α-cluster structure and exotic states in a self-consistent model for light nuclei

In this article we examine to what extent traces of α clustering can be found in mean-field ground states of $n\alpha$ nuclei from ${}^8\mathrm{Be}$ through ${}^{36}\mathrm{Ar}$ as well as in some superdeformed states in ${}^{32}\mathrm{S}$, ${}^{36}\mathrm{Ar}$, and ${}^{40}\mathrm{Ca}$. For this purpose we calculate the overlap of the mean-field Slater determinant with one containing pure Gaussians and perfect spin and isospin symmetry, optimizing the overlap by varying the α-particle positions and radii. In some cases a coherent sum over different configurations is also employed. We find quite large overlaps for some of the lighter systems that diminish for nuclei above ${}^{20}\mathrm{Ne}$ but again strong clustering in ${}^{36}\mathrm{Ar}$.

Figure 1

Visualization of the cluster geometry present in the mean-field ground or excited superdeformed states (denoted by asterisks) for the nontrivial cases. The figures only illustrate the topology; no attempt was made to reproduce correct scale lengths. Double links between particles indicate very small distances. The triangles and pentagon are perpendicular to the linear links.

Figure 2

Density contour lines for ${}^8\mathrm{Be}$.

Figure 3

Density contour lines for ${}^{20}\mathrm{Ne}$.

Figure 4

Density contour lines for ${}^{24}\mathrm{Mg}$ (left) and ${}^{28}\mathrm{Si}$ (right).

Figure 5

Density contour lines for ${}^{32}\mathrm{S}$ and ${}^{36}\mathrm{Ar}$.

Figure 6

Density contour lines for ${}^{28}\mathrm{Si}$ and ${}^{32}\mathrm{S}$ superdeformed states.

Figure 7

(Full curve) Overlap of the strongly deformed state found in ${}^{32}\mathrm{S}$ with a configuration of two ${}^{16}\mathrm{O}$ nuclei placed symmetrically at a given distance. (Dashed curve) Norm of the combined Slater determinant of the two ${}^{16}\mathrm{O}$ nuclei.

Figure 8

Density contour lines for ${}^{36}\mathrm{Ar}$ (left) and ${}^{40}\mathrm{Ca}$ (right) superdeformed states.