Third-order relativistic many-body calculations of energies and lifetimes of levels along the silver isoelectronic sequence

Energies of 5l_j (l= s, p, d, f, g) and 4f_j states in neutral Ag and Ag-like ions with nuclear charges Z = 48 - 100 are calculated using relativistic many-body perturbation theory. Reduced matrix elements, oscillator strengths, transition rates and lifetimes are calculated for the 17 possible 5l_j-5l'_{j'} and 4f_j-5l_{j'} electric-dipole transitions. Third-order corrections to energies and dipole matrix elements are included for neutral Ag and for ions with Z60. Comparisons are made with available experimental data for transition energies and lifetimes. Correlation energies and transition rates are shown graphically as functions of nuclear charge Z for selected cases. These calculations provide a theoretical benchmark for comparison with experiment and theory.Comment: 8 page

Finite nuclear size and Lamb shift of p-wave atomic states

We consider corrections to the Lamb shift of p-wave atomic states due to the finite nuclear size (FNS). In other words, these are radiative corrections to the atomic isotop shift related to FNS. It is shown that the structure of the corrections is qualitatively different from that for s-wave states. The perturbation theory expansion for the relative correction for a $p_{1/2}$-state starts from $\alpha\ln(1/Z\alpha)$-term, while for $s_{1/2}$-states it starts from $Z\alpha^2$ term. Here $\alpha$ is the fine structure constant and $Z$ is the nuclear charge. In the present work we calculate the $\alpha$-terms for $2p$-states, the result for $2p_{1/2}$-state reads $(8\alpha/9\pi)[\ln(1/(Z\alpha)^2)+0.710]$. Even more interesting are $p_{3/2}$-states. In this case the ``correction'' is by several orders of magnitude larger than the ``leading'' FNS shift.Comment: 4 pages, 2 figure

Modelling the electric field applied to a tokamak

The vector potential for the Ohmic heating coil system of a tokamak is obtained in semi-analytical form. Comparison is made to the potential of a simple, finite solenoid. In the quasi-static limit, the time rate of change of the potential determines the induced electromotive force through the Maxwell-Lodge effect. Discussion of the gauge constraint is included.Comment: 13 pages, 7 figures, final versio

Vacuum polarization calculations for hydrogenlike and alkalilike ions

Complete vacuum polarization calculations incorporating finite nuclear size are presented for hydrogenic ions with principal quantum numbers n=1-5. Lithiumlike, sodiumlike, and copperlike ions are also treated starting with Kohn-Sham potentials, and including first-order screening corrections. In both cases dominant Uehling terms are calculated with high accuracy, and smaller Wichmann- Kroll terms are obtained using numerical electron Green's functions.Comment: 23 pages, 1 figur

Endometriosis classification, staging and reporting systems: a review on the road to a universally accepted endometriosis classification,

BACKGROUND: In the field of endometriosis, several classification, staging and reporting systems have been developed. However, endometriosis classification, staging and reporting systems that have been published and validated for use in clinical practice have not been systematically reviewed up to now. OBJECTIVES: The aim of the current review is to provide a historical overview of these different systems based on an assessment of published studies. MATERIALS AND METHODS: A systematic Pubmed literature search was performed. Data were extracted and summarised. RESULTS: Twenty-two endometriosis classification, staging and reporting systems have been published between 1973 and 2021, each developed for specific and different purposes. There is still no international agreement on how to describe the disease. Studies evaluating different systems are summarised showing a discrepancy between the intended and the evaluated purpose, and a general lack of validation data confirming a correlation with pain symptoms or quality of life for any of the current systems. A few studies confirm the value of the Enzian system for surgical description of deep endometriosis. With regards to infertility, the endometriosis fertility index has been confirmed valid for its intended purpose. CONCLUSIONS: Of the 22 endometriosis classification, staging and reporting systems identified in this historical overview, only a few have been evaluated, in 46 studies, for the purpose for which they were developed. It can be concluded that there is no international agreement on how to describe endometriosis or how to classify it, and that most classification/staging systems show no or very little correlation with patient outcomes. WHAT IS NEW? This overview of existing systems is a first step in working towards a universally accepted endometriosis classification

Finite nuclear size effect on Lamb shift of s1/2, p1/2, and p3/2 atomic states

We consider one-loop self-energy and vacuum polarization radiative corrections to the shift of atomic energy level due to finite nuclear size. Analytic expressions for vacuum polarization corrections are derived. For the self-energy of p1/2 and p3/2 states in addition to already known terms we derive next-to-leading nonlogarithmic Z\alpha-terms. Together with contributions obtained earlier the terms derived in the present work give explicit analytic expressions for s1/2 and p1/2 corrections which agree with results of previous numerical calculations up to Z=100 (Z is the nuclear charge number). We also show that the finite nuclear size radiative correction for a p3/2 state is not small compared to the similar correction for a p1/2 state at least for small Z.Comment: 12 pages, 7 figure

Combined CI+MBPT calculations of energy levels and transition amplitudes in Be, Mg, Ca, and Sr

Configuration interaction (CI) calculations in atoms with two valence electrons, carried out in the V(N-2) Hartree-Fock potential of the core, are corrected for core-valence interactions using many-body perturbation theory (MBPT). Two variants of the mixed CI+MBPT theory are described and applied to obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr

Radiative Corrections to One-Photon Decays of Hydrogenic Ions

Radiative corrections to the decay rate of n=2 states of hydrogenic ions are calculated. The transitions considered are the M1 decay of the 2s state to the ground state and the E1(M2) decays of the $2p_{1/2}$ and $2p_{3/2}$ states to the ground state. The radiative corrections start in order $\alpha (Z \alpha)^2$, but the method used sums all orders of $Z\alpha$. The leading $\alpha (Z\alpha)^2$ correction for the E1 decays is calculated and compared with the exact result. The extension of the calculational method to parity nonconserving transitions in neutral atoms is discussed.Comment: 22 pages, 2 figure