content_image/358462.jpg content_image/358461.jpg content_image/358460.jpg content_image/358459.jpg content_image/358458.jpg
constant[3], c is the speed of light and is approximately equal to 137a.u.. The angular factor such as f ( θ 0 , φ 0 ; θ$_{L}$, φ$_{L}$ ) represents the dependence of the detached-electron wave function on the outgoing direction ( θ 0 , φ 0 ) for center 0, and it can be written as [25] 

<img src='content_image/358462.jpg'>

The angular factors f ( θ 1 , φ 1 ; θ$_{L}$, φ$_{L}$ ) and f ( θ 2 , φ 2 ; θ$_{L}$, φ$_{L}$ ) can be written out in a similar way. 

After substituting Eqs.(2) and Eqs.(3) in Eq.(1), we can get the explicit expression for the detached-electron wave function Ψ + $_{M}$. The resulting formula for Ψ + M can be simplified because the calculation of the photodetachment cross section requires the knowledge of Ψ + M at large distances where r 1 , r 0 and r 2 are much greater than the distance d between two neighboring centers. Let ( r, θ, φ ) be the spherical coordinates of the detached-electron relative to the origin. Then we approximate the phase terms using r 1 ≈ r − d cos θ , r 0 = r , r 2 ≈ r + d cos θ ; in other places we can set r 1 ≈ r 2 ≈ r 0 = r , θ 1 ≈ θ 2 ≈ θ 0 = θ . With these approximations, Ψ + M becomes 

<img src='content_image/358461.jpg'>

Eq.(4) describes the detached-electron wave of the linear triatomic anion when the detached- electron is far away from the anion. 

The differential cross section is [5] 

<img src='content_image/358460.jpg'>

where σ is the photodetachment cross section, ds is the differential area on a surface Γ such as the surface of a large sphere enclosing the anion, q is the coordinate on the surface Γ, n is the exterior norm vector at q and j is the detached-electron flux. 

The detached-electron flux in the radial direction can be evaluated as 

When Eq.(4) is substituted in Eq.(6), we get 

<img src='content_image/358459.jpg'>

<img src='content_image/358458.jpg'>

