3 The detached electron wave function Ψ + M is given by: Spherical polar coordinates ( r$_{1}$, θ$_{1}$, φ$_{1}$ ), ( r$_{2}$, θ$_{2}$, φ$_{2}$ ) and ( r$_{3}$, θ$_{3}$, φ$_{3}$ ) for the detached-electron relative to each center are used. The emitted waves, Ψ + 1 , Ψ + 2 and Ψ + 3 , can be expressed using Ref. [20] by: where C = 4 kBi ( k 2 $_{b}$+ k $^{2}$)$_{2}$, k$_{b}$ is related to the binding energy E$_{b}$ of H − by E$_{b}$ = k 2 b 2 , and B is a normalization constant, having value of 0 . 31552. The detached-electron wave function Ψ + $_{M}$( r, θ, φ ) from the three-center system can be obtained after the substitution of each center wave function in Eq. (1). The problem can be further simplified by using the idea that L is much larger than d . Let ( r, θ, φ ) be the spherical coordinates of the detached electron. For the phase terms, r$_{1}$ ≈ r − d cos θ , r$_{2}$ ≈ r + d cos θ and r$_{3}$ ≈ r are used, while in all other places r$_{1}$ ≈ r$_{2}$ ≈ r$_{3}$ ≈ r and θ$_{1}$ ≈ θ$_{2}$ ≈ θ$_{3}$ ≈ θ . With these approximations Ψ + $_{M}$( r, θ, φ ) reduces to: The detached-electron flux in the radial direction for the triatomic negative ion is calculated as in [1]: A large imaginary spherical surface Γ enclosing the triatomic negative ion is used to investigate the behavior of the total cross section. From the electron flux crossing the surface a generalized differential cross section dσ ( q ) ds can be obtained [20]: j$_{r}$ ( r, θ, φ ) = kC $^{2}$cos$^{2}$θ 3 r 2 [ 1 + 4 cos( kd cos θ ) + 4 cos $^{2}$( kd cos θ ) ] (3) III. DERIVATION OF THE TOTAL CROSS SECTION FOR THE TRIATOMIC NEGATIVE ION Ψ + $_{M}$( r, θ, φ ) = C cos θ √$_{3}$ [ 1 + 2 cos( kd cos θ ) ] exp( ikr ) r (2) Ψ + M = 1 √$_{3}$ (Ψ + 1 + Ψ + 2 + Ψ + 3 ) (1) Ψ + 1 ( r$_{1}$, θ$_{1}$, φ$_{1}$ ) = C cos θ$_{1}$ exp( ikr$_{1}$ ) kr$_{1}$ Ψ + 2 ( r$_{2}$, θ$_{2}$, φ$_{2}$ ) = C cos θ$_{2}$ exp( ikr$_{2}$ ) kr$_{2}$ Ψ + 3 ( r$_{3}$, θ$_{3}$, φ$_{3}$ ) = C cos θ$_{3}$ exp( ikr$_{3}$ ) kr$_{3}$ ,