Effective main quantum numbers of hydrogen-like states belong to the common fractions set

At the beginning of 2021 it became known about sensational opening in atomic physics regarding the theory of hydrogen-like atoms and ions (having only one outer shell electron). Chief matter of the opening consists in the fact that effective main quantum numbers of outer electron, i.e. in consideration of quantum defect (Rydberg correction), along with integers can be expressed in common fractions N1/N2, having substantial constraint on denominator quantity. Sensational results of the study caused quite predictable high interest, because it affects basic foundation of modern physics - atom theory. That's why in this paper to continue the theme the results of statistical analysis of a large database of hydrogen-like atoms and ions are presented. There were considered not only atoms and ions in ground state, but also excited states of atoms of lithium, potassium, sodium, cesium, argentum and rubidium. The statistical analysis made it possible to get reliable proofs of validity of the discovered experimental law and to turn the data array into the new knowledge about hydrogen-like states.

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