Resolving all-order method convergence problems for atomic physics applications

The development of the relativistic all-order method where all single, double, and partial triple excitations of the Dirac-Hartree-Fock wave function are included to all orders of perturbation theory led to many important results for study of fundamental symmetries, development of atomic clocks, ultracold atom physics, and others, as well as provided recommended values of many atomic properties critically evaluated for their accuracy for large number of monovalent systems. This approach requires iterative solutions of the linearized coupled-cluster equations leading to convergence issues in some cases where correlation corrections are particularly large or lead to an oscillating pattern. Moreover, these issues also lead to similar problems in the CI+all-order method for many-particle systems. In this work, we have resolved most of the known convergence problems by applying two different convergence stabilizer methods, reduced linear equation (RLE) and direct inversion of iterative subspace (DIIS). Examples are presented for B, Al, Zn$^+$, and Yb$^+$. Solving these convergence problems greatly expands the number of atomic species that can be treated with the all-order methods and is anticipated to facilitate many interesting future applications

Relativistic calculations of pionic and kaonic atoms hyperfine structure

We present the relativistic calculation of the hyperfine structure in pionic and kaonic atoms. A perturbation method has been applied to the Klein-Gordon equation to take into account the relativistic corrections. The perturbation operator has been obtained \textit{via} a multipole expansion of the nuclear electromagnetic potential. The hyperfine structure of pionic and kaonic atoms provide an additional term in the quantum electrodynamics calculation of the energy transition of these systems. Such a correction is required for a recent measurement of the pion mass

A theoretical study of the C- 4So_3/2 and 2Do_{3/2,5/2} bound states and C ground configuration: fine and hyperfine structures, isotope shifts and transition probabilities

This work is an ab initio study of the 2p3 4So_3/2, and 2Do_{3/2,5/2} states of C- and 2p2 3P_{0,1,2}, 1D_2, and 1S_0 states of neutral carbon. We use the multi-configuration Hartree-Fock approach, focusing on the accuracy of the wave function itself. We obtain all C- detachment thresholds, including correlation effects to about 0.5%. Isotope shifts and hyperfine structures are calculated. The achieved accuracy of the latter is of the order of 0.1 MHz. Intra-configuration transition probabilities are also estimated.Comment: 15 pages, 2 figures, 12 table

Tangential Touch between the Free and the Fixed Boundary in a Semilinear Free Boundary Problem in Two Dimensions

The main result of this paper concerns the behavior of a free boundary arising from a minimization problem, close to the fixed boundary in two dimensions

Third-order many-body perturbation theory calculations for the beryllium and magnesium isoelectronic sequences

Relativistic third-order MBPT is applied to obtain energies of ions with two valence electrons in the no virtual-pair approximation (NVPA). A total of 302 third-order Goldstone diagrams are organized into 12 one-body and 23 two-body terms. Only third-order two-body terms and diagrams are presented here, owing to the fact that the one-body terms are identical to the previously studied third-order terms in monovalent ions. Dominant classes of diagrams are identified. The model potential is a Dirac-Hartree-Fock $V^{N-2}$ potential, and B-spline basis functions in a cavity of finite radius are employed in the numerical calculations. The Breit interaction is taken into account through second order of perturbation theory and the lowest-order Lamb shift is also evaluated. Sample calculations are performed for berylliumlike ions with Z = 4--7, and for the magnesiumlike ion P IV. The third-order energies are in excellent agreement with measurement with an accuracy at 0.2% level for the cases considered. Comparisons are made with previous second-order MBPT results and with other calculations. The third-order energy correction is shown to be significant, improving second-order correlation energies by an order of magnitude

State-insensitive trapping of Rb atoms: linearly versus circularly polarized lights

