PROTON–4He ELASTIC SCATTERING AT ~ 1 GeV

Based on the (spin-independent) Sugar–Blanckenbecler eikonal expansion for the T-matrix, we parametrize the (spin-dependent) NN amplitude (SNN) which successfully describes the pp and pn elastic scattering observables at ~ 1 GeV up to the available momentum transfers. Using SNN, we calculate the differential cross-section, polarization, and spin-rotation function of ~ 1 GeV protons on 4 He within the framework of the Glauber model. The analysis also includes the phase variation in the NN amplitude. It is found that the use of SNN, in comparision with the usually parametrized one-term amplitude, improves the agreement with the experimental data. The introduction of a global phase variation provides only a slight improvement over the results with a constant phase. However, if we allow different phases in the central- and spin-dependent parts of the NN amplitude, the agreement with the polarization data improves further without affecting the differential cross-section results.

BOSONIZATION AND THE EIKONAL EXPANSION: SIMILARITIES AND DIFFERENCES

We compare two non-perturbative techniques for calculating the single-particle Green’s function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green’s function is first calculated for a fixed configuration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the quasi-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green’s function predicted by the eikonal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behavior of the spectral function, nor predicts the correct location of its singularities.