It is interesting that the average cross section is equal to the laser polarization depen- dent cross section in Eqs.(9)-(12) evaluated at a special angle satisfying θ$_{L}$ = arccos( 1 √ $_{3}$) (approximately 54 . 74 ◦ ). The same angle was noticed for the two-center system earlier[36]. The averaging process does not change the basic oscillatory structure of the cross section. However, the oscillation amplitudes in the average cross section are reduced to one third of the values obtained for the laser polarization dependent cross section at θ$_{L}$ = 0. In Fig.4(a) we compare the average cross section and the laser polarization dependent cross section at θ$_{L}$ = 0. The oscillations are better analyzed using a transformation. For the cross section σ ( E ) we define F ( x ) using the following integral In Fig.4(b) we present the corresponding transformations of the two cross sections in Fig.4(a). Several points can be derived from Fig.4 regarding the oscillations. First, there are two peaks in each transformation. The peaks correspond to two oscillations in each cross section. Second, the oscillation frequencies are not changed by the averaging procedure. Third, the oscillation amplitudes in the average cross section are considerable reduced. We now compare the average photodetachment cross section of the triatomic anion with that of the two-center negative ion studied earlier[36]. In Fig.5(a) we show the two cross sections. One can see that the oscillation in the photodetachment cross section for the triatomic anion is enhanced compared to that for the two-center system. In Fig.5(b) we show the corresponding transformations of the two cross sections in Fig.5(a). It is clear from Fig.5(b) that there are two oscillations for the triatomic anion but only one oscillation for the two-center system. Closed-orbit theory was extended previously to explain the oscillation in the cross sec- tion of the two-center system. The oscillation was identified as an interference between the detached-electron wave emitted at one center and the source of the wave at another center[36]. A similar explanation can be made here. For example, the detached-electron wave produced at center 1 will reach center 0 and 2 as it propagates out. The overlap of this 7 F ( x ) = ∫ E 2 E 1 [ σ ( E ) − σ 0 ( E )] sin[ π ( E − E 1 ) ( E 2 E 1 ) ] k $^{exp(}$− ikx ) dE. (18) IV. FOURIER ANALYSIS