Related papers: Statistics of multi-electron states and $J$-levels…
This paper is devoted to the analysis of the distribution of the total magnetic quantum number $M$ in a relativistic subshell with $N$ equivalent electrons of momentum $j$. This distribution is analyzed through its cumulants and through…
This paper is devoted to the analysis of the distribution of the total angular momentum in a relativistic configuration. Using cumulants and generating function formalism this analysis can be reduced to the study of individual subshells…
We propose closed-form expressions of the distributions of magnetic quantum number $M$ and total angular momentum $J$ for three and four fermions in single-$j$ orbits. The latter formulas consist of polynomials with coefficients satisfying…
The distributions $P(M_L,M_S)$ of the total magnetic quantum numbers $M_L$ and $M_S$ for $N$ electrons of angular momentum $\ell$, as well as the enumeration of $LS$ spectroscopic terms and spectral lines, are crucial for the calculation of…
The interplay of spins and orbital angular moments of the fermions play an important role for the structure of the many-fermion systems like atoms, nuclei, nucleons (baryons) or mesons. We start our study from the one-fermion eigenstates of…
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…
The multiple scattering theory (MST) is one of the most widely used methods in electronic structure calculations. It features a perfect separation between the atomic configurations and site potentials, and hence provides an efficient way to…
We present three explicit formulas for the number of electronic configurations in an atom, i.e. the number of ways to distribute $Q$ electrons in $N$ subshells of respective degeneracies $g_1$, $g_2$, ..., $g_N$. The new expressions are…
We present a new method for constructing the total angular momentum of many-nucleon states. We find that the restrictions imposed by the fermion antisymmetry on the total state are fully absorbed into the single-j space when the broken…
A program for computing pure angular momentum coefficients in relativistic atomic structure for any scalar one- and two-particle operator is presented. The program, written in Fortran 90/95 and based on techniques of second quantization,…
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…
We propose approximate and accurate formulas for the number of electron configurations in hot plasmas. Such a quantity is an ingredient of algorithms devoted to the generation of configurations or superconfigurations, which is a…
Analytical expressions of the total number of $J$ levels for three and four fermions in a nuclear $j^n$ shell are provided. The formulas were derived using a combination of sum rules for coefficients of fractional parentage, and "unusual"…
To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems -- such as those encountered in nuclear and particle physics -- that access only a restricted subset of energy levels and provide limited…
The connection between the intrinsic angular momentum (spin) of particles and the quantum statistics is established by considering the response of identical particles to a common background radiation field. For this purpose, the Hamiltonian…
A review of methods for finding general expressions for matrix elements (non-diagonal with respect to configurations included) of any one- and two-particle operator for an arbitrary number of shells in an atomic configuration is given.…
The electronic structure of the helium atom in the magnetic field regime B=0-100a.u. is investigated, using a full configuration interaction approach which is based on a nonlinearly optimized anisotropic Gaussian basis set of one-particle…
Angular momentum projection is used to obtain eigen states of angular momentum from general wave functions. Multi-configuration mixing calculation with angular momentum projection is an important microscopic method in nuclear physics. For…
A program RCFP will be presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. The list of quantities wich are supported by the present program includes the…
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…