spectrum generating algebra and its role in solvability of alkali elements

Hydrogen atom is always helpful in obtaining datafrom the other atoms. revision of the lie algebraic approachin studying the radial part of the hydrogen atom and usingthe tilting transformation are reasonable means to discussalkali elements. the characteristic difference between alkalielements and hydrogen atom is the screening effect inalkali elements which causes much more freedom to thehighest electron, valence electron. in this case, these atomshave another terms besides coulomb potential energy; sentencesof the order of inverse square of the distance andabove. so, we can consider we have dipole moments, quadrupolemoments and etc. therefore, these terms , although theyare small, make these elements attractive for applications inquantum information. also, we can consider them as rydbergatoms with strong long-range interactions. here, byconsidering an inverse square distance potential, lie algebraicmethods help us to obtain energy levels of both boundand excited states and corresponding wave functions too.