Complete and incomplete fusion of weakly bound nuclei

Existing quantum mechanics methods to study fusion reactions with weakly bound nuclei cannot evaluate separately the complete fusion and the incomplete fusion cross sections. We develop a semiclassical procedure that can calculate these cross sections, apply it to ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ collisions at energies just above the barrier, and show that its predictions for the different fusion cross sections are in good agreement with the data. We find that the contribution from the sequential fusion of the Li fragments to the complete fusion cross section is substantial in the case of ${}^6\mathrm{Li}$, reaching almost 40% of that from the direct process, which illustrates the importance of calculating correctly the different components of the fusion cross section.

Figure 1

Coordinates used in the main text to describe the breakup reaction of a weakly bound projectile by a heavy target.

Figure 2

Complete and total fusion cross sections for ${}^7\mathrm{Li}$ projectiles incident on ${}^{209}\mathrm{Bi}$.

Figure 3

Components of the CF cross section in the case of ${}^7\mathrm{Li}$ projectiles.

Figure 4

Similar to Fig. 2 for ${}^6\mathrm{Li}$ projectiles.

Figure 5

Similar to Fig. 3 for ${}^6\mathrm{Li}$ projectiles.

Figure 6

Comparison of the contribution from transfer and ICF channels in reactions induced by ${}^7\mathrm{Li}$ projectiles to the calculated cross section from ICF processes.

Figure 7

Similar to Fig. 6 for ${}^6\mathrm{Li}$ projectiles.

Figure 8

Contributions from the ${}^3\mathrm{H}$ (short-dashed line) and ${}^4\mathrm{He}$ (long-dashed line) fragments of ${}^7\mathrm{Li}$ to the calculated ICF cross section (solid line) in the ${}^7\mathrm{Li}{\text{−}}^{209}\mathrm{Bi}$ collision.

Figure 9

Contributions from the ${}^2\mathrm{H}$ (short-dashed line) and ${}^4\mathrm{He}$ (long-dashed line) fragments of ${}^6\mathrm{Li}$ to the calculated ICF cross section (solid line) in the ${}^6\mathrm{Li}{\text{−}}^{209}\mathrm{Bi}$ collision.