244 research outputs found

    Self-energy values for P states in hydrogen and low-Z hydrogenlike ions

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    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

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    The correlation relationship between the deuteron asymptotic normalization constant, ASA_{S}, and the triplet np scattering length, ata_{t}, is investigated. It is found that 99.7% of the asymptotic constant ASA_{S} is determined by the scattering length ata_{t}. It is shown that the linear correlation relationship between the quantities AS2A_{S}^{-2} and 1/at1/a_{t} provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant ASA_{S} and for the root-mean-square deuteron radius rdr_{d}, the results obtained with the experimental value recommended at present for the triplet scattering length ata_{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 (ata_{t}, rtr_{t}, PtP_{t}) and for the deuteron characteristics (ASA_{S}, rdr_{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

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    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

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    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 α\alpha

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    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 α\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 ZZ is presented. A comparison of the analytic results to the extrapolated numerical data for high ZZ 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

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    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

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    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

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    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

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    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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