Structure of the mirror nuclei ${}^9$Be and ${}^9$B in a microscopic cluster model

Abstract

The structure of the mirror nuclei ${}^9$Be and ${}^9$B is studied in a microscopic $\alpha +\alpha +n$ and $\alpha +\alpha +p$ three-cluster model using a fully antisymmetrized 9-nucleon wave function. The two-nucleon interaction includes central and spin-orbit components and the Coulomb potential. The ground state of ${}^9$Be is obtained accurately with the stochastic variational method, while several particle-unbound states of both ${}^9$Be and ${}^9$B are investigated with the complex scaling method.The calculation for ${}^9$Be supports the recent identification for the existence of two broad states around 6.5 MeV, and predicts the ${\frac{3}{2}}_2^{-}$ and ${\frac{5}{2}}_2^{-}$ states at about 4.5 MeV and 8 MeV, respectively. The similarity of the calculated spectra of ${}^9$Be and ${}^9$B enables one to identify unknown spins and parities of the ${}^9$B states. Available data on electromagnetic moments and elastic electron scatterings are reproduced very well. The enhancement of the $E$1 transition of the first excited state in ${}^9$Be is well accounted for. The calculated density of ${}^9$Be is found to reproduce the reaction cross section on a Carbon target. The analysis of the beta decay of ${}^9$Li to ${}^9$Be clearly shows that the wave function of ${}^9$Be must contain a small component that cannot be described by the simple $\alpha +\alpha +n$ model. This small component can be well accounted for by extending a configuration space to include the distortion of the $\alpha$-particle to $t+p$ and $h+n$ partitions.

24 pages

References in corpus (2)

• Precise solution of few-body problems with stochastic variational method on correlated Gaussian basis
• Microscopic multicluster description of the neutron-rich helium isotopes

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