Matrix Elements for Many-Electron Atoms: Electrostatic Interaction Energies for One-Open-Shell Configurations

1974 ◽  
Vol 52 (3) ◽  
pp. 238-240
Author(s):  
J. Karwowski ◽  
S. Fraga
Keyword(s):  
Electrostatic Interaction ◽  
Open Shell ◽  
Numerical Results ◽  
Interaction Energies ◽  
Matrix Elements ◽  
The Matrix ◽  
Racah Parameters

The matrix elements of the electrostatic interaction have been determined and tabulated, in terms of Slater–Condon integrals or Racah parameters, for the states arising from pN, dN, fN, and gN configurations; in particular, the results for gN configurations have never been determined before. The effect of the interaction between states of the same symmetry and multiplicity, arising from a given configuration, is exemplified with numerical results for Pr, 4f36s2.

scholarly journals Non-local matrix elements in B(s) → {K(*), ϕ}ℓ+ℓ−

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Nico Gubernari ◽  
Danny van Dyk ◽  
Javier Virto
Keyword(s):  
Light Cone ◽  
Truncation Error ◽  
Sum Rules ◽  
Form Factors ◽  
Numerical Results ◽  
Matrix Elements ◽  
Current State ◽  
Theoretical Predictions ◽  
The Matrix ◽  
Non Local

Abstract We revisit the theoretical predictions and the parametrization of non-local matrix elements in rare $$ {\overline{B}}_{(s)}\to \left\{{\overline{K}}^{\left(\ast \right)},\phi \right\}{\mathrm{\ell}}^{+}{\mathrm{\ell}}^{-} $$ B ¯ s → K ¯ ∗ ϕ ℓ + ℓ − and $$ {\overline{B}}_{(s)}\to \left\{{\overline{K}}^{\ast },\phi \right\}\gamma $$ B ¯ s → K ¯ ∗ ϕ γ decays. We improve upon the current state of these matrix elements in two ways. First, we recalculate the hadronic matrix elements needed at subleading power in the light-cone OPE using B-meson light-cone sum rules. Our analytical results supersede those in the literature. We discuss the origin of our improvements and provide numerical results for the processes under consideration. Second, we derive the first dispersive bound on the non-local matrix elements. It provides a parametric handle on the truncation error in extrapolations of the matrix elements to large timelike momentum transfer using the z expansion. We illustrate the power of the dispersive bound at the hand of a simple phenomenological application. As a side result of our work, we also provide numerical results for the Bs → ϕ form factors from B-meson light-cone sum rules.

scholarly journals On the Modular Operator of Mutli-component Regions in Chiral CFT

2021 ◽  
Author(s):  
Stefan Hollands
Keyword(s):  
Field Theory ◽  
Integral Equation ◽  
Hilbert Problem ◽  
Matrix Elements ◽  
New Approach ◽  
Conformal Field ◽  
The Matrix ◽  
Kms Condition ◽  
Modular Operator ◽  
Riemann Hilbert Problem

AbstractWe introduce a new approach to find the Tomita–Takesaki modular flow for multi-component regions in general chiral conformal field theory. Our method is based on locality and analyticity of primary fields as well as the so-called Kubo–Martin–Schwinger (KMS) condition. These features can be used to transform the problem to a Riemann–Hilbert problem on a covering of the complex plane cut along the regions, which is equivalent to an integral equation for the matrix elements of the modular Hamiltonian. Examples are considered.

scholarly journals Analytical angular solutions for the atom–diatom interaction potential in a basis set of products of two spherical harmonics: two approaches

2021 ◽  
Author(s):  
Mariusz Pawlak ◽  
Marcin Stachowiak
Keyword(s):  
Spherical Harmonics ◽  
Interaction Potential ◽  
Chem Phys ◽  
Basis Set ◽  
Matrix Elements ◽  
Trigonometric Functions ◽  
Variational Theory ◽  
Molecular Collision ◽  
The Matrix ◽  
Analytical Expressions

AbstractWe present general analytical expressions for the matrix elements of the atom–diatom interaction potential, expanded in terms of Legendre polynomials, in a basis set of products of two spherical harmonics, especially significant to the recently developed adiabatic variational theory for cold molecular collision experiments [J. Chem. Phys. 143, 074114 (2015); J. Phys. Chem. A 121, 2194 (2017)]. We used two approaches in our studies. The first involves the evaluation of the integral containing trigonometric functions with arbitrary powers. The second approach is based on the theorem of addition of spherical harmonics.

Electrostatic interaction energies with overlap effects from a localized approach

2007 ◽  
Vol 445 (4-6) ◽  
pp. 315-320 ◽  
Author(s):  
Fazle Rob ◽  
Rafał Podeszwa ◽  
Krzysztof Szalewicz
Keyword(s):  
Electrostatic Interaction ◽  
Interaction Energies

Notizen: The Dipole Moment Function of HF Molecule Using Morse Potential

1977 ◽  
Vol 32 (8) ◽  
pp. 897-898 ◽  
Author(s):  
Y. K. Chan ◽  
B. S. Rao
Keyword(s):  
Wave Equation ◽  
Dipole Moment ◽  
Potential Function ◽  
Electric Dipole ◽  
Morse Potential ◽  
Moment Function ◽  
Matrix Elements ◽  
The Matrix ◽  
Vibration Rotation ◽  
Experimental Values

Abstract The radial Schrödinger wave equation with Morse potential function is solved for HF molecule. The resulting vibration-rotation eigenfunctions are then used to compute the matrix elements of (r - re)n. These are combined with the experimental values of the electric dipole matrix elements to calculate the dipole moment coefficients, M 1 and M 2.

Leach Behavior of SRL TDS-131 Defense Waste Glass in Water at High&Low Flow Rates

1983 ◽  
Vol 26 ◽  
Author(s):  
Aaron Barkatt ◽  
William Sousanpour ◽  
Alisa Barkatt ◽  
Morad A. Boroomand ◽  
Pedro B. Macedo
Keyword(s):  
Contact Time ◽  
Protective Layer ◽  
High Flow ◽  
Low Flow ◽  
Matrix Elements ◽  
Flow Rates ◽  
Low Concentrations ◽  
Controlling Mechanism ◽  
The Matrix ◽  
Leach Behavior

ABSTRACTLeach tests carried out on SRL TDS-131 Defense Waste Class indicate that at high flow rates the controlling mechanism is simple corrosion. The matrix elements (Si, Al) are leached out at rates similar to those of the leaching of the alkalis and of boron, and the leaching process is nearly linear with time. At slow flow rates (below 1 m/yr) leaching becomes controlled by the build-up of a protective layer. Al and most of the Si remain in the leached surface layer. The leach rates decrease in the course of the test before leveling off at constant values which are almost inversely proportional to the contact time, indicating that leachate concentrations have become solubility-limited. The low concentrations observed at this stage indicate the formation of alteration products.

Sign in / Sign up

Export Citation Format

Share Document