299 research outputs found
Self-energy values for P states in hydrogen and low-Z hydrogenlike ions
We describe a nonperturbative (in Zalpha) numerical evaluation of the
one-photon electron self energy for 3P_{1/2}, 3P_{3/2}, 4P_{1/2} and 4P_{3/2}
states in hydrogenlike atomic systems with charge numbers Z=1 to 5. The
numerical results are found to be in agreement with known terms in the
expansion of the self energy in powers of Zalpha and lead to improved
theoretical predictions for the self-energy shift of these states.Comment: 3 pages, RevTe
Correlation Between the Deuteron Characteristics and the Low-energy Triplet np Scattering Parameters
The correlation relationship between the deuteron asymptotic normalization
constant, , and the triplet np scattering length, , is
investigated. It is found that 99.7% of the asymptotic constant is
determined by the scattering length . It is shown that the linear
correlation relationship between the quantities and
provides a good test of correctness of various models of nucleon-nucleon
interaction. It is revealed that, for the normalization constant and
for the root-mean-square deuteron radius , the results obtained with the
experimental value recommended at present for the triplet scattering length
are exaggerated with respect to their experimental counterparts. By
using the latest experimental phase shifts of Arndt et al., we obtain, for the
low-energy scattering parameters (, , ) and for the
deuteron characteristics (, ), results that comply well with
experimental data.Comment: 19 pages, 1 figure, To be published in Physics of Atomic Nucle
Two-Loop Bethe Logarithms for Higher Excited S Levels
Processes mediated by two virtual low-energy photons contribute quite
significantly to the energy of hydrogenic S states. The corresponding level
shift is of the order of (alpha/pi)^2 (Zalpha)^6 m_e c^2 and may be ascribed to
a two-loop generalization of the Bethe logarithm. For 1S and 2S states, the
correction has recently been evaluated by Pachucki and Jentschura [Phys. Rev.
Lett. vol. 91, 113005 (2003)]. Here, we generalize the approach to higher
excited S states, which in contrast to the 1S and 2S states can decay to P
states via the electric-dipole (E1) channel. The more complex structure of the
excited-state wave functions and the necessity to subtract P-state poles lead
to additional calculational problems. In addition to the calculation of the
excited-state two-loop energy shift, we investigate the ambiguity in the energy
level definition due to squared decay rates.Comment: 14 pages, RevTeX, to appear in Phys. Rev.
Convergence of the Magnus series
The Magnus series is an infinite series which arises in the study of linear
ordinary differential equations. If the series converges, then the matrix
exponential of the sum equals the fundamental solution of the differential
equation. The question considered in this paper is: When does the series
converge? The main result establishes a sufficient condition for convergence,
which improves on several earlier results.Comment: 11 pages; v2: added justification for conjecture, minor
clarifications and correction
The Magnus expansion and some of its applications
Approximate resolution of linear systems of differential equations with
varying coefficients is a recurrent problem shared by a number of scientific
and engineering areas, ranging from Quantum Mechanics to Control Theory. When
formulated in operator or matrix form, the Magnus expansion furnishes an
elegant setting to built up approximate exponential representations of the
solution of the system. It provides a power series expansion for the
corresponding exponent and is sometimes referred to as Time-Dependent
Exponential Perturbation Theory. Every Magnus approximant corresponds in
Perturbation Theory to a partial re-summation of infinite terms with the
important additional property of preserving at any order certain symmetries of
the exact solution. The goal of this review is threefold. First, to collect a
number of developments scattered through half a century of scientific
literature on Magnus expansion. They concern the methods for the generation of
terms in the expansion, estimates of the radius of convergence of the series,
generalizations and related non-perturbative expansions. Second, to provide a
bridge with its implementation as generator of especial purpose numerical
integration methods, a field of intense activity during the last decade. Third,
to illustrate with examples the kind of results one can expect from Magnus
expansion in comparison with those from both perturbative schemes and standard
numerical integrators. We buttress this issue with a revision of the wide range
of physical applications found by Magnus expansion in the literature.Comment: Report on the Magnus expansion for differential equations and its
applications to several physical problem
QED Calculation of E1M1 and E1E2 Transition Probabilities in One-Electron Ions with Arbitrary Nuclear Charge
The quantum electrodynamical theory of the two-photon transitions in
hydrogenlike ions is presented. The emission probability for 2s1/2 -> 2E1+1s1/2
transitions is calculated and compared to the results of the previous
calculations. The emission probabilities 2p12 -> E1E2+1s1/2 and 2p1/2 ->
E1M1+1s1/2 are also calculated for the nuclear charge Z values 1-100. This is
the first calculation of the two latter probabilities. The results are given in
two different gauges.Comment: 14 pages, 4 tables, 1 figur
Modeling Cluster Production at the AGS
Deuteron coalescence, during relativistic nucleus-nucleus collisions, is
carried out in a model incorporating a minimal quantal treatment of the
formation of the cluster from its individual nucleons by evaluating the overlap
of intial cascading nucleon wave packets with the final deuteron wave function.
In one approach the nucleon and deuteron center of mass wave packet sizes are
estimated dynamically for each coalescing pair using its past light-cone
history in the underlying cascade, a procedure which yields a parameter free
determination of the cluster yield. A modified version employing a global
estimate of the deuteron formation probability, is identical to a general
implementation of the Wigner function formalism but can differ from the most
frequent realisation of the latter. Comparison is made both with the extensive
existing E802 data for Si+Au at 14.6 GeV/c and with the Wigner formalism. A
globally consistent picture of the Si+Au measurements is achieved. In light of
the deuteron's evident fragility, information obtained from this analysis may
be useful in establishing freeze-out volumes and help in heralding the presence
of high-density phenomena in a baryon-rich environment.Comment: 31 pages REVTeX, 19 figures (4 oversized included as JPEG). For full
postscript figures (LARGE): contact [email protected]
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
Relativistic and Radiative Energy Shifts for Rydberg States
We investigate relativistic and quantum electrodynamic effects for
highly-excited bound states in hydrogenlike systems (Rydberg states). In
particular, hydrogenic one-loop Bethe logarithms are calculated for all
circular states (l = n-1) in the range 20 <= n <= 60 and successfully compared
to an existing asymptotic expansion for large principal quantum number n. We
provide accurate expansions of the Bethe logarithm for large values of n, for
S, P and circular Rydberg states. These three expansions are expected to give
any Bethe logarithms for principal quantum number n > 20 to an accuracy of five
to seven decimal digits, within the specified manifolds of atomic states.
Within the numerical accuracy, the results constitute unified, general formulas
for quantum electrodynamic corrections whose validity is not restricted to a
single atomic state. The results are relevant for accurate predictions of
radiative shifts of Rydberg states and for the description of the recently
investigated laser-dressed Lamb shift, which is observable in a strong
coherent-wave light field.Comment: 8 pages; RevTeX
Extension of the sum rule for the transition rates between multiplets to the multiphoton case
The sum rule for the transition rates between the components of two
multiplets, known for the one-photon transitions, is extended to the
multiphoton transitions in hydrogen and hydrogen-like ions. As an example the
transitions 3p-2p, 4p-3p and 4d-3d are considered. The numerical results are
compared with previous calculations.Comment: 10 pages, 4 table
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