https://biblio.ugent.be/publication/685594/file/1130605.pdf

Review of Particle Physics

I will first review the experimental limits placed on the oblique correction parameters S and T. Then, I will discuss how the value of S can be estimated for running and walking technicolor theories.

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Estimation of oblique electroweak corrections

/pdf/review-of-particle-physics-1996-1997-jeg703df6k.pdf

Review of Particle Physics, 1996-1997

Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

One of the most significant developments in computational atomic and molecular physics in recent years has been the introduction of B-spline basis sets in calculations of atomic and molecular structure and dynamics. B-splines were introduced in applied mathematics more than 50 years ago, but it has been in the 1990s, with the advent of powerful computers, that the number of applications has grown exponentially. In this review we present the main properties of B-splines and discuss why they are useful to solve different problems in atomic and molecular physics. We provide an extensive reference list of theoretical works that have made use of B-spline basis sets up to 2000. Among these, we have focused on those applications that have led to the discovery of new interesting phenomena and pointed out the reasons behind the success of the approach.

https://iopscience.iop.org/article/10.1088/0034-4885/64/12/205/pdf

Applications of B-splines in atomic and molecular physics

A procedure is given for constructing basis sets for the radial Dirac equation from B splines. The resulting basis sets, which include negative-energy states in a natural way, permit the accurate evaluation of the multiple sums over intermediate states occurring in relativistic many-body calculations. Illustrations are given for the Coulomb-field Dirac equation and tests of the resulting basis sets are described. As an application, relativistic corrections to the second-order correlation energy in helium are calculated. Another application is given to determine the spectrum of thallium (where finite--nuclear-size effects are important) in a model potential. Construction of B-spline basis sets for the Dirac-Hartree-Fock equations is described and the resulting basis sets are applied to study the cesium spectrum.

Finite basis sets for the Dirac equation constructed from B splines

All-order methods recently developed for high-accuracy calculation of energies and matrix elements in Li are extended and applied to cesium. We employ a relativistic, linearized, coupled-cluster formalism, incorporating single, double, and an important subset of triple excitations. A coupled-cluster formulation of the matrix element of a one-body operator, incorporating the random-phase approximation exactly, is used to calculate hyperfine constants and transition-matrix elements. We find agreement with experiment at the 0.5% level or better for ionization energies and dipole-matrix elements, and at the 1% level for hyperfine constants. Modifications of the method that have the potential of higher accuracy are discussed.

Relativistic all-order calculations of energies and matrix elements in cesium

A many-body calculation of the parity-nonconserving amplitude for the 6${\mathit{s}}_{1/2}$\ensuremath{\rightarrow}7${\mathit{s}}_{1/2}$ transition in atomic cesium with an error of order 1% is presented, ${\mathit{E}}_{\mathrm{PNC}}$=-0.906[9] (${\mathit{Q}}_{\mathit{W}}$/-N)i\ensuremath{\Vert}e\ensuremath{\Vert}${\mathit{a}}_{0}$\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}11}$. Using this result to determine ${\mathit{Q}}_{\mathit{W}}$ from high-precision measurements of the transition leads to a quantitative test of the standard model. The various sources contributing to this transition are discussed and their uncertainties estimated. A discussion of radiative corrections with emphasis on the role of the top-quark mass is given.

High-accuracy calculation of the 6 s 1 / 2 →7 s 1 / 2 parity-nonconserving transition in atomic cesium and implications for the standard model

Energies of 3s and 3p states of sodiumlike ions are calculated from Z=11 to Z=92 starting from a Dirac-Fock potential and including second- and third-order Coulomb correlation corrections, the lowest-order Breit interaction with retardation treated exactly, second- and third-order correlation corrections to the Breit interaction, and corrections for reduced mass and mass polarization. The calculated energies are compared to measured energies to determine the size of the omitted quantum electrodynamics corrections.

Many-body perturbation-theory calculations of energy levels along the sodium isoelectronic sequence.

Valence removal energies, hyperfine constants, and E1 transition amplitudes are calculated for the 2${s}_{1/2}$, 2${p}_{1/2}$, 2${p}_{3/2}$, and 3${s}_{1/2}$ states of Li and ${\mathrm{Be}}^{+}$. This calculation is an extension of earlier second- and third-order many-body perturbation theory (MBPT) calculations, in which now an infinite subset of MBPT terms is evaluated using all-order methods. Agreement with experiment at the 0.01% level for energies, and at the 0.1% level for matrix elements, is found. Issues involved with those higher-order terms omitted by the technique are discussed.

S. A. Blundell

Papers

Finite basis sets for the Dirac equation constructed from B splines

Relativistic all-order calculations of energies and matrix elements in cesium

High-accuracy calculation of the 6 s 1 / 2 →7 s 1 / 2 parity-nonconserving transition in atomic cesium and implications for the standard model

Many-body perturbation-theory calculations of energy levels along the sodium isoelectronic sequence.

Relativistic all-order calculations of energies and matrix elements for Li and Be+