S-wave repulsion in the pion-nucleus optical potential and the subthreshold pion-nucleonTmatrix

Abstract

A covariant theory of the pion-nucleus interaction has been used to calculate off-shell matrix elements of the first-order pion-nucleus optical potential in momentum space. The matrix elements $〈k|{v}_{l}(W)|k〉$ are calculated for $^{16}\mathrm{O}$ and $^{40}\mathrm{Ca}$, as a function of $k$, the momentum in the $\ensuremath{\pi}$-nucleus center-of-mass system, for $W={m}_{\ensuremath{\pi}}+{M}_{N}$. (As in our previous studies we have carried out a full integration over the Fermi motion of the target nucleons. Off-shell effects related to nuclear binding are treated carefully.) As this calculation is sensitively dependent upon the subthreshold $\ensuremath{\pi}NT$ matrix, two different models for the $T$ matrix are studied. One is the well known separable model of Londergan, McVoy, and Moniz. The second model includes terms describing the direct and crossed Born terms and therefore has the appropriate $s$- and $u$-channel nucleon poles. (In the calculations using this model both the pion and the nucleon are allowed to go off the mass shell.) The remaining part of the amplitude in the second model is represented by a separable form. For small $k$, the matrix elements of the optical potential calculated with these two models are significantly larger than those obtained when use is made of the fixed-scatterer approximation. Phenomenological optical potentials which describe low-energy pion-nucleus scattering data or pionic-atom data exhibit $s$-wave repulsion which is about 2-8 times that obtained from calculations made in the fixed-scatterer approximation. (The uncertainty in this enhancement factor reflects the uncertainty in the free-space values of the $\ensuremath{\pi}N$ scattering lengths). We conclude that the explanation of a significant fraction of the $s$-wave repulsion in the low energy pion-nucleus interaction may lie in a careful treatment of off-shell effects using a good model for the subthreshold $\ensuremath{\pi}NT$ matrix.NUCLEAR REACTIONS Pion-nucleus interactions, off-shell effects in the pion-nucleus interaction at low energy; pionic atoms.