Investigation of ${}^9\mathrm{Be}$ from a nonlocalized clustering concept

The nonlocalized aspect of clustering, which is a new concept for self-conjugate nuclei, is extended for the investigation of the $N\ne Z$ nucleus ${}^9\mathrm{Be}$. A modified version of the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave function is introduced with a new phase factor. It is found that the constructed negative-parity THSR wave function is very suitable for describing the cluster states of ${}^9\mathrm{Be}$. Namely, the nonlocalized clustering is shown to prevail in ${}^9\mathrm{Be}$. The calculated binding energy and radius of ${}^9\mathrm{Be}$ are consistent with calculations in other models and with experimental values. The squared overlaps between the single THSR wave function and the Brink + generator coordinate method wave function for the $3/2^{-}$ rotational band of ${}^9\mathrm{Be}$ are found to be near 96%. Furthermore, by showing the density distribution of the ground state of ${}^9\mathrm{Be}$, the $\pi$-orbit structure is naturally reproduced by using this THSR wave function.

Figure 1

Contour maps of binding energy surface with the $\beta$ parameters in the THSR wave function. Left part (a) is the contour map of parameters ${\beta }_{\alpha ,xy}$ and ${\beta }_{\alpha ,z}$ and the right part (b) is the contour map of parameters ${\beta }_{n,xy}$ and ${\beta }_{n,z}$. The optimum value is marked on each map labeled with coordinates. Parameter $b$ is taken as the variational optimum value $b=1.35$ fm.

Figure 2

Density distribution of the intrinsic ground state of ${}^9\mathrm{Be}$. The grayscale of each point in the figure stands for the nucleon density on $x-z$ plane of the $y=0$ cross section. The unit of the density is ${\mathrm{fm}}^{-3}$.

Figure 3

Density distribution $\rho \left({\mathbf{r}}_n^{\prime }\right)$ of the extra neutron of the intrinsic ground state of ${}^9\mathrm{Be}$. The grayscale of each point in left part (a) of the figure stands for the nucleon density on $x-z$ plane of the $y=0$ cross section. The gray scale of each point in right part (b) of the figure stands for the nucleon density on the $x-y$ plane of the $z=0$ cross section. The unit of the density is ${\mathrm{fm}}^{-3}$.