Distorted-wave impulse-approximation (p,π) calculations: Effects of realistic wave functions and factors determining resonance position

Abstract

In a recent paper a general impulse approximation formalism for ($p,\ensuremath{\pi}$) reactions in nuclei was developed which incorporated distortion, spin, and antisymmetrization effects. Here we discuss two further considerations in connection with this model with particular reference to its application to the reactions $\mathrm{pd}\ensuremath{\rightarrow}t{\ensuremath{\pi}}^{+}$ and $\mathrm{pd}\ensuremath{\rightarrow}^{3}\mathrm{He}{\ensuremath{\pi}}^{0}$. First, realistic wave functions for $t$ and $^{3}\mathrm{He}$ which produce the dip in the electromagnetic form factor are incorporated. We find results qualitatively similar to those found previously when simple analytic wave functions were used. This is in contrast to the work of Locher and Weber who found that the dip in the electromagnetic form factor produced a similar dip in the ($p,\ensuremath{\pi}$) cross section. In the present model correct antisymmetrization of the wave functions and inclusion of spin components of the wave functions, in particular the $D$ state of the deuteron, fill the dip. Second, we examine the factors which affect the energy at which a bump due to the $\ensuremath{\Delta}(1232)$ resonance would appear in the ($p,\ensuremath{\pi}$) cross section. This is motivated by a recent experiment which found no evidence of a bump at 450 MeV where it would be expected from simple kinematic arguments. We find that distortion and form factor effects both tend to push the bump to lower energies and that the net result is that the model predicts a smooth falloff with energy of the fixed angle cross section above 350 MeV, in qualitative agreement with the experiment, and a bump below 350 MeV, where there are no data. The physical mechanisms responsible for the shift, and some possible approaches which might improve quantitative agreement, are then briefly discussed.[NUCLEAR REACTIONS ($p,\ensuremath{\pi}$) reactions in distorted-wave impulse approximation. Effects of realistic wave functions on cross section and of form factors and distortion on resonance position. Differential cross section and energy dependence of fixed angle cross section for $^{2}\mathrm{H}(p,{\ensuremath{\pi}}^{+})^{3}\mathrm{H}$ and $^{2}\mathrm{H}(p,{\ensuremath{\pi}}^{0})^{3}\mathrm{He}$ at 250-800 MeV.]