Nuclear charge radius

On one hand, the large magnitude of the change of the mean-squared nuclear charge radius, A(r ) = (r )e — (r )g, between the excited state and the ground... 

The consideration of these problems (138, 187) lead us to the conclusion that the polarizing power of the cations as measured by the effective nuclear charge alone, is most probably the influential parameter necessary to understand these effects. The polarizing power given otherwise as formal charge/radius or formal charge/radius or even better, effective nuclear charge/radius, cannot explain these effects as well. 

The general result for the nuclear charge radius and the Darwin-Foldy contribution for a nucleus with arbitrary spin was obtained in [9]. It was shown there that one may write a universal formula for the sum of these contributions irrespective of the spin of the nucleus if the nuclear charge radius is defined with the help of the same form factor for any spin. However, for historic reasons, the definitions of the nuclear charge radius are not universal, and respective formulae have different appearances for different spins. We will discuss here only the most interesting cases of the spin zero and spin one nuclei. 

The main part of the nuclear size (Za) contribution which is proportional to the nuclear charge radius squared may also be easily obtained in a simpler way, which clearly demonstrates the source of the logarithmic enhancement of this contribution. We will first discuss in some detail this simple-minded approach, which essentially coincides with the arguments used above to obtain the main contribution to the Lamb shift in (2.4), and the leading proton radius contribution in (6.3). 

The IS s of nuclei far from stability turned out to be the most informative data obtained by optical spectroscopy. This is because the nuclear charge radius depends on collective as well as on single-particle effects. The integral IS s (6 with A being a reference isotope) exhibit the gross behaviour of nuclear matter as a function of varying neutron number. These can be compared with predictions of macroscopic models like the Droplet Model [MEY83], which describes the overall trend quite well. 

One can study muonic atoms [14,15,16]. The muon orbit lies lower and much more close to the nucleus and its energy levels are much more affected by the strong interactions. However, to determine the nuclear contributions (for e. g. the one for the Lamb shift, which is completely determined by the nuclear charge radius) it is not necessary to know the QED part with an accuracy as high as in the case of the hydrogen atom. As a result, one can try to determine the parameters due to the nuclear structure and apply them afterwards to normal atoms. 

We cannot calculate the nuclear structure but we can describe the leading correction to the Lamb shift with the help of a simple delta-like potential, which depends on a single parameter, the nuclear charge radius R, calculated as fW) The parameter must be found experimentally. Usually this contribution is small enough and if necessary some corrections can be calculated. 

Accurate calculations for the Lamb shift and hfs of hydrogen-like atoms are limited by their nuclear structure and higher-order QED corrections. In the case of low-Z Lamb shift, the finite-nuclear-size effects can be taken into account easily if we know the nuclear charge radius. 

From the effects of quasihydrostatic pressure on the transition energy of the 77.3 keV gamma rays of Au in metallic gold, a value of A(r >= +9X10" has been derived for the change of the mean-squared nuclear charge radius. The positive sign of implies an increase in p(0) with increas-... 

B. Nerlo-Pomorska, K. Pomorski, Simple formula for nuclear charge radius, Z. Phys. A 348 (1994) 169-172. 

As stated in Section 1, one of fhe goals of this work is to use the comparison between theory and experiment for the isotope shift to determine the nuclear charge radius for various isotopes of helium and other atoms. One of the most interesting and important examples is the charge radius of the Tialo nucleus He. For a light atom such as helium, the energy shift due to the finite nuclear size is given to an excellent approximation by... 

Since the goal of the experiment is to determine the nuclear charge radius for He, the final step is to adjust fc so as to eliminate the small discrepancy of 0.046(56) MHz shown in Table 4.7. The various contributions to the isotope shift in Table 4.7 can be collected together and expressed in the form... 

As a consequence of these advances, helium and lithium now join the ranks of hydrogen and other two-body systems as examples of fundamental atomic systems. The high precision theory that is now available creates new opportunities to develop measurement tools that would otherwise not exist. One such example discussed here is the determination of the nuclear charge radius for the halo nuclei He and Li. This opens up a new area of study at the interface between atomic physics and nuclear physics, and it provides important input data for the determination of effective nuclear forces. Other similar experiments have been performed on the lithium isotopes [66], including the halo nucleus Li [65], and further work is in progress on He at Argonne and Be at GSI/TRIUMF. 

Lyman et al. and Pidd and Hammer have made measurements at lower energies which can only be interpreted in terms of a nuclear charge radius. 

Nuclear charge radius, elektrostatischer Kern-radius 505. 

According to O Eq. (25.56), one obtains that the energy shift due to electric monopole interaction is proportional to the product of the s electronic density and the second moment of the nuclear charge distribution also called the mean square nuclear charge radius (see also O Sect. 2.2.3.1 in Chap. 2, Vol. 1). When the nucleus is considered to be a homogeneously charged sphere with a radius R (often called charge equivalent nuclear radius), then... 

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]. 

---