Geometry of Borromean Halo Nuclei

We discuss the geometry of the highly quantal nuclear three-body systems composed of a core plus two loosely bound particles. These Borromean nuclei have no single bound two-body subsystem. Correlation plays a prominent role. From consideration of the $B(E1)$ value extracted from electromagnetic dissociation, in conjunction with HBT-type analysis of the two valence-halo particles correlation, we show that an estimate of the over-all geometry can be deduced. In particular we find that the opening angle between the two neutrons in $^{6}$He and $^{11}$Li are, respectively, $\theta_{nn} = {83^{\circ}}^{+20}_{-10}$ and ${66^{\circ}}^{+22}_{-18}$. These angles are reduced by about 12% to $\theta_{nn} = {78^{\circ}}^{+13}_{-18}$ and ${58^{\circ}}^{+10}_{-14}$ if the laser spectroscopy values of the rms charge radii are used to obtain the rms distance between the cores and the center of mass of the two neutrons. The opening angle in the case of $^{11}$Li is more than 20% larger than recently reported by Nakamura \cite{Nak06}. The analysis is extended to $^{14}$Be and the two-proton Borromean nucleus $^{17}$Ne where complete data is still not available. Using available experimental data and recent theoretical calculations we find, $\theta_{nn} = {64^{0}}^{+9}_{-10}$ and $\theta_{pp} = 110^{0}$, respectively.