Dynamical model for the ABC effect

We present a model for ABC production, which is experimentally observed in the missing mass spectrum of the reaction $\text{dp}\text{→}{}^3\text{He}\text{+ (}\text{MM}\text{)°}$. The reaction is assumed to be split in two successive steps, namely: (i) N₁p → d_i1 followed by (ii) $\text{N}{}_2\text{d}{}_{\mathrm{<mtext>i</mtext>}}\text{→}{}^3\text{He}\text{π}{}_2\text{,}\text{N}{}_1$ and N₂ being the two nucleons of the incident deuteron and d_i an intermediate deuteron. The total amplitude is factorized into the product of the two amplitudes of reactions (i) and (ii). We know that at low energy these two reactions are dominated by a Δ production. This implies that the total cross sections are given by Breit-Wigner type formulae and that the angular distributions are peaked in the backward and forward directions. The two main results are: (i) at given incident energy, the ABC effect results from the angular distribution of the two intermediate reactions; (ii) the energy dependence of the ABC is deduced from those of the intermediate processes. The resulting fits are generally excellent when the Fermi motion in the initial deuteron is taken into account.