Related papers: Integration over spin-angular variables in atomic …
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
General method is suggested to find non-relativistic and relativistic matrix elements of one- and two-electron operators for any number of open shells in atom, requiring neither coefficients of fractional parentage nor unit tensors. It is…
In this paper a library for spin--angular integration in LS-coupling for many-electron atoms is presented. The software is an implementation of a methodology based on the second quantization in coupled tensorial form, the angular momentum…
The tensorial form of the spin-other-orbit interaction operator in the formalism of second quantization is presented. Such an expression is needed to calculate both diagonal and off-diagonal matrix elements according to an approach, based…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…
Matrix elements between nonorthogonal Slater determinants represent an essential component of many emerging electronic structure methods. However, evaluating nonorthogonal matrix elements is conceptually and computationally harder then…
In this work we show how constructing Wigner functions of heterogeneous quantum systems leads to new capability in the visualization of quantum states of atoms and molecules. This method allows us to display quantum correlations…
Electronic structure methods that exploit nonorthogonal Slater determinants face the challenge of efficiently computing nonorthogonal matrix elements. In a recent publication, H. G. A. Burton, J. Chem. Phys. 154, 144109 (2021), I introduced…
A scheme is presented to calculate on a first-principles level the spin-lattice coupling (SLC) parameters needed to perform combined molecular-spin dynamics (MSD) simulations. By treating changes to the spin configuration and atomic…
The 2(2s+1)-component relativistic basis spinors for the arbitrary spin particles are established in position, momentum and four-dimensional spaces, where s=0,1 / 2,1, 3 / 2, 2, ... . These spinors for integral- and half-integral spins are…
This library (collection of subroutines) is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage,…
An alternative method to the density matrix formalism for the derivation of general expressions of the interaction of polarized atoms with polarized photons and electrons is presented. The expression for the cross-section describing the…
A complete set of generalized spin-squeezing inequalities is derived for an ensemble of particles with an arbitrary spin. Our conditions are formulated with the first and second moments of the collective angular momentum coordinates. A…
For any mean value of a cartesian component of a spin vector we identify the smallest possible uncertainty in any of the orthogonal components. The corresponding states are optimal for spectroscopy and atomic clocks. We show that the…
The state of quantum systems, their energetics, and their time evolution is modeled by abstract operators. How can one visualize such operators for coupled spin systems? A general approach is presented which consists of several shapes…
A generalized vector particle theory with the use of an extended set of Lorentz group irredicible representations, including scalar, two 4-vectors, and antisymmetric 2-rang tensor, is investigated. Initial equations depend upon four complex…
We present a theory for the estimation of a scalar or a vector magnetic field by its influence on an ensemble of trapped spin polarized atoms. The atoms interact off-resonantly with a continuous laser field, and the measurement of the…
The \textit{Spirit} framework is designed for atomic scale spin simulations of magnetic systems of arbitrary geometry and magnetic structure, providing a graphical user interface with powerful visualizations and an easy to use scripting…
The relativistic approach to electroweak properties of two-particle composite systems developed in previous work is generalized here to the case of nonzero spin. This approach is based on the use of the instant form of relativistic…