Application of symbolic programming for atomic many-body theory

TL;DR

This paper introduces a Mathematica-based symbolic programming approach and a specialized package, NCoperators, for automating the generation of atomic stationary perturbation theory expressions, integrating multiple quantum theory methods.

Contribution

The paper presents a novel Mathematica package, NCoperators, that automates the generation of perturbation theory expressions using RSPT, SQR, and AMT, adaptable for atomic spectroscopy research.

Findings

Automated generation of perturbation theory expressions.

Compatibility with traditional and C code output.

Applicability across various atomic spectroscopy problems.

Abstract

In the present paper by using Mathematica system a symbolic programming method for generation of the expressions of the expansion terms of atomic stationary perturbation theory (PT) is presented. For this purpose, the package named as NCoperators was developed. In producing the PT terms, this package accommodates the features of the Rayleigh-Schr\"odinger perturbation theory (RSPT), the second quantization method (SQR) and angular momentum theory (AMT). The package was built in such a way that it could be applicable in various areas of theoretical atomic spectroscopy. Many functions of the NCoperators can be easily adapted for users to their own demand by easily transforming the functions developed. The package gives a possibility of generating formulas in traditional output form. For some quantities the expressions obtained in Mathematica can be converted into C code. Although the NCoperators package was developed for Unix OS, it can be easily adopted for other OSs if some of the parameters to be changed.