Incomplete fusion in $^{193}$Ir($^{12}$C, x)$^{205}$Bi reaction at $E_{lab}$ $pprox$ 5-7 AMeV

Low-energy heavy-ion induced reactions often involve incomplete fusion, but the dependence of ICF on various entrance-channel parameters remains unclear. In this work, we measure channel-by-channel production cross-sections of different evaporation residues populated via complete and/or incomplete fusion in $^{12}$C+$^{193}$Ir system at $E_{lab}$ $\approx$ 64–84 MeV ($\approx$ 5–7 AMeV) using the stacked-foil activation technique followed by offline $γ$-spectroscopy. Experimentally measured excitation functions have been analyzed in the framework of the statistical model code PACE4 using different values of the level-density parameter ($a$ = A/9-A/15 MeV${^{-1}}$). In the analysis of excitation functions, the $xn$ and $pxn$ channels (after correcting with their precursor contributions) have been explained fairly well with $a$ = A/13 MeV${^{-1}}$; however, almost all $α$-emitting channels showed substantial enhancement over PACE4 predictions, which has been attributed to incomplete fusion. The incomplete fusion fraction ($F_{ICF}$) increases linearly with energy from 12% to 18% at 64 and 84 MeV, respectively. For better insights into the onset and strength of ICF, the variations of $F_{ICF}$ have been studied as a function of different entrance-channel parameters, which are found to increase with mass asymmetry, Coulomb factor, and neutron skin thickness. Further analysis of the data suggests the onset of ICF below the critical angular momentum ($\ell<\ell_{crit}$). Projectile breakup-driven incomplete fusion is found to suppress complete fusion by $\approx12%$ and $\approx6%$ w.r.t. the universal fusion function and the improved fusion function, respectively. These findings highlight the critical role of projectile structure at 5–7 AMeV energies, with implications for high-spin spectroscopy and reaction modeling.

💡 Research Summary

In this work the authors investigate the competition between complete fusion (CF) and incomplete fusion (ICF) in the low‑energy heavy‑ion reaction 12C + 193Ir at laboratory energies of 64–84 MeV (≈5–7 AMeV). Using the stacked‑foil activation technique followed by offline high‑resolution γ‑spectroscopy, they identified eight evaporation residues (201Bi, 200Bi, 201Pb, 200Pb, 200Tl, 199Tl, 198Tl, and 196Au) and measured their production cross sections with overall uncertainties below 13 %.

The experimental excitation functions were compared with calculations from the statistical model code PACE4, which treats only the decay of a fully equilibrated compound nucleus formed by CF. By varying the level‑density parameter a = A/K (MeV⁻¹) the authors found that K = 13 (a = A/13 MeV⁻¹) reproduces the xn (4n, 5n) and pxn (p3n, p4n) channels very well, indicating that these residues are populated exclusively via CF after appropriate precursor corrections.

In stark contrast, all α‑emitting channels (αn, α2n, α3n, 2αn) exhibit cross sections that are one to two orders of magnitude larger than the PACE4 predictions. Since PACE4 does not include projectile breakup or partial capture, the authors attribute this excess to ICF processes in which the 12C projectile breaks up into an α particle and an 8Be cluster; the 8Be fragment then fuses with the 193Ir target while the α particle continues forward as a spectator. This breakup‑fusion (BUF) mechanism explains the observed enhancement of 200Tl, 199Tl, 198Tl, and 196Au.

The incomplete‑fusion fraction, defined as the excess α‑channel yield relative to the total measured yield, rises linearly from about 12 % at 64 MeV to 18 % at 84 MeV. To explore the systematic dependence of ICF on entrance‑channel properties, the authors examine several parameters: mass asymmetry μ = (A_T − A_P)/(A_T + A_P), the Coulomb factor Z_P Z_T, and the neutron‑skin thickness ΔR_np of the interacting nuclei. All three show a positive correlation with the ICF fraction, and the combined parameter Z_P Z_T · ΔR_np yields the strongest linear trend. This suggests that larger charge product and thicker neutron skins promote projectile breakup and thus enhance ICF.

A notable finding is that ICF is observed even for angular momenta below the critical value ℓ_crit, contrary to the conventional picture that ICF only occurs for ℓ > ℓ_crit. The authors argue that at these low energies the α‑cluster structure of 12C lowers the breakup barrier, allowing partial fusion to start at relatively low impact parameters.

The suppression of complete fusion by projectile breakup is quantified by comparing the measured CF cross sections with the universal fusion function (UFF) and an improved fusion function (IGF). The breakup‑induced CF suppression amounts to ≈12 % relative to the UFF and ≈6 % relative to the IGF. This suppression underscores the importance of ICF in shaping the overall fusion yield at near‑barrier energies.

Overall, the paper provides a comprehensive experimental dataset for a heavy‑ion system at 5–7 AMeV, demonstrates that ICF can contribute a sizable (up to ~20 %) fraction of the total reaction yield, and establishes clear correlations between ICF strength and entrance‑channel parameters. These results have direct implications for high‑spin spectroscopy (where ICF can selectively populate high‑spin states), for the synthesis of heavy and super‑heavy nuclei (where ICF may open alternative pathways), and for the refinement of reaction‑model codes that must now incorporate projectile breakup and partial capture even below ℓ_crit. Future work extending the study to projectiles with different cluster structures and to targets with varying deformation and neutron excess will be essential to develop a universal description of incomplete fusion at low energies.