Investigation of series over fine structure coefficient for relativistic energy of hydrogen-like atoms

In this work, relativistic energy eigenvalue formula that derived from the exact solution of the relativistic Dirac equation for Hydrogen-like atoms and the Maclaurin series expansion over fine structure coefficient of it are used.Series expansion method is useful to find the approximations to the relativistic energy values. Therefore, we have searched the approximations to the relativistic energy which is found by using the terms of series expansion formula, called quasirelativistic. By taking into account the terms respectively, energy eigenvalues determined from the first term were same as non-relativistic energy eigenvalues and from second term were same as energy eigenvalues obtained from the Pauli approximation. Also third and fourth terms have been considered and we determined the quasirelativistic energy values from further approximations. The calculations have been done for Hydrogen-like atoms having the atomic number to 10 (Hydrogen to Neon). In order to find how energy changes with relativistic effects, the differences between quasirelativistic, relativistic and non-relativistic energy values of atomic orbitals which are dealing with the additions come from relativistic effects are investigated.Calculated numerical energy values of atomic orbitals for different Hydrogen-like atoms are discussed. Finally, we have found a brief relation between relativistic effects and changing parameters; quantum numbers ( etc.) of atomic orbitals, atomic number for different Hydrogen-like atoms.