Mean square charge radii isotopes

The change in mean-squared-charge radius is obtained from the isotope shift using standard techniques [HEI74]. For thallium the normal mass shift is approximately 8 MHz between masses and the specific mass shift is smaller than the experimental error. The resulting field shift is proportional, to good approximation, to an electronic factor times 6. For the case of T1 the electronic factor is not directly calculable but should be virtually the same for all isotopes. 

We shall briefly review the relationship between spectroscopic observables and nuclear properties/ These properties include spins, magnetic dipole and electric quadrupole moments, as well as the variation in the mean square charge radius within a sequence of isotopes. They manifest themselves in the hyperfine structures and isotope shifts. The hyperfine energies of the different F states within a hyperfine multiplet / - / F J + I, given by the well-known formula... 

Similarly, the isotope shift of an optical transition is related to the change in the nuclear mean square charge radius between the... 

In addition to the mass variation by isotopic substitution also the nuclear size will vary slightly giving rise to small changes in the Coulomb interaction between the electrons and the nucleus. This isotope effeet which is called field shift in the theory of atomic spectra [78Hei] can be traced back to yield a very similar form as of eq. (6) where the mean square nuclear charge radius A,B is used as the expansion parameter instead of and the new molecular parameter is introduced [82Tie]. 

With the envisioned higher resolution, it should be possible to determine a better value of the electron/proton mass ratio from a precise measurement of the isotope shift. And a measurement of the absolute frequency or wavelength should provide a new value of the Rydberg constant with an accuracy up to 1 part in 10, as limited by uncertainties in the fine structure constant and the mean square radius of the proton charge distribution. A comparison with one of the Balmer transitions, or with a transition to or between Rydberg states could provide a value for the IS Lamb shift that exceeds the accuracy of the best radiofrequency measurements of the n=2 Lamb shift. Such experiments can clearly provide very stringent tests of quantum electrodynamic calculations, and when pushed to their limits, they may well lead to some surprising fundamental discovery. 

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