Effects of projectile break-up on fusion cross sections at energies near and above the Coulomb barrier: a case of incomplete fusion

In the present work, the experimental studies of projectile break-up (incomplete fusion) at energies $\ensuremath{\approx}4$--7 MeV/nucleon have been performed by using offline $\ensuremath{\gamma}$-ray spectroscopy. The excitation functions of reaction residues populated in the $^{19}\mathrm{F}+^{175}\mathrm{Lu}$ system via complete fusion and/or incomplete fusion processes were measured and analyzed within the framework of the statistical model code pace4. The measured excitation functions of $xn$ and $pxn$ channels are found to be well reproduced by the predictions of pace4, which clearly indicates the population of these residues, predominantly, via complete fusion processes. However, in the case of residues involving $\ensuremath{\alpha}$ particles in the exit channels, the experimentally measured cross sections are found to show a significant enhancement when compared with pace4 predictions. This enhancement points toward the onset of incomplete fusion reactions at the studied range of energies and is found to be projectile energy dependent. Further, an attempt was made to study the influence of projectile (strongly bound) break-up on fusion cross sections, above the Coulomb barrier, within the framework of the universal fusion function, which is a benchmark function that does not depend on the system parameters. The experimental fusion function was deduced for the complete fusion (CF) cross section $(\ensuremath{\sum}{\ensuremath{\sigma}}_{\text{CF}}=\ensuremath{\sum}{\ensuremath{\sigma}}_{xn+pxn}^{\text{expt}})$ and total fusion (TF) cross section $(\ensuremath{\sum}{\ensuremath{\sigma}}_{\text{TF}}=\ensuremath{\sum}{\ensuremath{\sigma}}_{\text{CF}\phantom{\rule{4.pt}{0ex}}\text{+}\phantom{\rule{4.pt}{0ex}}\text{ICF}}^{\text{expt}})$ for three strongly bound projectiles $^{13}\mathrm{C},^{16}\mathrm{O}$, and $^{19}\mathrm{F}$ (present work) on different target nuclei and compared with the universal fusion function. Analysis of data indicates 10--$35%$ complete fusion suppression above the barrier, indicating that it is essentially due to the prompt break-up (incomplete fusion) of the strongly bound projectiles. Moreover, the deduced complete fusion suppression factor for the present work shows a conspicuous exponential relation with the break-up threshold of the projectile.