$\alpha$-particle formation and clustering in nuclei

The nucleonic localization function has been used for a decade to study the formation of $\alpha$ particles in nuclei, by providing a measure of having nucleons of a given spin in a single place. However, differences in interpretation remain, compared to the nucleonic density of the nucleus. In order to better understand the respective role of the nucleonic localization function and the densities in the $\alpha$-particle formation in cluster states or in the $\alpha$-decay mechanism, both an analytic approximation and microscopic calculations, using energy density functionals, are undertaken. The nucleonic localization function is shown to measure the anticentrifugal effect, and is not sensitive to the level of compactness of the $\alpha$ particle itself. It probes the purity of the spatial overlap of four nucleons in the four possible (spin, isospin) states. The density provides, in addition, information on the compactness of an $\alpha$-particle cluster. The respective roles of the nucleonic localization function and the density are also analyzed in the case of $\alpha$ particle emission. More generally, criteria to assess the prediction of $\alpha$ cluster in nuclear states are provided.

Figure 1

Nucleonic density, localization function $C$ [Eq. (2)] and $Z$ [Eq. (9)] functions for ${}^{16}\mathrm{O}$, calculated with the 3D HO approximation, for a given (spin, isospin) value.

Figure 2

Density parameter $r_0$ (11) and NLF (2) calculated with the surface approximation (12), in the case of ${}^{16}\mathrm{O}$.

Figure 3

NLF function using the deformed HO approach, for $r_{\perp }=0$ and $b_{\perp }=b_z$, for ${}^8\mathrm{Be}$ and ${}^{20}\mathrm{Ne}$.

Figure 4

Microscopic calculations of the density (left part of the figures) and NLF (right part of the figures) in the ground state of ${}^{20}\mathrm{Ne}$, using the SLy5 (top) and DD-ME2 (bottom) EDF.

Figure 5

Microscopic calculations of the density (left part of the figures) and NLF (right part of the figures) during the $\alpha$ decay of ${}^{212}\mathrm{Po}$, using the DD-ME2 EDF.

Figure 6

Microscopic calculations of the density (left part of the figures) and NLF (right part of the figures) for ${}^4\mathrm{He}$ (left) and ${}^{16}\mathrm{O}$ (right), using the DD-ME2 EDF.