A New Energy-dependent Δ Width in Coherent Pion Production

Abstract

A new derivation for the energy-dependent Δ width inside nuclei is presented which includes the all important, energy-dependent nuclear form factor describing the decay of the Δ particle from its harmonic oscillator, bound state back to a captured nucleon and outgoing pion. Additional improvements include relativistic kinematics, generalisation beyond the static limit in the kinematics, and inclusion of the ΔN Π energy-dependent vertex form factor. The new decay width provides a reasonable cut-off at high pion momenta and gives the correct momentum dependence in the limit of single-particle decay at low momenta. The results of calculations for the energy-dependent widths and their effects on the energy distributions of exclusive coherent pion production for ¹² C+ ¹² C → ¹² C+ ¹² C* (T = 1)+ Π ⁰ at incident energies below and above the pion threshold are shown and discussed. The new energy dependence is compared to the free Δ width used previously and it is seen that the new results give a smoother and more realistic shape to the pion energy distributions.