Charge distribution in Pb (208) and Pb (206) and isotope shift

We have analysed the muonio x-rays in Pb (208) and determined the two parameters in the Fermi charge distribution. We find the contribution of the volume effect to the isotope shift in Pb (208)-Pb(206) disagrees with theexperiments. The ratio isΔEexp / ΔEvol = 0.55for 2p1/2 - ls1/2 transition.We disouss another effect which may cause isotope shift. We caloulate the distortion effect using the pairing force model and show that the effect is very small for the case of Pb(206).Then we introduce a new parameter "s" in the Fermi charge distribution to give a modified charge distribution with a central depression in charge density. By fitting to the observed isotope shift, we find the value of s is 0.3 f-1for Pb(206). We compare the transition energies and splittings with the measurements. The good agreement shows that the compressibility of the nucleus plays a role in determining the charge distribution in Pb (206). The magnitude of this effect on the effective radius is about 0.14%.