Dirac's fine-structure formula for an "abnormally high" nuclear charge
  In Dirac's fine-structure formula for the hydrogenlike atoms a critical role is played by the square root of the following expression: the unity minus the square of the product of the atomic number by the fine-structure constant (which is approximately equal to 1/137). Indeed, for a fictitious, ideal nucleus for which the above product is greater than or equal to one, the mentioned square root becomes imaginary, or zero. I prove in this Note that the origin of such theoretical "breaking down" is quite simple and is inherent in the special theory of relativity of classical physics. 
A. Loinger (Dipartimento di Fisica dell'Universita' di Milano, Italy)