Molecular orbital structures in10Be

Abstract

The structure of ${}^{10}\mathrm{Be}$ is investigated using a microscopic $\ensuremath{\alpha}+\ensuremath{\alpha}+n+n$ model based on the molecular orbit (MO) model. The low-lying states are characterized by several configurations of valence neutrons, which are constructed as combinations of three basic orbits. The model space employed is extended from the traditional MO models, and the orbits are expressed as linear combinations of local Gaussians. Their positions are determined variationally. Using this model, we reanalyze the structure of ${}^{9}\mathrm{Be}$ and show that this extension enables us to use the original two-body spin-orbit interaction determined from a scattering phase-shift analysis of $\ensuremath{\alpha}\ensuremath{-}n.$ In ${}^{10}\mathrm{Be},$ all of the observed positive-parity bands and the negative-parity bands are described within the model. The ${0}^{+}$ ground state of ${}^{10}\mathrm{Be}$ is described by a dominant ${(3/2}^{\ensuremath{-}}{)}^{2}$ configuration. The state has a rather large binding energy (8.38 MeV from the $\ensuremath{\alpha}+\ensuremath{\alpha}+n+n$ threshold experimentally), and the mechanism leading to binding, such as a pairing effect and reduction of the kinetic energy between two clusters, is discussed in detail. In spite of this large binding, the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ clustering in the ground state persists due to a coupling effect between the ${}^{6}\mathrm{He}+\ensuremath{\alpha}$ configuration and the ${}^{5}\mathrm{He}{+}^{5}\mathrm{He}$ configuration, which provides a smooth potential for the valence neutrons. The second ${0}^{+}$ state of ${}^{10}\mathrm{Be}$ has a large $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ structure with a ${(1/2}^{+}{)}^{2}$ configuration. An enlargement of the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ distance due to two-valence neutrons along the $\ensuremath{\alpha}\ensuremath{-}\ensuremath{\alpha}$ axis makes their wave function smooth and reduces the kinetic energy drastically. Furthermore, the contribution of the spin-orbit interaction due to coupling between the ${S}_{z}=0$ and the ${S}_{z}=1$ configurations is important. We also show the mediation effect of two valence neutrons between two $\ensuremath{\alpha}$ clusters.