365 research outputs found
Correlated exponential functions in high precision calculations for diatomic molecules
Various properties of the general two-center two-electron integral over the
explicitly correlated exponential function are analyzed for the potential use
in high precision calculations for diatomic molecules. A compact one
dimensional integral representation is found, which is suited for the numerical
evaluation. Together with recurrence relations, it makes possible the
calculation of the two-center two-electron integral with arbitrary powers of
electron distances. Alternative approach via the Taylor series in the
internuclear distance is also investigated. Although numerically slower, it can
be used in cases when recurrences lose stability. Separate analysis is devoted
to molecular integrals with integer powers of interelectronic distances
and the vanishing corresponding nonlinear parameter. Several methods
of their evaluation are proposed.Comment: 26 pages, includes two tables with exemplary calculation
Higher-order binding corrections to the Lamb shift of 2P states
We present an improved calculation of higher-order corrections to the
one-loop self energy of 2P states in hydrogen-like systems with small nuclear
charge Z. The method is based on a division of the integration with respect to
the photon energy into a high- and a low-energy part. The high-energy part is
calculated by an expansion of the electron propagator in powers of the Coulomb
field. The low-energy part is simplified by the application of a
Foldy-Wouthuysen transformation. This transformation leads to a clear
separation of the leading contribution from the relativistic corrections and
removes higher order terms. The method is applied to the 2P_{1/2} and 2P_{3/2}
states in atomic hydrogen. The results lead to new theoretical values for the
Lamb shifts and the fine structure splitting.Comment: 18 pages, LaTeX. In comparison to the journal version, it contains an
added note (2000) which reflects the current status of Lamb shift
calculation
Helium 2 3S - 2 1S metrology at 1557 nm
An experiment is proposed to excite the 'forbidden' 1s2s 3S1 - 1s2s 1S0
magnetic dipole (M1) transition at 1557 nm in a collimated and slow atomic beam
of metastable helium atoms. It is demonstrated that an excitation rate of 5000
/s can be realised with the beam of a 2W narrowband telecom fiber laser
intersecting the atomic beam perpendicularly. A Doppler-limited sub-MHz
spectroscopic linewidth is anticipated. Doppler-free excitation of 2% of
trapped and cooled atoms may be realised in a one-dimensional optical lattice
geometry, using the 2W laser both for trapping and spectroscopy. The very small
(8 Hz) natural linewidth of this transition presents an opportunity for
accurate tests of atomic structure calculations of the helium atom. A
measurement of the 3He - 4He isotope shift allows for accurate determination of
the difference in nuclear charge radius of both isotopes.Comment: accepted for publication in Europhysics Letter
Prospects for precision measurements of atomic helium using direct frequency comb spectroscopy
We analyze several possibilities for precisely measuring electronic
transitions in atomic helium by the direct use of phase-stabilized femtosecond
frequency combs. Because the comb is self-calibrating and can be shifted into
the ultraviolet spectral region via harmonic generation, it offers the prospect
of greatly improved accuracy for UV and far-UV transitions. To take advantage
of this accuracy an ultracold helium sample is needed. For measurements of the
triplet spectrum a magneto-optical trap (MOT) can be used to cool and trap
metastable 2^3S state atoms. We analyze schemes for measuring the two-photon
interval, and for resonant two-photon excitation to high
Rydberg states, . We also analyze experiments on the
singlet-state spectrum. To accomplish this we propose schemes for producing and
trapping ultracold helium in the 1^1S or 2^1S state via intercombination
transitions. A particularly intriguing scenario is the possibility of measuring
the transition with extremely high accuracy by use of
two-photon excitation in a magic wavelength trap that operates identically for
both states. We predict a ``triple magic wavelength'' at 412 nm that could
facilitate numerous experiments on trapped helium atoms, because here the
polarizabilities of the 1^1S, 2^1S and 2^3S states are all similar, small, and
positive.Comment: Shortened slightly and reformatted for Eur. Phys. J.
Nuclear polarizability of helium isotopes in atomic transitions
We estimate the nuclear polarizability correction to atomic transition
frequencies in various helium isotopes. This effect is non-negligible for high
precision tests of quantum electrodynamics or accurate determination of the
nuclear charge radius from spectroscopic measurements in helium atoms and ions.
In particular, it amounts to kHz for 1S-2S transition in 4He+.Comment: 11 pages, 4 figures, to be published in Phys. Rev. A. Revised
version: misprints corrected, new references adde
Breit Hamiltonian and QED Effects for Spinless Particles
We describe a simplified derivation for the relativistic corrections of order
for a bound system consisting of two spinless particles. We devote
special attention to pionium, the bound system of two oppositely charged pions.
The leading quantum electrodynamic (QED) correction to the energy levels is of
the order of and due to electronic vacuum polarization. We analyze
further corrections due to the self-energy of the pions, and due to recoil
effects, and we give a complete result for the scalar-QED leading logarithmic
corrections which are due to virtual loops involving only the scalar
constituent particles (the pions); these corrections are of order for S states.Comment: 12 pages, LaTeX; references added (J. Phys. B, in press
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