3. Given that $\triangle A B C$ is an equilateral triangle, the ellipse $\Gamma$ has one focus at $A$, and the other focus $F$ lies on the line segment $B C$. If the ellipse $\Gamma$ passes exactly through points $B$ and $C$, then its eccentricity is $\qquad$.
According to the problem, $|B A|+|B F|=|C A|+|C F|=2 a \Rightarrow F$ is the midpoint of $B C$. Without loss of generality, assume the side length of $\triangle A B C$ is 2, then $2 a=3, 2 c=\sqrt{3} \Rightarrow e=\frac{c}{a}=\frac{\sqrt{3}}{3}$.