Evolution of clustering structure through the momentum distributions in ${}^{8\text{–}10}\mathrm{Be}$ isotopes

We investigate the evolution of clustering structure through the momentum distributions in the ${}^{8\text{–}10}\mathrm{Be}$ isotopes. The nucleon dynamics within the intercluster antisymmetrization are discussed via the momentum distribution of a Brink type $\alpha \text{−}\alpha$ wave function. For the state with a small $\alpha \text{−}\alpha$ distance, we observe a significant depression with a dip structure at zero momentum and an enhanced tail in a relatively higher momentum region. In addition, we find the “cluster structure” in the intrinsic frame of momentum space, which is complementary to its significant $\alpha$-cluster dissolution in the coordinate space because of the strong antisymmetrization. For the physical ${}^{8\text{–}10}\mathrm{Be}$ isotopes, the Tohsaki-Horiuchi-Schuck-Röpke (THSR) wave functions are adopted. The evolution from the dilute clustering state to the compact one is demonstrated by a successive depression at zero momentum of nucleon distribution for the two $\alpha$ clusters within ${}^{8\text{–}10}\mathrm{Be}$ isotopes. For the compact ${}^{10}\mathrm{Be}$ nucleus, the momentum distribution of all nucleons shows significant depression at zero momentum with a dip structure, which is found to be contributed by both the intercluster antisymmetrization and the $p$-orbit occupation of the valence neutrons. This study proposes a new window for the investigations of the $\alpha$-clustering effects via the low-momentum components of nuclei, which is expected to be extended to the heavier nuclear clustering states.

Figure 1

The intrinsic momentum distributions of the ${}^8\mathrm{Be}$ nucleus described by the Brink wave function along the $z$ axis. “$D_z$” is the relative distance between $\alpha$ clusters in the $z$ axis. “2 free $\alpha$-clusters” denotes the nucleon momentum distribution of two free $\alpha$ clusters.

Figure 2

The intrinsic nucleon momentum distributions of the $\alpha \text{−}\alpha$ Brink wave function as functions of the $\alpha \text{−}\alpha$ distance $D_z$ in the $x\text{−}z$ cross section.

Figure 3

The intrinsic proton momentum distributions of ${}^{8\text{–}10}\mathrm{Be}$ isotopes in the $x\text{−}z$ cross section.

Figure 4

The nucleon momentum distributions of the two $\alpha$ clusters within the ${}^{8\text{–}10}\mathrm{Be}$ isotopes. Curves denoted with parentheses are for the ${}^8\mathrm{Be}$ ($0_1^{+}$), ${}^9\mathrm{Be}$ ($3/2_1^{-}$), and ${}^{10}\mathrm{Be}$ ($0_1^{+}$) nuclei in the laboratory frames. Curves denoted with “intrinsic” are for the intrinsic frames before angular momentum projections.

Figure 5

The total momentum distributions of the ${}^8\mathrm{Be}\left(0_1^{+}\right)$, ${}^9\mathrm{Be}(3/2_1^{-})$, and ${}^{10}\mathrm{Be}\left(0_1^{+}\right)$ isotopes with THSR wave function.

Figure 6

Decomposition of momentum distributions in ${}^{10}\mathrm{Be}$ ($0_1^{+}$) into components contributed by $\alpha$ clusters and valence neutrons.