${}^{6,7}\mathrm{Li}+{}^{27}\mathrm{Al}$ reactions close to and below the Coulomb barrier

The reactions ${}^{6,7}\mathrm{Li}+{}^{27}\mathrm{Al}$ were compared with the reactions ${}^{17,18}\mathrm{O}+{}^{16}\mathrm{O}$ which form the same compound nuclei ${}^{33,34}\mathrm{S}$. Cross-section data for the reactions ${}^{6,7}\mathrm{Li}+{}^{27}\mathrm{Al}$ were derived from experimentally determined γ-ray production cross sections for transitions in several residual nuclei. For the reactions ${}^{17,18}\mathrm{O}+{}^{16}\mathrm{O}$ experimental results from the literature were used. It could be shown that the weakly bound projectiles ${}^{6,7}\mathrm{Li}$ undergo not only fusion processes, but also breakup reactions quite in contrast to the tightly bound projectiles ${}^{18}\mathrm{O}$ and ${}^{17}\mathrm{O}$, respectively. Especially below the Coulomb barrier such direct reactions play an important role in competition to complete fusion. Calculations based on the statistical model agree well with the available data for ${}^{17,18}\mathrm{O}+{}^{16}\mathrm{O}$, but failed to represent the behavior of the experimentally determined production cross sections for the evaporation residues in the reactions ${}^{6,7}\mathrm{Li}+{}^{27}\mathrm{Al}$. But coupled-channel codes and calculations based on a nucleus-nucleus proximity potential are able to reproduce the energy dependence of the complete fusion cross sections.

Figure 1

Overview of the experimental setup in the target area.

Figure 2

Target assembly.

Figure 3

Prompt γ spectrum from the reaction ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$ at 13 MeV. Indicated are the peaks which could be used for the calculations.

Figure 4

Count rate of the 1779-keV transition in the radioactive decay of ${}^{28}\mathrm{Al}$. The ion beam was turned on at $t=0$ and kept constant for 1200 s, then, it was turned off, and the typical decay of the reaction product could be observed. The solid line fits the buildup and the decay of ${}^{28}\mathrm{Al}$ using the known decay constant [26].

Figure 5

empire [22] results for cross-section ratios for the formation of the evaporation residue and the CF concerning the compound nucleus ${}^{34}\mathrm{S}$ formed by the reaction ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$ (a) and ${}^{18}\mathrm{O}+{}^{16}\mathrm{O}$ (b) at the same excitation energy. Shown are RPs which are measured in this experiment.

Figure 6

Complete fusion cross section in millibarns as a function of the projectile energy for the reactions (a) ${}^6\mathrm{Li}+{}^{27}\mathrm{Al}$; (b) ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$. The CB is at 8.1 MeV (derived from a proximity potential). The diamonds are data derived from our experiments; the open circles are data from Kalita et al. [29], and the triangle indicates the lowest data point from Padron et al. [30].

Figure 7

Cross-section ratios σ(${}^{32}\mathrm{P}$)/σ(CF) from Ref. [21] (open circles) with estimated uncertainties. The triangles indicate a correction to the data by using calculated σ(${}^{26}\mathrm{Mg}$)/σ(CF) values. The upper dashed line is the result of an empire [22] calculation for the ${}^{18}\mathrm{O}+{}^{16}\mathrm{O}$ reaction, and the lower dashed line is the result of the calculation for the ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$ reaction.

Figure 8

Complete fusion excitation function for the reaction ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$. The full circles are the results from our ccfull [28] calculations using the σ(${}^{32}\mathrm{P}$)/σ(CF) ratio from the reaction ${}^{18}\mathrm{O}+{}^{16}\mathrm{O}$ as published in Ref. [21]. The open diamond represents a datum from Kalita et al. [29]. The CB was calculated from a proximity potential.

Figure 9

Ratio of the formation cross section for different reaction products versus the complete fusion cross section: Experimental and calculated (compound nucleus) data for the reaction ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$ and ${}^{18}\mathrm{O}+{}^{16}\mathrm{O}$. The solid lines with the full diamonds are the results from this experiment, the dashed lines with the open triangles are the results from the ${}^{18}\mathrm{O}+{}^{16}\mathrm{O}$ experiment [21], and the solid lines with the full squares are the results from empire [22] calculations. The experimental observed increase at low energies for the reaction ${}^7\mathrm{Li}+{}^{27}\mathrm{Al}$ is an indication for additional other reaction mechanisms than the pure compound reaction.

Figure 10

Ratio of the formation cross section for ${}^{31}\mathrm{P}$ versus the complete fusion cross section: Full diamonds with uncertainty bars are from the ${}^{17}\mathrm{O}+{}^{16}\mathrm{O}$ experiments [21] (uncertainty on the order of 25% derived from the diagrams in Ref. [21]), and the solid line represents compound nucleus calculations for the reaction ${}^6\mathrm{Li}+{}^{27}\mathrm{Al}$ (empire code [22]) data. empire gives nearly the same results for ${}^{17}\mathrm{O}+{}^{16}\mathrm{O}$.

Figure 11

Ratio of the formation cross section for (a) ${}^{28}\mathrm{Si}$ and (b) ${}^{25}\mathrm{Mg}$ versus the complete fusion cross section for ${}^{17}\mathrm{O}+{}^{16}\mathrm{O}$ (full squares, dashed line) and ${}^6\mathrm{Li}+{}^{27}\mathrm{Al}$ (full diamonds, solid line). In the figure the results of the compound nucleus calculations (empire [22], short dashed line) cannot be differentiated between the two formation processes. Only for ${}^{25}\mathrm{Mg}$ at the lowest energy of the compound nucleus a small difference in the ratio can be seen (higher values for the ${}^6\mathrm{Li}+{}^{27}\mathrm{Al}$ reaction).

Figure 12

Ratio of the formation cross section for ${}^{28}\mathrm{Al}$ versus the complete fusion cross section. The solid lines with the open circles are the experimental data from this experiment; dotted lines are compound nucleus calculations (empire [22]).