9,008 research outputs found
Lamb Shift of 3P and 4P states and the determination of
The fine structure interval of P states in hydrogenlike systems can be
determined theoretically with high precision, because the energy levels of P
states are only slightly influenced by the structure of the nucleus. Therefore
a measurement of the fine structure may serve as an excellent test of QED in
bound systems or alternatively as a means of determining the fine structure
constant with very high precision. In this paper an improved analytic
calculation of higher-order binding corrections to the one-loop self energy of
3P and 4P states in hydrogen-like systems with low nuclear charge number is
presented. A comparison of the analytic results to the extrapolated numerical
data for high ions serves as an independent test of the analytic
evaluation. New theoretical values for the Lamb shift of the P states and for
the fine structure splittings are given.Comment: 33 pages, LaTeX, 4 tables, 4 figure
Lamb Shift in Light Muonic Atoms - Revisited
In connection with recent and proposed experiments, and new theoretical
results, my previous calculations of the Lamb shift in muonic hydrogen will be
reviewed and compared with other work. In addition, numerical results for
muonic deuterium and helium will be presented. Some previously neglected (but
very small) effects are included.Comment: 41 pages. This paper has appeared in Annals of Physics, vol. 327, pp
733-763 (2012). The present version has corrected several misprints, and
updated some references to take into account new result
Sixth-Order Vacuum-Polarization Contribution to the Lamb Shift of the Muonic Hydrogen
The sixth-order electron-loop vacuum-polarization contribution to the
Lamb shift of the muonic hydrogen ( bound
state) has been evaluated numerically. Our result is 0.007608(1) meV. This
eliminates the largest uncertainty in the theoretical calculation. Combined
with the proposed precision measurement of the Lamb shift it will lead to a
very precise determination of the proton charge radius.Comment: 4 pages, 5 figures the totoal LS number is change
Two-loop self-energy contribution to the Lamb shift in H-like ions
The two-loop self-energy correction is evaluated to all orders in Z\alpha for
the ground-state Lamb shift of H-like ions with Z >= 10, where Z is the nuclear
charge number and \alpha is the fine structure constant. The results obtained
are compared with the analytical values for the Z\alpha-expansion coefficients.
An extrapolation of the all-order numerical results to Z=1 is presented and
implications of our calculation for the hydrogen Lamb shift are discussed
Two-Loop Bethe Logarithms
We calculate the two-loop Bethe logarithm correction to atomic energy levels
in hydrogen-like systems. The two-loop Bethe logarithm is a low-energy quantum
electrodynamic (QED) effect involving multiple summations over virtual excited
atomic states. Although much smaller in absolute magnitude than the well-known
one-loop Bethe logarithm, the two-loop analog is quite significant when
compared to the current experimental accuracy of the 1S-2S transition: it
contributes -8.19 and -0.84 kHz for the 1S and the 2S state, respectively. The
two-loop Bethe logarithm has been the largest unknown correction to the
hydrogen Lamb shift to date. Together with the ongoing measurement of the
proton charge radius at the Paul Scherrer Institute its calculation will bring
theoretical and experimental accuracy for the Lamb shift in atomic hydrogen to
the level of 10^(-7).Comment: 4 pages, RevTe
A self-consistent value of the electric radius of the proton from the Lamb shift in muonic hydrogen
Recently a high-precision measurement of the Lamb shift in muonic hydrogen
has been performed. An accurate value of the proton charge radius can be
extracted from this datum with a high accuracy. To do that a sufficient
accuracy should be achieved also on the theoretical side, including an
appropriate treatment of higher-order proton-structure effects. Here we
consider a higher-order contribution of the finite size of the proton to the
Lamb shift in muonic hydrogen. Only model-dependent results for this correction
have been known up to date. Meantime, the involved models are not consistent
either with the existing experimental data on the electron-proton scattering or
with the value for the electric charge radius of the proton extracted from the
Lamb shift in muonic hydrogen. We consider the higher-order contribution of the
proton finite size in a model-independent way and eventually derive a
self-consistent value of the electric radius of the proton. The re-evaluated
value of the proton charge radius is found to be R_E=0.84022(56) fm
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