Symmetry dependence of rms Charge Radii

The nucleon number dependence of rms charge radii is often approximated by some simple formula containing the mass number only, R(A)=r(A)A1/3, where r(A) is a slowly varying function of A. However, for nuclei off the stability line, the mass number A=N + Z is not enough to characterise the dependence of the R(Z, N) radius surface on the nucleon numbers Z and N. In the present work, an additional term has been included, depending on the symmetry parameter I=(N − Z)/A. Several parametrisations were tried, using weighted least-squares procedures for the fit to a present-day data base. The best fit (with χ2/n=17) was found for R(A, I)=r(A)A1/3 + bI/(I − Istab), where Istab=(Nstab − Zstab)/A is the value of the symmetry parameter of the stable isobar with mass number A, and bI=−0.83 fm. The formula R(A, I)=[r(A) + aI(I − Istab)]A1/3 is only slightly inferior to the previous one, moreover, it is supported by simple model calculations; here aI=−0.20 fm (χ2/n=20). The difficulty in determining the right parametrisation is caused by the fact that the surface Rexp(A, I) is not smooth: there are strong shell and deformation effects. To avoid the distorting effect of these deviations on the parameter values, more than half of the original data had to be omitted.