Distribution of charge and matter in nuclei: Charge density difference of 206Pb and 205Tl.

Abstract

We contrast two calculations of the charge density difference of $^{206}\mathrm{Pb}$ and $^{205}\mathrm{Tl}$. In the simplest model this difference in charge density is due to the occupation of an additional 3${s}_{1/2}$ orbital in $^{206}\mathrm{Pb}$. A standard mean-field calculation of the charge difference does not yield a satisfactory result. One may modify this result by assigning the 3${s}_{1/2}$ orbital an occupation probability of seventy percent, with a corresponding increase to thirty percent of the occupation probability of a 2${d}_{3/2}$ orbital. However, this modification of the mean-field analysis, while solving one problem, is seen to create a new problem in the fit to the data. In this work we present an alternative analysis: We maintain unit occupation probability for the 3${s}_{1/2}$ orbital but use the medium-modified proton electromagnetic form factor we have calculated previously. Our model is able to give a better fit to the data without the introduction of free parameters into the analysis. Medium-modified form factors have recently been shown to be effective in explaining the charge distribution of $^{208}\mathrm{Pb}$ and their application to the interpretation of the $^{206}\mathrm{\ensuremath{-}}^{205}$Tl charge density difference yields a result which is consistent with the experimental data and superior to that obtained in the adjusted mean-field analysis described above.