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

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}.