Pion-He scattering length

We present relativistic three-body calculations for the real part of the π-⁴He scattering length Re a. Nucleon binding, exclusion principle and Fermi motion are all included in a very careful manner. Because of our careful evaluation of the single-scattering process the remaining discrepancies with the experimental data can be attributed to higher-order mechanisms involving more than one nucleon. In particular for the πA S-wave interaction at threshold, one expects that these higher-order contributions arise largely from the absorption effect. We have performed our calculations for four current models of the input πN t-matrix. Using a πN t-matrix which reproduces the low energy πN phase shifts correctly leads to Re a_abs -Im a_abs, if we attribute the discrepancy of the calculated value with the accurately determined empirical value of Re a to pion absorption. We determine the strength parameter B₀ in a p² optical potential term from an adjustment to the π-⁴He scattering length. Finally some cross sections are calculated for T^lab_π = 10 MeV and T^lab_π = 15 MeV.