Application of the extended pairing model to heavy isotopes

Relative binding energies (RBEs) within three isotopic chains (${}^{100-130}$Sn, ${}^{152-181}$Yb, and ${}^{181-202}$Pb) have been studied using the exactly solvable extended pairing model (EPM) \cite{FPan04}. The unique pairing strength $G$, which reproduces the experimental RBEs, has been determined. Within EPM, $\log (G)$ is a smooth function of the model space dimension $\dim (A)$, as expected for an effective coupling strength. In particular, for the Pb and Sn isotopes $G$ can be described by a two parameter expression that is inversely proportional to the dimensionality of the model space, $G=\alpha \dim (A{)}^{-\beta }$ with $\beta \approx 1$. PACS Classification: 21.10.Dr Binding energies, 71.10.Li Pairing interactions in model systems, and 21.60.Cs Shell model.