Experimental study of cross sections in the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ system at $\approx 3–7\mathrm{MeV}/\text{nucleon}$ relevant to the incomplete fusion process

Background: The reaction mechanism in the low mass region particularly at low projectile energies in heavy-ion fusion processes has not been fully understood. More and more experimental data on fusion processes are required for the accurate description of reaction processes involved at low projectile energies. In the literature, cross section data for the fusion process using a ${}^{12}\mathrm{C}$ beam in the lower mass region and at low projectile energies are scarce.

Purpose: To understand the dynamics of fusion processes and to test various existing theoretical models, the measurements of reaction cross sections in the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ system have been carried out.

Method: The experiments were performed for the measurement of the cross sections for the residues produced in the interaction of the ${}^{12}\mathrm{C}$ ion with a ${}^{27}\mathrm{Al}$ target nucleus at 20 different energies covering the energy range from $\approx 39$ to $85\mathrm{MeV}$. The off-line $\gamma -\text{ray}$ spectrometry based activation technique has been used to measure the cross sections.

Results: The measured excitation functions were compared to those evaluated with the code pace4 based on the statistical approach and Monte Carlo procedure. The enhancement of experimental cross sections as compared to the theoretical predictions of code pace4 has been observed. The SUMRULE model predictions indicate that incomplete fusion processes are associated with smaller values of the angular momenta than that of its critical value required for complete fusion processes.

Conclusions: In the lower mass region, phenomena such as incomplete fusion and direct reaction processes are of importance even at energies as low as $\approx 3–7\mathrm{MeV}/\text{nucleon}$, where fusion evaporation channels are expected to be dominant.

Figure 1

Observed $\gamma$-ray spectrum of a ${}^{27}\mathrm{Al}$ sample irradiated by ${}^{12}{\mathrm{C}}^{6+}$ beam at $\approx 42$ MeV.

Figure 2

Calculated EFs for dominant reaction channels and total fusion cross sections obtained from pace4 code in the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ system.

Figure 3

Experimentally measured and theoretically calculated cross sections for the reaction ${}^{27}\mathrm{Al}{{(}^{12}\mathrm{C},\alpha n)}^{34}\mathrm{Cl}$ along with the measured cross sections by Landenbauer-Bellis et al. [25].

Figure 4

Experimentally measured cross sections for the reaction ${}^{27}\mathrm{Al}{{(}^{12}\mathrm{C},2\alpha 3p)}^{28}\mathrm{Mg}$.

Figure 5

Experimentally measured cross sections for the reaction ${}^{27}\mathrm{Al}{{(}^{12}\mathrm{C},3\alpha 2pn)}^{24}\mathrm{Na}$. The measured values of the cross sections for the residue ${}^{24}\mathrm{Na}$ by Landenbauer-Bellis et al. [25] are also shown for comparison.

Figure 6

Fusion $\ell$ distributions calculated by using the code ccfull for the ${}^{12}\mathrm{C}+{}^{27}\mathrm{Al}$ system at $E_{\mathrm{lab}}$ = 40, 50, 60, 70, and 80 MeV, respectively.