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