244 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, $A_{S}$, and the triplet np scattering length, $a_{t}$, is
investigated. It is found that 99.7% of the asymptotic constant $A_{S}$ is
determined by the scattering length $a_{t}$. It is shown that the linear
correlation relationship between the quantities $A_{S}^{-2}$ and $1/a_{t}$
provides a good test of correctness of various models of nucleon-nucleon
interaction. It is revealed that, for the normalization constant $A_{S}$ and
for the root-mean-square deuteron radius $r_{d}$, the results obtained with the
experimental value recommended at present for the triplet scattering length
$a_{t}$ 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 ($a_{t}$, $r_{t}$, $P_{t}$) and for the
deuteron characteristics ($A_{S}$, $r_{d}$), results that comply well with
experimental data.Comment: 19 pages, 1 figure, To be published in Physics of Atomic Nucle

### 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

### 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 $\alpha$

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 $\alpha$ 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 $Z$ is
presented. A comparison of the analytic results to the extrapolated numerical
data for high $Z$ 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

### Deuteron Magnetic and Quadrupole Moments with a Poincar\'e Covariant Current Operator in the Front-Form Dynamics

The deuteron magnetic and quadrupole moments are unambiguosly determined
within the front-form Hamiltonian dynamics, by using a new current operator
which fulfills Poincar\'e, parity and time reversal covariance, together with
hermiticity and the continuity equation. For both quantities the usual
disagreement between theoretical and experimental results is largely removed.Comment: To appear in Phys. Rev. Let

### Precise Neutron Magnetic Form Factors

Precise data on the neutron magnetic form factor G_{mn} have been obtained
with measurements of the ratio of cross sections of D(e,e'n) and D(e,e'p) up to
momentum transfers of Q^2 = 0.9 (GeV/c)^2. Data with typical uncertainties of
1.5% are presented. These data allow for the first time to extract a precise
value of the magnetic radius of the neutron.Comment: 10 pages, 2 figures, submitted to Physics Letters

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