Effect of Dynamical Deformation in Elastic Electron Scattering on the Charge Distributions of the Calcium Isotopes

Abstract

The presence of dynamical deformations in the ground-state distributions of the calcium isotopes provides a basis for understanding two well-known but very different effects observed in elastic electron scattering from these isotopes.The first, seen at low momentum transfer, is the anomalous isotope dependence of the nuclear radius. It is shown that there is a deformation-dependent contribution to the rms radius, whose magnitude can be obtained from inelastic electron and $\ensuremath{\alpha}$-particle scattering via a sum rule and which leads to a prediction of the isotopic dependence in substantial agreement with experiment.The second observed effect, visible at high momentum transfer, is the appearance of oscillations in the $^{40}\mathrm{Ca}$ and $^{48}\mathrm{Ca}$ distributions, as revealed by fits to the elastic electron scattering data at 750 MeV. It is shown that an additional contribution of dynamical deformations to monopole elastic electron scattering, observable only at high momentum transfer, may be interpreted as due to an effective spherically symmetric charge distribution superimposed upon the smoothly varying distribution obtained at lower energies. This modulating is calculated explicitly and exhibits an oscillatory behavior.