Isotopic and Lamb shifts of the energy levels

Let us consider first the isotopic shift of the energy levels, conditioned by the difference of masses of various isotopes (the mass effect, causing the 

Here m is the electron mass, M stands for the mass of a given isotope, and E denotes the total energy of an atom for motionless nucleus. The specific shift of energy is described by the matrix element 

In (22.37) ip is the wave function of an atom with motionless nucleus. The one-electronic submatrix element of the gradient operator (n/ V ni/i) is non-zero only for h = / 1. Therefore, the matrix element of operator (22.38) inside a shell of equivalent electrons vanishes and one has to account for this interaction only between shells. For the configuration, consisting of j closed and two open shells, it is defined by the following formula [156]  

The summation in (22.39) over i runs through all closed shells, whereas 

It is much more difficult to take into account the influence of finite dimensions and form of the nucleus (volume effect) on the atomic energy levels, because we do not know exactly the nuclear volume, or its form, or the character of the distribution of the charge in it. Therefore, in such cases one sometimes finds it by subtracting its part (22.35) from the experimentally measured total isotopic shift. Further on, having the value of the shift caused by the volume effect, we may extract information on the structure and properties of the nucleus itself. For the approximate determination of the isotope shift, connected with the differences dro of the nuclear radii of two isotopes, the following formula may be used [15]  

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