Isotope shift and changes of nuclear radius

Abstract

A new derivation of the expression for the nuclear charge distribution dependent isotope shift (I.S.) is given. This derivation shows clearly what approximation are made. The result, essentially the same as already obtained previously by the author, is as simple as the perturbation theory expression for the I.S. but is independent of the limitations of this. It depends on the charge distribution as a whole only through the root-mean-square radius, 〈r 2〉 1 2 and on the difference of charge distribution between isotopes only through δ〈r 2〉 1 2 . The implications of the electron scattering results for the I.S. are considered both for its dependence of 〈r 2〉 1 2 and on δ〈r 2〉 1 2 . A renewed discussion is given of the effect nuclear compressibility on the I.S. first considered by Wilets, Hill and Ford. For this the dependence of the symmetry energy on the density is shown to be as important as the Coulomb energy. Thus the I.S. cannot be uniquely related to the compressibility coefficient of nuclear matter but may now however be used to obtain information about the density dependence of the symmetry energy. The implications of the I.S. data for changes of radius between isotopes and between nuclei along the mass valley are also briefly considered.