Validation of the ${}^{10}\mathrm{Be}$ Ground-State Molecular Structure Using ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ Triple Differential Reaction Cross-Section Measurements

The cluster structure of the neutron-rich isotope ${}^{10}\mathrm{Be}$ has been probed via the $(p,p\alpha )$ reaction at $150\mathrm{MeV}/\mathrm{nucleon}$ in inverse kinematics and in quasifree conditions. The populated states of ${}^6\mathrm{He}$ residues were investigated through missing mass spectroscopy. The triple differential cross section for the ground-state transition was extracted for quasifree angle pairs $({\theta }_p,{\theta }_{\alpha })$ and compared to distorted-wave impulse approximation reaction calculations performed in a microscopic framework using successively the Tohsaki-Horiuchi-Schuck-Röpke product wave function and the wave function deduced from antisymmetrized molecular dynamics calculations. The remarkable agreement between calculated and measured cross sections in both shape and magnitude validates the molecular structure description of the ${}^{10}\mathrm{Be}$ ground-state, configured as an $\alpha \text{−}\alpha$ core with two valence neutrons occupying $\pi$-type molecular orbitals.

Figure 1

Schematic view of ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}$ reaction setup.

Figure 2

Excitation energy spectra for ${}^{10}\mathrm{Be}(p,p\alpha ){}^6{\mathrm{He}}^{*}$ reaction. (a) Integrated over the full solid angle covered by proton and cluster detectors. The vertical dashed line indicates the 2-neutron separation energy (0.975 MeV). The red and blue solid lines show spectra corresponding to events gated by ${}^6\mathrm{He}$ and ${}^4\mathrm{He}$ residues, respectively. (b) Same for events corresponding to the quasifree angle pair (${\theta }_p/{\theta }_{\alpha }=65°/-7.7°$) with an angular bin size of $\pm 1°$. See text for details.

Figure 3

(a) TDX distribution of ${}^{10}\mathrm{Be}(p,p\alpha ){}^6\mathrm{He}(\mathrm{g}.\mathrm{s}.)$ reaction extracted at the coplanar angle pair ${\theta }_p/{\theta }_{\alpha }=65°/-7.7°$, which is chosen to include recoilless condition of the residual nucleus. The arrow indicates the proton kinetic energy $T_p$ at the recoilless condition. The red and blue solid lines are the DWIA predictions using the THSR and AMD structural models, respectively. The blue dashed line (dot-dashed line) is the TDX for an artificial state describing the compact shell-model-like (loosely bound gaslike) structure of ${}^{10}\mathrm{Be}$ nucleus [19]. (b) The corresponding phase volume distribution. The horizontal dashed line indicates the product of solid angles $\mathrm{\Delta }{\mathrm{\Omega }}_p·\mathrm{\Delta }{\mathrm{\Omega }}_{\alpha }$. (c) and (d) are the density distribution of the protons and valence neutrons in the ground state of ${}^{10}\mathrm{Be}$ predicted by the THSR model, adapted from Refs. [19, 36].