Let an ellipse $$E:{{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$, ${a^2} \gt {b^2}$, passes through $$\left( {\sqrt {{3 \over 2}} ,1} \right)$$ and has eccentricity ${1 \over {\sqrt 3 }}$. If a circle, centered at focus F($\alpha$, 0), $\alpha$> 0, of E and radius ${2 \over {\sqrt 3 }}$, intersects E at two points P and Q, then PQ2 is equal to :