Three-body analysis of ¹¹Li and its b-decay

to deuteron channel and to halo analog state

¹¹Be* (18.3 MeV)

S KUMAR and V S BHASIN

Department of Physics and Astrophysics, University of Delhi, Delhi 110 007, India

Abstract. The ground state wave function of $^{11}$Li obtained in a

three-body model proposed earlier (S Kumar and V S Bhasin, {\it Phys.~Rev.}

{\bf 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 of $^{11}$Li above the breakup threshold.

The formalism is extended further to study the $\beta$-decay of $^{11}$Li to

two channels. One is the $\beta$-transition of $^{11}$Li into a high lying excited state

of $^{11}$Be at 18.3 MeV, i.e., $^{11}$Be$^{*}$ and the second is the decay to

deuteron $+$ $^{9}$Li channel. The $^{11}$Be$^{*}$ state has been considered as a halo analog

state identified as a bound three-body ($^{9}$Li $+$ n $+$ p) system. The n-$^{9}$Li interaction

incorporates both the virtual state and the p-wave resonance observed experimentally. For

p-$^{9}$Li interaction, a Coulomb corrected separable interaction is constructed using charge

indepedendence for strong interaction part. The n-p interaction is operative only in $^{3}$S$_{1}$

state corresponding to the isotopic spin $T_{h} = 0$. As a result the $^{11}$Be$^{*}$

state has the same isotopic spin as that of $^{9}$Li 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 $\beta$-decay of $^{11}$Li to

$^{11}$Be$^{*}$, i.e., $B_{\rm GT}=1.5$ and the value of the branching ratio to $^{9}$Li $+$ deuteron

channel to be $1.3 \times 10^{-4}$. These results are found to be in rather good agreement with

the recent experimental findings.

Keywords. $^{11}$Li; neutron halo; $\beta$-decay; complex scaling method; n-n correlation.

PACS Nos 21.45.+v; 21.10.Dr; 21.60.Gx; 27.20.+n