content_image/358527.jpg content_image/358526.jpg
explained using closed-orbit theory. Atomic units will be used unless specially noted. 

## II. FORMULAS FOR TOTAL PHOTODETACHMENT CROSS SECTION 

The linear triatomic anion interacting with a laser is shown schematically in Fig.1. Sym- bols 1,0 and 2 represent the three atomic centers in the system. It is convenient to choose the z-axis in the direction of the three-center axis and the middle center denoted by 0 as the origin of coordinates. Let d be the distance between two adjacent centers. The laser polarization direction is denoted as ( θ$_{L}$, φ$_{L}$ ) with respect to the z axis. 

In the triatomic anion, one active electron is assumed. This is an extension of the two- center model for photodetachment[34–36] to a three-center model by Afaq et al. [38]. In the photodetachment process, there are two steps: in the first step, the active electron absorbs one photon energy E$_{ph}$ and escapes from the negative anion as an electron wave from each center; in the second step, the outgoing waves from each center propagate out to large distances. The interference of the outgoing waves from each center produces oscillatory cross section. 

For the general case, as illustrated in Fig. 1, Let Ψ + 1 , Ψ + 0 and Ψ + 2 be the detached-waves from center 1, 0 and 2 respectively. Following the previous approach in the two-center case[36], the outgoing detached-electron wave Ψ + M from the triatomic anion can be written as a linear combination given by[36] 

<img src='content_image/358527.jpg'>

Let ( r 1 , θ 1 , φ 1 ), ( r 0 , θ 0 , φ 0 ) and ( r 2 , θ 2 , φ 2 ) represent the spherical coordinates of the detached- electron relative to the three centers respectively. The detached-electron wave generated from each center has been worked previously[25]. They can be written as 

<img src='content_image/358526.jpg'>

where k = √$_{2}$$_{E}$ and E is the detached-electron energy; k$_{b}$ is related to the binding energy E$_{b}$ of H − by E$_{b}$ = k 2 b 2 . The photon energy is given by E$_{ph}$ = E + E$_{b}$ . B is a normalization 

