Application of the extended pairing model to heavy isotopes

TL;DR

This paper applies the extended pairing model to analyze relative binding energies in heavy isotopes, demonstrating a smooth relationship between pairing strength and model space dimension, and providing a new parametrization for it.

Contribution

It introduces a novel application of the exactly solvable extended pairing model to heavy isotopes, establishing a simple inverse relationship between pairing strength and model space size.

Findings

Pairing strength G can be described by a two-parameter inverse proportionality to model space dimension.

The model accurately reproduces experimental relative binding energies for Sn, Yb, and Pb isotopes.

G varies smoothly with the model space dimension, confirming theoretical expectations.

Abstract

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.