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The electron-phonon interaction in $C_{70}$ anions is studied by making useof a lattice relaxation approach. We find there exists a Jahn-Teller effect in$C_{70}^{3-}$ system, due to an extra electron being doped to the doubledegenerate $E_{1}^{''}$ state. As a result of this effect, the original$D_{5h}$ symmetry of the ground state becomes unstable, which causes distortionof the lattice configuration. The only symmetry maintained in the final stateof the relaxation is the $x-y$ plane reflection symmetry. We further find thatbesides the Jahn-Teller active $A_{1}^{'}, A_{2}^{'}, E_{2}^{'}$ modes, thenon-Jahn-Teller active $E_{1}^{'}$ vibrations also contribute to the relaxationprocess, which come from the nonlinear effect and are two or three orderssmaller than those of the Jahn-Teller active modes. We suggest that the$C_{70}^{3-}$ molecule is a promising Berry Phase candidate in this effective$E \otimes e$ Jahn-Teller system.Comment: 14 pages, to appear in Mod. Phys. Lett. B (1997

E⊗e Jahn–Teller Effect in ${\rm C}_{70}^{3-}$ Systems