Impact Parameter Formalism. IV : The Non-Zero Spin Case

概要

論文の詳細を見る
An extension of our impact parameter formalism to the elastic scattering of particles with spin is proposed; this is valid for arbitrary physical energies and scattering angles. The helicity representation of the full scattering amplitude and the Jacob-Wick partial wave expansion are used. Our impact parameter amplitude is related to both the full scattering and the partial wave amplitudes without introducing any approximation. A function a_ν(β) is defined by a_ν(β)=∫^1_0y dyJ_ν(βν)T(y), where we assume y^<1/2>T(y)EL^2(0, 1) and Re ν>-1/2 or an integer ν. The function β^<-ν>a_ν(β) is an even entire function of exponential type 1 and β^<1/2>a_ν(β)EL^2(0,∞). It satisfies the relation a_<ν+2m>(β)=∫^∞_0α dα φ_ν(α,β) a_<ν+2m>(α) where m is a positive integer and the entire function φ_ν(α,β) is defined by φ_ν(α,β)=∫^1_0y dy J_ν(αy)J_ν(βy). If we choose T(y) to be a helicity amplitude, ν an integer related with helicities of the initial and final states, and ν=sin(θ/2), θ being the scattering angle, then a_ν(β) is our impact parameter amplitude.
理論物理学刊行会の論文
1966-10-25