Three-body analysis of¹¹Li and itsβ-decay to deuteron channel and to halo analog state¹¹Be* (18.3 MeV)

Abstract

The ground state wave function of¹¹Li obtained in a three-body model proposed earlier (S Kumar and V S Bhasin,Phys. Rev. C65, 034007 (2002)) has been employed to study the probability distributions, momentum distributions and n−n correlation. Complex scaling method has been used to find the energy positions and widths of the three resonant states of¹¹Li above the breakup threshold. The formalism is extended further to study the β-decay of¹¹Li to two channels. One is the β-transition of¹¹Li into a high lying excited state of¹¹Be at 18.3 MeV, i.e.,¹¹Be* and the second is the decay to deuteron +⁹Li channel. The¹¹Be* state has been considered as a halo analog state identified as a bound three-body (⁹Li + n + p) system. The n-⁹Li interaction incorporates both the virtual state and the p-wave resonance observed experimentally. For p-⁹Li interaction, a Coulomb corrected separable interaction is constructed using charge indepedendence for strong interaction part. The n-p interaction is operative only in³S₁ state corresponding to the isotopic spin T^h =0. As a result the¹¹Be* state has the same isotopic spin as that of⁹Li core, i.e.,T = 3/2. Using these realistic parameters as input and without invoking any other free parameter, the model has been used to predict the strength of the Gamow-Teller β-decay of¹¹Li to¹¹Be*, i.e.,Bgt = 1.5 and the value of the branching ratio to⁹Li + deuteron channel to be 1.3 × 10^-4. These results are found to be in rather good agreement with the recent experimental findings.