Phase Shift Analysis and Real Amplitude of High Energy Proton-Proton Elastic Scattering

概要

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Phase shifts δ_l and the absolute values η_l of the partial wave S matrix elements are evaluated for proton-proton scattering up to l=30 in the energy region of 10 GeV/c to 25 Gev/c. We assume Orear's formula (dσ/dΩ)=B^2p^2e^<γt>+(A/s)e^<-apsinθ>, where the first term comes from the imaginary amplitude and the second is attributed to the real part. No spin dependence is assumed. The results show that the asymptotic behavior of δ_l for low partial waves has the two possibilities: δ_l is negative, increases and tends to zero, or decreases and tends to -90° as the energy increases. This fact depends critically on the values of B and γ. The partial wave unitary relation still holds up to l=30, which was shown by Sumi to be violated for large l in the eikonal approximation. Next the contribution to the imaginary part from the elastic intermediate state is shown to dominate over inelastic states at rather small momentum transfer t≈-0.6. Finally a possible form of the real amplitude is given from the imaginary part with the exponential t-dependence and the one-pion-exchange model, by taking absorption into account. For the simple and extreme case the ratio of the real to the imaginary part is about -0.5 in the forward angle.
理論物理学刊行会の論文
1966-12-25