Radiative corrections to the magnetic-dipole transition amplitude in B-like ions

The one-electron quantum-electrodynamic corrections to the magnetic-dipole transition amplitude between the fine-structure levels (1s² 2s² 2p) ²P_3/2 - ²P_1/2 in boronlike ions are calculated to all orders in αZ. The results obtained serve for improving the theoretical accuracy of the lifetime of the (1s² 2s² 2p) ²P_3/2 level in boronlike argon.     

Vacuum polarization in muonic atoms: the Lamb shift at low and medium Z

In muonic atoms the Uehling potential (an effect of a free electronic vacuum polarization loop) is responsible for the leading contribution to the Lamb shift causing the splitting of states with Δn=0 and Δl≠0. Here we consider the Lamb shift in the leading nonrelativistic approximation, i.e., within an approach based on a certain Schr?dinger equation. That is valid for low and medium Z as long as (Zα)²≪1. The result is a function of a few parameters, including κ=Zαm_μ/m_e, n and l. We present various asymptotics and in particular we study a region of validity of asymptotics with large and small κ. Special attention is paid to circular states, which are considered in a limit of n≫1.     

Corrections to the wave function and the hyperfine structure in exotic atoms

We present an analytical evaluation of radiative corrections in exotic atoms induced by the one-loop electronic vacuum polarization. We evaluate corrections to the energy levels, to the wave function (at the origin) and to the hyperfine structure. We treat all corrections analytically within a non-relativistic approximation. Agreement is found with a few available numerical results. The analytical treatment allows to determine the asymptotic forms of the corrections in the limit of a small atomic radius, which for the atomic systems considered corresponds to a large mass of the constituent particle as compared to the electron mass. The asymptotics can be verified using the effective charge approach. Received: 28 January 1998 / Accepted: 13 March 1998     

Renormalization of the two-photon vacuum polarization and the self energy vacuum polarization for a tightly bound electron

The renormalization method of Bogoljubov-Parasiuk-Hepp-Zimmermann (BPHZ) is used in order to derive the renormalized energy shift due to the gauge invariant K?llén-Sabry diagram of the two-photon vacuum polarization (VPVP) as well as the self energy vacuum polarization S(VP)E beyond the Uehling approximation. It is outlined, that no outer renormalization is required for the two-photon vacuum polarization and that only the inner renormalization has to be accomplished. It is shown that the so-called nongauge invariant spurious term is absent for a wide class of vacuum polarization (VP) diagrams if one applies the widely used spherical expansion of bound and free-electron propagator. This simplifies significantly calculations in bound state quantum electrodynamics. As one result of our paper the use of the BPHZ-approach in bound state QED is established. Received 28 September 2001     

Lamb shift in muonic hydrogen—I. Verification and update of theoretical predictions

In view of the recently observed discrepancy of theory and experiment for muonic hydrogen [R. Pohl et al., Nature 466 (2010) 213], we reexamine the theory on which the quantum electrodynamic (QED) predictions are based. In particular, we update the theory of the 2P–2S Lamb shift, by calculating the self-energy of the bound muon in the full Coulomb + vacuum polarization (Uehling) potential. We also investigate the relativistic two-body corrections to the vacuum polarization shift, and we analyze the influence of the shape of the nuclear charge distribution on the proton radius determination. The uncertainty associated with the third Zemach moment 〈r³〉₂ in the determination of the proton radius from the measurement is estimated. An updated theoretical prediction for the 2S–2P transition is given.     

