not perpendicular to the axis, we observe a hint of oscillation as illustrated in the insert. In fact, the oscillations will become strong and obvious as the parameter S = kd is increased to be comparable or greater than π . In Fig.3 we show the photodetachment cross sections in Eqs.(9)-(12) for several d and θ$_{L}$ values. The following points can be derived directly from Fig.3. First, we do not observe obvious oscillation in the photodetachment cross sections for the perpendicular laser polarization ( θ$_{L}$ = π $_{2}$) even when d is increased. But when the laser polarization direction is not perpendicular to the anion axis, there are strong oscillations. Second, the oscillation amplitude depends on the laser polarization direction. In fact, the oscillation amplitude increases and reaches maximum as the laser polarization direction is turned from perpendicular to parallel direction with respect to the anion axis ( θ$_{L}$ = 0). However, the oscillation frequency is not sensitive to the laser polarization direction. The modulation function A 3 suggests the oscillation frequency increases but the oscillation amplitude decreases as the parameter d is increased. The oscillations are easily observed when d $^{is approximately around 30}$− 100 a 0 in our system. The limits of the photodetachment cross sections of the anion can be obtained from the limits of I ( S ). Using Taylor series expansion,one can show The above results are independent of the value of θ$_{L}$ . Therefore we conclude from Eqs.(9)- (12) that in the low energy limit the total photodetachment cross section of the three-center system is three times of the photodetachment cross section of a single-center system and in the large photon energy limit the photodetachment cross section of the three-center system approaches the photodetachment cross section of a single-center system. It is also straightforward to get the photodetachment cross section averaged over the orientations of the anion. Let us assume the direction of the anion is random with respect to the laser polarization direction. Defining the averaging by The integrals can be evaluated to give the following results, 6 ¯ σ ( E, d ) = σ 0 ( E ) ¯ A 3 ( kd ) , (16) ¯ A 3 ( kd ) = 1 + 4 3 sin( kd ) kd + 2 3 sin(2 kd ) 2 kd . (17) ¯ σ ( E, d ) = ∫ π 0 sin θ$_{L}$dθ$_{L}$ ∫ 2 π 0 σ ( E, d, θ$_{L}$ ) dφ$_{L}$/ ∫ π 0 sin θ$_{L}$dθ$_{L}$ ∫ 2 π 0 dφ$_{L}$. (15) lim $^{S}$→ $_{0}$I ( S, θ$_{L}$ ) = 1 , lim $^{S}$→∞ I ( S, θ$_{L}$ ) = 0 . (14)