Expectation values of quantum powers < r^a > using quantum defects for Li O Na Mg using symbolic Mathematics, and new tools such as Topbase to produce quantum defects of these elements

TL;DR

This paper demonstrates how to use symbolic programming and tools like Topbase to efficiently compute expectation values of quantum powers for elements like Li, O, Na, Mg, utilizing quantum defects to generate accurate atomic data.

Contribution

It introduces a method combining symbolic mathematics and quantum defect data to calculate atomic expectation values for multiple elements and transitions.

Findings

Successfully computed expectation values < r^a > for selected elements.

Provided a framework for rapid and accurate atomic data generation.

Validated the approach with known quantum defect data.

Abstract

How to use recent symbolic programming language as < Mathematica > to build good quality programmes that yield valuable data in a short computation time. It is shown how to build good wave functions for any couple of states (both having proper quantum defects) a->|nala> and b-> |nblb> for a transition a->b . The correct normalization of these wave functions |nala > and |nblb > once obtained, enables the production of atomic useful data : such as line strengths, or average quantities as < a|r^{a}|a >, < b|r^{a}|b > and < a|r^a|b > with a values a {-2,-1,0,1,2}.