Lamb shift in muonic hydrogen—II. Analysis of the discrepancy of theory and experiment

Currently, both the g factor measurement of the muon as well as the Lamb shift 2S–2P measurement in muonic hydrogen are in disagreement with theory. Here, we investigate possible theoretical explanations, including proton structure effects and small modifications of the vacuum polarization potential. In particular, we investigate a conceivable small modification of the spectral function of vacuum polarization in between the electron and muon energy scales due to a virtual millicharged particle and due to an unstable vector boson originating from a hidden sector of an extended standard model. We find that a virtual millicharged particle which could explain the muonic Lamb shift discrepancy alters theoretical predictions for the muon anomalous magnetic moment by many standard deviations and therefore is in conflict with experiment. Also, we find no parameterizations of an unstable virtual vector boson which could simultaneously explain both “muonic” discrepancies without significantly altering theoretical predictions for electronic hydrogen, where theory and experiment currently are in excellent agreement. A process-dependent correction involving electron screening is evaluated to have the right sign and order-of-magnitude to explain the observed effect in muonic hydrogen. Additional experimental evidence from light muonic atoms and ions is needed in order to reach further clarification.     

Wave functions for two- and three-electron atoms and isoelectronic ions

We have developed simple wave functions for two- and three-electron atoms and ions, which have the correct structure when one of the electrons is far away, or when two of the particles are close to each other. These essentially parameter-free wave functions allow us to deduce fairly accurate values for the energies, , for multipolar polarizabilities of two-electron atoms and ions, and for the coefficients of the asymptotic density. Received: 5 August 1998 / Received in final form: 27 November 1998     

QED and relativistic corrections in superheavy elements

In this paper we review the different relativistic and QED contributions to energies, ionic radii, transition probabilities and Landé g-factors in super-heavy elements, with the help of the MultiConfiguration Dirac-Fock method (MCDF). The effects of taking into account the Breit interaction to all orders by including it in the self-consistent field process are demonstrated. State of the art radiative corrections are included in the calculation and discussed. We also study the non-relativistic limit of MCDF calculation and find that the non-relativistic offset can be unexpectedly large.     

An analysis of states in the phase space: the diatomic molecules

Summary The paper concerns a theoretical model to calculate the number of allowed states for the electrons in the diatomic molecules through the quantum-statistical analysis of the phase space. The approach is a straightforward extension of that already discussed in the case of many-electron atoms. Simple formulae are derived that enable to calculate the dissociation energy, bond length and vibrational frequency of diatomic molecules in a good agreement with the experimental data.     

Nuclear size correction to the hyperfine splitting in low- hydrogen-like atoms

The finite nuclear size effect on the hyperfine splitting of low-Z hydrogen-like atoms is studied in the external field approximation. A simple non-relativistic formula is proposed which expresses the nuclear size correction to the hyperfine splitting in terms of moments of the nuclear charge and magnetization distribution. The numerical results obtained via this formula are compared with corresponding results derived by means of the Zemach formula. A relativistic formula for the nuclear size correction to the hyperfine splitting is also derived. Received 18 March 2002 / Received in final form 14 November 2002 Published online 28 January 2003 RID="a" ID="a"e-mail: plunien@physik.tu-dresden.de     

Spectral patterns and ultrafast dynamics in planar acetylene

A diabatic correlation diagram procedure is used to classify energy and intensity patterns in a planar model for coupled stretches and bends of acetylene using an effective spectroscopic fitting Hamiltonian. Analysis with polyad phase spheres accounts for the observed patterns in terms of classical phase space structure and bifurcations of the normal modes. Received 29 August 2000 and Received in final form 14 September 2000     

A simple model potential description of the alkaline earth isoelectronic sequences

We have developed a simple model potential with a hard core and the correct large-r Coulombic behaviour, to describe the interaction of an electron with a closed shell. One has an exact, analytic ground state wave function for this potential. This potential is used to develop two-electron perturbed and unperturbed wave functions, with the correct asymptotic behaviour and cusp conditions. These wave functions allow us to obtain accurate values for the two-electron energies, polarisabilities, hyperpolarisabilities, and dispersion coefficients of alkaline earth sequences. Many of these results are the only ones available in the literature. Received 29 July 1999 and Received in final form 16 November 1999     

The quantum mechanical two-Coulomb-centre problem in the Dirac equation framework in 2+1 dimensions

With the help of perturbation theory the asymptotic expansions (at small and large internuclear distances R) of the eigenvalues (potential curves) E(R) of the two-Coulomb-centre problem in 2+1 dimensions are obtained. We compare the results obtained with the data from similar approximation for two-Coulomb-centre problem in 3+1 dimensions.     

