Contribution of incomplete fusion to the evaporation residue cross sections in the $^{30}$Si$+^{186}$W reaction

Abstract

The formation of the evaporation residues in the $^{30}$Si$+^{186}$W reaction leading to the compound nucleus $^{216}$Ra$^*$ has been studied in the framework of the dinuclear system (DNS) model. The capture, complete fusion, quasifission, and incomplete fusion cross sections have been calculated at the collision energies $E_{c.m.}=107.6-172.2$MeV by averaging over the orientation angles of the axial symmetry axes of the deformed $^{30}$Si and $^{186}$W nuclei. The incomplete fusion is considered as the breakup of the DNS with the emission of the $α$ particle from its very mass-asymmetric configuration, which is populated by the nucleon transfer in collisions with large orbital angular momentum. The survival probabilities of the excited $^{216}$Ra and of the conjugate nucleus $^{212}$Rn formed after the $α$-particle emission have been calculated using the statistical model. It is shown that the complete fusion is the main source of the evaporation residues at the lower collision energies, while above $E_{c.m.}=128$MeV the Rn isotopes formed in the incomplete fusion give more than half of the calculated evaporation residue cross section. The sum of both contributions describes the slow decrease of the measured total evaporation residue cross section at these energies, where the yield of the Ra isotopes decreases by an order of magnitude. The calculation of the de-excitation of $^{216}$Ra$^*$ with the emission of protons and $α$ particles shows that the contribution of the complete fusion to the cross sections of the isotopes $^{212}$Rn and $^{211}$Rn is negligible, and these isotopes are formed in the incomplete fusion. The fusion probability calculated for the partial waves $\ell\leq30\hbar$ is about 0.75 in comparison with the value $0.57\pm0.08$ extracted from the experimental data at the same collision energies.