Classical and Quantal Scattering. I. The Classical Action

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Abstract
Classical scattering is based on the action A = S − S0, where S is the action over the actual trajectory and S0 is over the equivalent without interaction. For two‐body spherical potential scattering A = Δ(L, E) − LΘ, where Θ is the deflection angle and Δ is the classical phase, the classical limit of 2ℏδl (E). A new, rapidly convergent integral expression is given for Δ (L, E). From this is derived a convergent expansion in 1/E valid for fixed L≠O, and an equivalent form in 1/L valid for fixed E. The lowest term in 1/L agrees with Massey and Mohr, and higher terms are evaluated.