Effective Principal Quantum Numbers of Hydrogen-Like States Belong to the Set of Common Fractions.

At the beginning of 2021, the sensational discovery was made in nuclear physics in the theory of hydrogen-like atoms and ions (having one electron in their outer shells). The essence of the discovery is that taking into account the quantum defect (the Rydberg corrections), the effective principal quantum numbers of the outer electrons can be expressed, along with integers, in terms of common fractions of the form N1/N2 with a significant limitation on the denominator value. Quite expectedly, the results of research caused increased interest because they addressed the foundations of modern physics – the atomic theory. Therefore, in this work we have continued this topic and present some results of statistical analysis of a large array of hydrogen-like states of atoms and ions. Both the ground and excited states of a wide variety of hydrogen-like atoms and ions, including lithium, potassium, sodium, cesium, argentum, and rubidium atoms are considered. Statistical analysis has allowed the correctness of the discovered regularity to be proved and the experimental data array to be transformed into new knowledge on the hydrogen-like states. [ABSTRACT FROM AUTHOR]