2. Given $F_{1}$ and $F_{2}$ are the left and right foci of the ellipse $E$, and the parabola $C$ has $F_{1}$ as its vertex and $F_{2}$ as its focus. Let $P$ be a point of intersection between the ellipse and the parabola. If the eccentricity $e$ of the ellipse $E$ satisfies $\left|P F_{1}\right|=e\left|P F_{2}\right|$, then the value of $e$ is ( ).
(A) $\frac{\sqrt{2}}{2}$
(B) $2-\sqrt{3}$
(C) $\frac{\sqrt{3}}{3}$
(D) $2-\sqrt{2}$
2. (C).

From $\frac{\left|P F_{1}\right|}{r}=\left|P F_{2}\right|$, we know that the directrix of the ellipse E coincides with the directrix of the parabola $\mathrm{C}$.

According to the problem, the equation of the directrix of the parabola $C$ is $x=-3 c$, and the left directrix of the ellipse $E$ is $x=-\frac{a^{2}}{c}$, where $a$ and $c$ are the semi-major axis and the semi-focal distance of the ellipse, respectively.
Thus, $-\frac{a^{2}}{c}=-3 c$.
Therefore, $e=\frac{c}{a}=\frac{\sqrt{3}}{3}$.