Mechanism of cluster emission in nucleon-induced preequilibrium reactions

A model is proposed for the preequilibrium emission of light composite particles in the framework of the exciton model. The model contains two new points: One is the calculation of the formation factor $F_{l,m}\left(\epsilon \right)$ which stands for the probability that the composite particle of an energy $\epsilon$ is composed of $l$ particles above the Fermi level and $m$ particles below. Information of the intrinsic wave function of the composite particle is incorporated in the $F_{l,m}\left(\epsilon \right)$. Another new point is the inclusion of the pickup type contribution in the particle emission mechanism. We allow some nucleons which constitute the emitted composite particle to come from levels below the Fermi energy. This model is applied to six kinds of ($p, \alpha$) reactions of incident energies of several tens of MeV on ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}$, ${}_{}{}^{118}{}_{}{}^{}\mathrm{Sn}$, and ${}_{}{}^{120}{}_{}{}^{}\mathrm{Sn}$ targets. Calculated results reproduce nicely the high energy part of the experimental energy spectra and indicate that its main component is the "three-particle pickup" reaction coming from $2p-1h$ and $3p-2h$, but "two-particle pickup" also contributes substantially.