Optimized effective potential energies and ionization potentials for the atoms Li to Ra

A systematic application of the optimized effective potential equations for atoms in both the non-relativistic and relativistic cases is carried out. The ground state energy and the ionization potential of the atoms Li through to Ra is obtained. In the relativistic case, a trial wave function including all of the jj configurations that contribute to the ground state term within the electronic configuration are included. The results are compared with the corresponding Hartree-Fock and Dirac-Hartree-Fock values.     

Electron-pair densities of group 2 atoms in their and terms

Electron-pair intracule (relative motion) and extracule (center-of-mass motion) densities are studied in both position and momentum spaces for the ¹ P and ³ P terms of the group 2 atoms Be (atomic number Z =4), Mg (Z =12), Ca (Z =20), Sr (Z =38), Ba (Z =56), and Ra (Z =88). In position space, the ¹ P - ³ P difference in the intracule densities shows that the probability of a small interelectronic distance is larger in the triplet for all the six atoms, as reported for the lightest Be atom in the literature. The position-space extracule density clarifies that the triplet electrons are more likely to be at opposite positions with respect to the nucleus than the singlet electrons for all the atoms. In momentum space, the singlet generally has a larger probability of a small relative momentum between two electrons as a na?ve manifestation of the Fermi hole in the triplet. The extracule density in momentum space shows that the ¹ P term has a distribution larger in a large center-of-mass momentum region than the ³ P term. Received: 26 August 1998 / Received in final form: 1 February 1999     

Relativistic quantum similarities in atoms in position and momentum spaces

A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr (Z=1-103). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations.     

Transition energies of atomic lawrencium

Transition energies of the superheavy element lawrencium, including the ionization potential, excitation energies and electron affinities, are calculated by the intermediate Hamiltonian coupled cluster method. A large basis set (37s31p26d21f16g11h6i) is used, as well as an extensive P space (6s5p4d2f1g). The outer 43 electrons are correlated. Accuracy is monitored by applying the same approach to lutetium, the lighter homologue of Lr, and comparing with experimentally known energies. QED corrections are included. The main goal is to predict excitation energies, in anticipation of planned spectroscopy of Lr. The ground state of Lr is , unlike the of Lu. Predicted Lr excitations with large transition moments in the prime range for the planned experiment, 20 000–30 000 cm^-1, are 7p→8s at 20 100 cm^-1 and 7p→7d at 28 100 cm^-1. The average absolute error of 20 excitation energies of Lu is 423 cm ^-1, and the error limits for Lr are put at 700 cm^-1. The two electron affinities measured recently for Lu are reproduced within 55 cm^-1, and a third bound state of Lu^- is predicted.     

Electron capture into few-electron heavy ions: Independent particle model

We apply the density matrix theory to re-investigate the radiative electron capture into heavy ions with one valence electron. Attention has been paid particularly to the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. Simple method, based on an independent particle model, which takes into account the Pauli principle, is proposed for evaluating the alignment of the excited ionic states. By making use of this method, detailed calculations are performed for electron capture into (initially) hydrogen-like and lithium-like europium, gold and uranium ions, and are compared with the results of the multiconfiguration Dirac-Fock approach.As seen from the calculations and from the comparison with available experimental results, the independent particle model provides a good estimate for the alignment parameters of few-electron heavy ions. Therefore, our simple model may help to understand the basic properties of the X-ray emission from heavy, few-electron ions without the need for invoking sophisticated MCDF calculations.     

Application of B-splines finite basis sets to relativistic two-photon decay rates of level in hydrogenic ions

A theoretical study of the one- and two-photon spontaneous emission rates from the 2 s1/2 state of one-electron ions is presented. High-precision values of the relativistic emission rates for ions with nuclear charge Z up to 100 are obtained through the use of finite basis sets for the Dirac equation constructed from B-splines. Furthermore, we analyze the influence of the inclusion of quantum electrodynamics corrections in the initial and final state energies. Received: 6 January 1998 / Accepted: 31 March 1998