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Related papers: Bethe Logarithms for Rydberg States: Numerical Val…

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We consider the role of high-lying Rydberg states of simple atomic systems such as $^1$H in setting constraints on physics beyond the Standard Model. We obtain highly accurate bound states energies for a hydrogen atom in the presence of an…

High Energy Physics - Phenomenology · Physics 2020-03-06 Matthew P. A. Jones , Robert M. Potvliege , Michael Spannowsky

The Rydberg formula along with the Ritz quantum defect ansatz has been a standard theoretical tool used in atomic physics since before the advent of quantum mechanics, yet this approach has remained limited by its non-relativistic…

Atomic Physics · Physics 2022-12-12 David M. Jacobs

Comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogen-like ions can yield information on values of fundamental constants and test theory. With the results of a calculation…

Atomic Physics · Physics 2009-02-02 U. D. Jentschura , P. J. Mohr , J. N. Tan , B. J. Wundt

We present a counting formula that relates the number of physical Bethe states of integrable models with a twisted boundary condition to the number of states in the untwisted or partially twisted limit.

Mathematical Physics · Physics 2025-04-30 Hongfei Shu , Peng Zhao , Rui-Dong Zhu , Hao Zou

We report a theoretical scheme using a B-spline basis set to improve the poor computational accuracy of circular Rydberg states of hydrogen atoms in the intermediate magnetic field. This scheme can produce high accuracy energy levels and…

Atomic Physics · Physics 2015-05-30 L. B. Zhao , B. C. Saha , M. L. Du

We present results on the self-energy correction to the energy levels of hydrogen and hydrogenlike ions. The self energy represents the largest QED correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We focus on the…

We use quantum electrodynamics and the Bethe-Salpeter equation to calculate the bound state energies for a two-particle system comprised of a spin-0 and spin-1/2 particle. We generalize our treatment to include the finite size of the…

Atomic Physics · Physics 2015-05-27 David Owen , Roger Barrett

The method and status of a study to provide numerical, high-precision values of the self-energy level shift in hydrogen and hydrogen-like ions is described. Graphs of the self energy in hydrogen-like ions with nuclear charge number between…

Quantum Physics · Physics 2009-11-10 Eric-Olivier Le Bigot , Ulrich D. Jentschura , Paul Indelicato , Peter J. Mohr

We calculate the one- and two-loop corrections of order alpha(Zalpha)^6 and alpha^2(Zalpha)^6 respectively, to the Lamb shift in hydrogen-like systems using the formalism of nonrelativistic quantum electrodynamics. We obtain general results…

Atomic Physics · Physics 2009-11-11 Ulrich D. Jentschura , Andrzej Czarnecki , Krzysztof Pachucki

We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe…

High Energy Physics - Theory · Physics 2009-01-22 M de Leeuw

We use Boij-S\"oderberg theory to provide some order of magnitude bounds on algebraic Betti numbers.

Commutative Algebra · Mathematics 2025-10-16 Daniel Erman

Analytic calculations of the Lamb shift represent a considerable challenge due to the size and the complexity of the expressions that occur in intermediate steps. In the current work, we present a method for the treatment of the bound-state…

High Energy Physics - Phenomenology · Physics 2007-05-23 Ulrich D. Jentschura

The R\'enyi entropies $R_{p}[\rho], 0<p<\infty$ of the probability density $\rho_{n,l,m}(\vec{r})$ of a physical system completely characterize the chemical and physical properties of the quantum state described by the three integer quantum…

Quantum Physics · Physics 2016-04-01 I. V. Toranzo , J. S. Dehesa

Interactions in atomic and molecular systems are dominated by electromagnetic forces and the theoretical framework must be in the quantum regime. The physical theory for the combination of quantum mechanics and electromagnetism, quantum…

Chemical Physics · Physics 2023-01-26 Edit Mátyus , Dávid Ferenc , Péter Jeszenszki , Ádám Margócsy

Bound states of the power-law and logarithmic potentials are calculated using a generalized pseudospectral method. The solution of the single-particle Schr\"odinger equation in a nonuniform and optimal spatial discretization offers accurate…

Quantum Physics · Physics 2015-06-16 Amlan K. Roy

In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…

Exactly Solvable and Integrable Systems · Physics 2011-02-16 A. Lima-Santos

The nature of the theory of circular Rydberg states of hydrogenlike ions allows highly-accurate predictions to be made for energy levels. In particular, uncertainties arising from the problematic nuclear size correction which beset low…

Atomic Physics · Physics 2010-03-30 U. D. Jentschura , P. J. Mohr , J. N. Tan

The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the…

High Energy Physics - Phenomenology · Physics 2013-05-30 Wolfgang Lucha , Franz F. Schoberl

The calculation of bound state properties using renormalization group techniques to compute the corresponding Regge trajectories is presented. In particular, we investigate the bound states in different charge sectors of a scalar theory…

High Energy Physics - Theory · Physics 2009-10-31 A. Weber , J. C. Lopez Vieyra , C. R. Stephens , S. Dilcher , P. O. Hess

We consider the $1s$ Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the…