Angular coefficients for symmetry-adapted configuration states in jj-coupling.

In atomic structure and collision theory, the efficient spin-angular integration is known to be crucial and often decides, how accurate the properties and behavior of atoms can be predicted numerically. Various methods have been developed in the past to keep the computation (and implementation) of the spin-angular integration feasible for complex shell structures, including open d - and f -shell elements. To support such computations, we here provide a new implementation of the angular coefficients for jj -coupled and symmetry-adapted configuration states that is entirely built upon the quasi-spin formalism. The module SpinAngular is based on Julia, a new programming language for scientific computing, and supports a simple access to all (completely) reduced tensors, coefficients of fractional parentage for subshells with j ≤ 9 / 2 as well as the re-coupling coefficients from this formalism. Moreover, this module has been worked out for multiple purposes, including 1) the accurate calculation of atomic properties, 2) further studies on spin-angular integration theory, 3) the development of new or existing computer programs as well as 4) the manipulation of reduced matrix elements from this theory. The present implementation will therefore help advance the algebraic evaluation of many-electron (transition) amplitudes and to apply the theory to newly emerging research areas. Program title: SpinAngular CPC Library link to program files: https://doi.org/10.17632/jjpff3pysn.1 Code Ocean capsule: https://doi.org/10.24433/CO.3772334.v1 Licensing provisions: MIT License Programming language: Julia Nature of problem: For symmetric one- and two-particle operators, the (many-electron) matrix elements between symmetry-adapted configuration states can always be written as a sum of angular coefficient x interaction strength. While the interaction strengths describe the physical interaction and just depends on the (one-electron) orbitals of the active shells, the angular coefficients arise from the (many-electron) spin-angular integrals and are determined geometrically by the occupation and coupling of all electrons. These angular coefficients need to be calculated efficiently and often require special care. Solution method: The spin-angular approach [1] is implemented for (tensorial coupled) one-particle operators of arbitrary rank, scalar two-particle operators as well as for the manipulation of reduced matrix elements from this theory. [1] G. Gaigalas, Z. Rudzikas, C. Froese Fischer, J. Phys. B, At. Mol. Opt. Phys. 30 (1997) 3747. [ABSTRACT FROM AUTHOR]