Study of the two-nucleon mechanism of pion absorption in nuclei

Abstract

The two-nucleon mechanism of pion absorption by nuclei is investigated in the energy region of the πN P 33 Δ-resonance. The basic absorption process is governed by a πNN … NΔ … NN transition matrix, derived from the phenomenological Hamiltonian of M. Betz and T.-S. H. Lee ( Phys. Rev. C, 23 (1981) , 375), which was constructed to describe NN scattering phase-shifts up to 1 GeV. The model allows a realistic description of pion absorption on a pair of bound nucleons with quantum numbers and relative radial wave functions different from those of the physical deuteron. The deuteron-like 3 S 1 ( T = 0) pairs are shown to play a privileged role, in accordance with the assumption underlying the conventional quasideuteron model. We then enbed the two-nucleon mechanism into complex nuclei, using the impulse approximation. The many-body effects on the two-body absorption mechanism are analyzed in detail by using the Faddeev wavefunction for 3He and harmonic oscillator shell-model wavefunction for 1 p-shell target nuclei in our calculations. All nonlocal effects owing to nucleon Fermi motion and NΔ off-shell propagation are treated rigorously. The main features of ( π +, p) reactions on 3He, 4He, and 12C are predicted correctly, when large pion distortion effects are taken into account by using the isobar-hole model with all of the parameters pradetermined from earlier studies of pion nucleus scattering. The predicted cross sections at the two-body absorption peaks overestimate the data by a factor ranging from 1.2 ∼ 2 for the ( π +, p) reactions, and as much as a factor of ∼ 4 for the coincidence ( π +, pp) on 12C. Our results indicate that a consistent description of all inclusive data can be obtained only when we further assume that the outgoing nucleons must be strongly rescattered by nuclear medium in 12C and heavier nuclei. When the calculated absorption cross sections are integrated over entire kinematic regions at each pion energy, we find that the calculated values are only about 1 3 to 1 2 of the total absorption cross section extracted from earlier measurements. By combining our results and calculations by K. Masutani and K. Yazaki ( Nucl. Phys. A, 407 (1983) , 309), it is concluded that a large part of total absorption cross section could originate from the inelastic absorption process: ( π, π′ N) nucleon knockout followed by pion absorption. We are, however, unable to calculate microscopically this inelastic absorption cross section unambiguously, and hence the existence of other absorption mechanisms and possible contributions to proton spectra from targer fragmentation cannot be excluded from our analysis. These possibilities become even more likely when the weaker ( π −, p) cross section is found to be undertestimated by the theory by a very large factor. The origin of this problem is identified to be the suppression, by nuclear geometry and isospin selection rules, of the two-body process πNN … NΔ … NN initiated by π −. We discuss the necessary experimental information for future improvements of the theory.