Three-body structure of low-lyingBe12states

Abstract

We investigate to what extent a description of $^{12}\mathrm{Be}$ as a three-body system made of an inert $^{10}\mathrm{Be}$ core and two neutrons is able to reproduce the experimental $^{12}\mathrm{Be}$ data. Three-body wave functions are obtained with the hyperspherical adiabatic expansion method. We study the discrete spectrum of $^{12}\mathrm{Be}$, the structure of the different states, the predominant transition strengths, and the continuum energy spectrum after high-energy fragmentation on a light target. Two ${0}^{+}$, one ${2}^{+}$, one ${1}^{\ensuremath{-}}$, and one ${0}^{\ensuremath{-}}$ bound states are found; the first four are known experimentally, whereas the ${0}^{\ensuremath{-}}$ is predicted as an isomeric state. An effective neutron charge, reproducing the measured $B(E1)$ transition and the charge rms radius in $^{11}\mathrm{Be}$, leads to a computed $B(E1)$ transition strength for $^{12}\mathrm{Be}$ in agreement with the experimental value. For the $E0$ and $E2$ transitions, the contributions from core excitations could be more significant. The experimental $^{10}\mathrm{Be}$-neutron continuum energy spectrum is also well reproduced, except in the energy region corresponding to the $3/{2}^{\ensuremath{-}}$ resonance in $^{11}\mathrm{Be}$ where core excitations contribute.