Possible improvements in the derivation of δ<r ²> from optical isotope shifts

Abstract

It is shown that writing the correction factor K in the proper form, the value of δ<r ²> derived from the optical isotope shift may be made more reliable. Instead of the generally used parabolic Z dependence, the quantity 1—K depends primarily on the actual slope δ<r ²> /δA, which may vary considerably from one isotope pair to another. This slope dependence is illustrated first for a spherical uniform nuclear charge distribution. Then, the case of the more realistic two-parameter Fermi charge distribution is investigated. Practical formulae of 1—K are given for both model distributions. The improved evaluation is especially important in cases where δ<r ²> values are much lower or higher than the liquid drop value. In these cases the improvement in δ<r ²> values may lead to substantial changes in nuclear structure characteristics, e.g. in deformation parameters. Results are compared to those obtained by an alternative approach, the “two-parameter model” based on a deformed uniform distribution.