Question

Show that the imaginary part of the complex potential V = −(U +iW) in the optical model has the effect of removing particle flux from the elastic channel.

Answer 1

Introduce the complex potential V = −(U +iW) in the Schrodinger’s equation 

∇²ψ + 2m²(E + U + iW)ψ = 0   ...(1)

where v is the particle velocity and the mean free path λ = 1/K. When steady state has reached the first term on the LHS of (7) vanishes. Provided W > 0, the imaginary part of the complex potential has the effect of absorbing flux from the incident channel.