Behavior of the Scattering Amplitude for Large Angular Momentum
1963; American Institute of Physics; Volume: 4; Issue: 11 Linguagem: Inglês
10.1063/1.1703920
ISSN1527-2427
Autores Tópico(s)Spectroscopy and Quantum Chemical Studies
ResumoLanger's theory on the asymptotic behavior of the solutions of differential equations is applied to angular momentum, giving stronger results than were possible hitherto by Born approximation. It is shown that, for potentials V(r) analytic in the right-hand r plane satisfying |r2V(r)| < ∞ at r = 0 and |r| = ∞, the phase shift has the asymptotic form (λ = l + ½) δ→ lim λ→∞−(2λ12)12V(λ/k)2k2−λ−1 ∫ λ/k+λ−12/k∞V(r)r dr(k2r2/λ2−1)12, Re λ>0,in the λ plane and for all complex k. Consequently, (a) all Regge trajectories are bounded for analytic potentials; there are no poles for |λ| → ∞ in the right-half λ plane, (b) stronger limits can be given for the feasibility of the Watson-Sommerfeld transformation. The pathological behavior of the cut off potentials (e.g., square-well) is attributed to the nonanalyticity of the potential.
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