We study the cancellation of differential ac Stark shifts in the 5s and 5p states of rubidium atom using the linearly and circularly polarized lights by calculating their dynamic polarizabilities. Matrix elements were calculated using a relativistic coupled-cluster method at the single, double and important valence triple excitations approximation including all possible non-linear correlation terms. Some of the important matrix elements were further optimized using the experimental results available for the lifetimes and static polarizabilities of atomic states. "Magic wavelengths" are determined from the differential Stark shifts and results for the linearly polarized light are compared with the previously available results. Possible scope of facilitating state-insensitive optical trapping schemes using the magic wavelengths for circularly polarized light are discussed. Using the optimized matrix elements, the lifetimes of the 4d and 6s states of this atom are ameliorated.Comment: 13 pages, 13 tables and 4 figure

Exploring Biorthonormal Transformations of Pair-Correlation Functions in Atomic Structure Variational Calculations

Multiconfiguration expansions frequently target valence correlation and correlation between valence electrons and the outermost core electrons. Correlation within the core is often neglected. A large orbital basis is needed to saturate both the valence and core-valence correlation effects. This in turn leads to huge numbers of CSFs, many of which are unimportant. To avoid the problems inherent to the use of a single common orthonormal orbital basis for all correlation effects in the MCHF method, we propose to optimize independent MCHF pair-correlation functions (PCFs), bringing their own orthonormal one-electron basis. Each PCF is generated by allowing single- and double- excitations from a multireference (MR) function. This computational scheme has the advantage of using targeted and optimally localized orbital sets for each PCF. These pair-correlation functions are coupled together and with each component of the MR space through a low dimension generalized eigenvalue problem. Nonorthogonal orbital sets being involved, the interaction and overlap matrices are built using biorthonormal transformation of the coupled basis sets followed by a counter-transformation of the PCF expansions. Applied to the ground state of beryllium, the new method gives total energies that are lower than the ones from traditional CAS-MCHF calculations using large orbital active sets. It is fair to say that we now have the possibility to account for, in a balanced way, correlation deep down in the atomic core in variational calculations

Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation

The connection between many-body theory (MBPT)--in perturbative and non-perturbative form--and quantum-electrodynamics (QED) is reviewed for systems of two fermions in an external field. The treatment is mainly based upon the recently developed covariant-evolution-operator method for QED calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a structure quite akin to that of many-body perturbation theory. At the same time this procedure is closely connected to the S-matrix and the Green's-function formalisms and can therefore serve as a bridge between various approaches. It is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A Bloch equation in commutator form that can be used for an "extended" or quasi-degenerate model space is derived. It has the same relation to the BS equation as has the standard Bloch equation to the ordinary Schroedinger equation and can be used to generate a perturbation expansion compatible with the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic

The electron electric dipole moment enhancement factors of Rubidium and Caesium atoms

The enhancement factors of the electric dipole moment (EDM) of the ground states of two paramagnetic atoms; rubidium (Rb) and caesium (Cs) which are sensitive to the electron EDM are computed using the relativistic coupled-cluster theory and our results are compared with the available calculations and measurements. The possibility of improving the limit for the electron EDM using the results of our present work is pointed out.Comment: AISAMP7 Conference paper, Accepted in Journal of Physics: Conference Series: 200

Precision Measurement of the p(e,e \u27 p)pi(0) Reaction at Threshold

New results are reported from a measurement of pi(0) electroproduction near threshold using the p(e , e\u27p)pi(0) reaction. The experiment was designed to determine precisely the energy dependence of s- and p-wave electromagnetic multipoles as a stringent test of the predictions of chiral perturbation theory (ChPT). The data were taken with an electron beam energy of 1192 MeV using a two-spectrometer setup in Hall A at Jefferson Lab. For the first time, complete coverage of the. phi*(pi) and. theta*(pi) angles in the p pi(0) center of mass was obtained for invariant energies above threshold from 0.5 up to 15 MeV. The 4-momentum transfer Q(2) coverage ranges from 0.05 to 0.155 (GeV/c)(2) in fine steps. A simple phenomenological analysis of our data shows strong disagreement with p-wave predictions from ChPT for Q(2) \u3e 0.07 (GeV/c)(2), while the s-wave predictions are in reasonable agreement