Related Techniques for the Determination of Nuclear Structure

Abstract

The elastic scattering of electrons by nuclei is caused by the electrostatic field of the nucleus, and so the analysis of such scattering experiments gives information about nuclear charge distributions. Isotope shifts can, in principle, give values of the change between isotopes in the mean square radius of the nuclear charge distribution, δ〈r ²〉, but sometimes in practice they give only relative values between different isotope pairs. In such cases, inaccurate (but absolute) values of δ〈r²〉 from other techniques can be combined with accurate (but only relative) values of δ〈r ²〉 from optical isotope shift work. Iron is an example of where this technique might be used, but the information available from electron scattering is of little help; 〈r ²〉 has been determined for ⁵⁴Fe, ⁵⁶Fe, and ⁵⁸Fe, but the uncertainties in the values are about a quarter of their differences between isotopes. Muonic x-ray energy studies on the other hand can give values of δ〈r ²〉 of a useful precision for combination with optical isotope shift measurements. This often seems to be the case but, even so, the importance of electron scattering data should not be underestimated. The analysis of muonic x-ray energies to give precise information about nuclear charge distributions would be impossible without the information that had previously been obtained from electron scattering experiments about nuclear charge distributions. Since the first measurements of Lyman et al. (1951), the analysis of electron scattering experiments has given more information on nuclear charge distributions than has any other technique. From the scattering at one electron energy it is not possible to deduce the actual nuclear charge distribution, but only a set of charge distributions that are consistent with the scattering data. However, by repeating the experiment with different electron energies it is possible to obtain a fairly unique distribution from what is common to the different sets of charge distributions.