Extracting this term from (2.31) gives

and for the purposes of combining with previous results and for numerical computation (3.8) can be re-written

In (3.9) the numerical value of G_e in all orbitals is determined from (2.41) by insertion of appropriate values for k^// and taking the summation to 200 terms to ensure convergence. In performing this evaluation it is to be noted that any spherical body possessing mass, if spinning at a high enough angular rate, will be subject to centrifugal force. Unless such a body is infinitely rigid it will consequently distort by expanding normal to the axis of rotation. It is necessary to allow for this condition here and an allowance of ~ +7.5% has been inserted to cover the centrifugal force expansion of G_e due to its high spin rate. This is not in conflict with the Lorentz - Fitzgerald contraction of the circumference because G_e is normal to the direction of spin motion.

In the above allowance for centrifugal distortion, and for the general determination of G_e, cognisance has been taken of the requirement to optimise the orbital energy intervals so as to ensure that the Lamb Shift in all orbitals was present. This will be discussed in more detail in Sections 5 and 6 below.

The result of this evaluation of G_e for all orbitals in the first eight shells are shown in Table 3.1 below.

It is emphasised that other than for orbitals 2s and 1s, these values only apply at the point of transition. Also, some of the values of G_e so determined are considerably greater than the physical radius of a free electron and it is therefore important to remember that these values only apply to the spin matter wave radius of electrons extant within the structure of the hydrogen atom.

The further significance of the values determined for G_e in Table 3.1 will also be discussed in Section 5.