Evidence of nuclear clustering throughout a major shell

We apply a cluster model to an extensive set of heavy even-even nuclei in the rare-earth region and determine the optimal core-cluster decomposition of each nucleus from a least-squares fit to the energy spectrum of its ground-state band. Good fits are obtained using a mass-symmetric form of the core-cluster interaction. We find that the core-cluster charge products deduced from the fits and the corresponding $B(E2)$ values are strongly correlated, in support of an underlying cluster picture of these nuclei.

Figure 1

Comparison of calculated (T) ground-state band excitation energies with experiment (E) for isotopes of Hf from the ground state spin $0^{+}$ to ${10}^{+}$. The core-cluster combinations used are listed in Table . The radius parameter R of Eq. (4) is given above the spectrum of each isotope.

Figure 2

Values of $B(E2)/A_T^{4/3}$ against $(Z_1{Z}_2/Z_T){}^2$ deduced from experimental data (full circles; see text for details). The solid line is a quadratic best fit to the data drawn to guide the eye.