A general theory is given for the isotope shift of energy levels in heavy atoms. The methods used here are based neither on the simple perturbation theory nor on the solution of the Darwin-Gordon differential equations for the region inside the nucleus. It is sufficient to solve an integral equation from which result both the distortion effect of the wave function due to the spatial extension of the nucleus, and the specific nuclear effects of surface and deformation.

The screening effects of the electrons in the closed shells, the effect of nuclear compressibility as well as other effects ar also analyzed.

The article probably exhausts the main causes which account for the global effect of isotope shift. The values obtained theoretically for the isotopic constants of the nuclei, fairly well agree with the experimental ones.