Spectral and scattering theory for a Schrödinger operator with a class of momentum-dependent long-range potentials

Let be the selfadjoint operator for the static electromagnetic field where W _j for 0, 1, 2, ..., n is a sum of (i) a short-range potential and (ii) a smooth long-range potential decreasing at as |x|^- with in (0, 1]. Then for >1/2, asymptotic completeness holds for the scattering system (H, H ₀).     

Semicoherent elastic pion-carbon scattering at 25 and 40 GeV/c

In the frame of a systematic study of hadron-nucleus interactions performed at the Serpukhov accelerator (CERN-IHEP 5th experiment), semicoherent elastic scattering on carbon $\text{π}{}^{\mathrm{?12}}\text{C}\text{a}\text{?}\text{π}{}^{\mathrm{?12}}\text{C}{}^1\text{(4.44}\text{MeV}\text{)}$ was investigated with 25 and 40 GeV/c incident pions.The experimental data were obtained with a counter technique, looking at the coincidence between the scattered pion and the 4.44 MeV photon from the J^P = 2⁺ carbon excited state detected by a NaI counter.The value obtained for the integrated cross section at 40 GeV/c in the 0.0032 ? |t| ? 0.27 (GeV/c)² four-momentum transfer range isσ = 1.16 ± 0.11 mb.According to the theoretical models, this t-range at 40 GeV/c covers more than 99% of the angular distribution, so the above value almost corresponds to the total semicoherent elastic cross section.