Nuclear size, electric monopole transitions, and the location of $0_2^{+}$ states

The work addresses the isotopic shift of nuclear radii for the even-even ${}^{36-52}$Ca isotopes using the interacting boson model (IBM) that includes the mixing from normal and intruder configurations. We obtain a good agreement between the calculated and experimental data, particularly for the dip at ${}^{48}$Ca. A direct correlation between nuclear size and electric monopole transitions is established to compute the electric monopole transition strengths, ${\rho }^2(E0)$. We further study the isotopic shift for the even-even ${}^{32-46}$Ar and ${}^{44-50}$Ti isotopes.