Unified description of collective nuclei with the interacting boson model

It was recently demonstrated that the empirical linear correlation of ${E(4}_{1}^{+})$ with ${E(2}_{1}^{+})$ is reproduced by the interacting boson model 1 (IBA-1) if a constant value for the coefficient $\ensuremath{\kappa}$ of the Q$\ensuremath{\cdot}$Q term is used. This constancy motivates the present investigation of whether it is possible to find sets of IBA-1 parameters, with fixed $\ensuremath{\kappa}$, that reproduce the data for a more general set of observables and a wide range of nuclei. A consistent procedure, based on contour plots of key observables, was used to extract $\ensuremath{\epsilon}$ and $\ensuremath{\chi}$ values for 145 nuclei spanning the $Z$ = 50--82 shell, which give reasonable overall agreement with the data with smoothly varying parameters. The constant $\ensuremath{\kappa}$ constraint sometimes leads to parameter values different than normal: finite $\ensuremath{\epsilon}$ values $(\ensuremath{\sim}$ 0.1 MeV) even for rotational nuclei and large $\ensuremath{\chi}$ values for transitional and vibrational nuclei that even increase towards the vibrational region. Finally, a systematic correlation of $\ensuremath{\epsilon}$ values with ${E(2}_{1}^{+})$ was found.