
values but are compatible with the two known terms of the analytical
-expansion.Comment: 13 LaTex pages, 2 figure
Evidence for the absence of regularization corrections to the partial-wave renormalization procedure in one-loop self energy calculations in external fields
The equivalence of the covariant renormalization and the partial-wave
renormaliz ation (PWR) approach is proven explicitly for the one-loop
self-energy correction (SE) of a bound electron state in the presence of
external perturbation potentials. No spurious correctio n terms to the
noncovariant PWR scheme are generated for Coulomb-type screening potentia ls
and for external magnetic fields. It is shown that in numerical calculations of
the SE with Coulombic perturbation potential spurious terms result from an
improper treatment of the unphysical high-energy contribution. A method for
performing the PWR utilizing the relativistic B-spline approach for the
construction of the Dirac spectrum in external magnetic fields is proposed.
This method is applied for calculating QED corrections to the bound-electron
-factor in H-like ions. Within the level of accuracy of about 0.1% no
spurious terms are generated in numerical calculations of the SE in magnetic
fields.Comment: 22 pages, LaTeX, 1 figur
New non-unitary representations in a Dirac hydrogen atom
New non-unitary representations of the SU(2) algebra are introduced for the
case of the Dirac equation with a Coulomb potential; an extra phase, needed to
close the algebra, is also introduced. The new representations does not require
integer or half integer labels. The set of operators defined are used to span
the complete space of bound state eigenstates of the problem thus solving it in
an essentially algebraic way
Electric dipole moment of the electron in YbF molecule
Ab initio calculation of the hyperfine, P-odd, and P,T-odd constants for the
YbF molecule was performed with the help of the recently developed technique,
which allows to take into account correlations and polarization in the
outercore region. The ground state electronic wave function of the YbF molecule
is found with the help of the Relativistic Effective Core Potential method
followed by the restoration of molecular four-component spinors in the core
region of ytterbium in the framework of a non-variational procedure. Core
polarization effects are included with the help of the atomic Many Body
Perturbation Theory for Yb atom. For the isotropic hyperfine constant A,
accuracy of our calculation is about 3% as compared to the experimental datum.
The dipole constant Ad (which is much smaller in magnitude), though better than
in all previous calculations, is still underestimated by almost 23%. Being
corrected within a semiempirical approach for a perturbation of 4f-shell in the
core of Yb due to the bond making, this error is reduced to 8%. Our value for
the effective electric field on the unpaired electron is 4.9 a.u.=2.5E+10 V/cm.Comment: 7 pages, REVTE
Enhancement of the electric dipole moment of the electron in the YbF molecule
We calculate an effective electric field on the unpaired electron in the YbF
molecule. This field determines sensitivity of the molecular experiment to the
electric dipole moment of the electron. We use experimental value of the
spin-doubling constant to estimate the admixture of the configuration with the
hole in the 4f-shell of Ytterbium to the ground state of the molecule. This
admixture reduces the field by 7%. Our value for the effictive field is 5.1
a.u. = 2.5 10^{10} V/cm.Comment: 5 pages, LATEX, uses revtex.st
A useful form of the recurrence relation between relativistic atomic matrix elements of radial powers
Recently obtained recurrence formulae for relativistic hydrogenic radial
matrix elements are cast in a simpler and perhaps more useful form. This is
achieved with the help of a new relation between the and the
terms ( is a Dirac matrix and are constants) in the
atomic matrix elements.Comment: 7 pages, no figure
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