First-order and higher-order interferences in the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ and ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reactions

First-order and higher-order interferences effects on the total, Coulomb, and nuclear breakup cross sections in the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ and ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reactions are studied at 68 $\mathrm{MeV}/\mathrm{u}$ incident energy. A partial-wave analysis is first performed, and shows that the differential total breakup cross sections are dominated by the $p$ waves. However, considered alone, they largely underestimate the data, hence the importance of the other partial-wave contributions. It is also shown that the first-order interference reduces by more than $60\%$ the total breakup cross sections, by less than $3\%$ the Coulomb breakup cross sections, and by more than $85\%$ the nuclear breakup cross sections, for both reactions. On the other hand, the higher-order interferences are found to reduce by less than $9\%$ the total breakup cross section, less than $1\%$ the Coulomb breakup cross section, and less than $7\%$ the nuclear breakup cross section for the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ reaction. For the ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reaction however, the higher-order interference reduces by less than $7\%$ the total breakup cross section, by less than $1\%$ the Coulomb breakup cross section, and by less than $4\%$ the nuclear breakup cross section. It is finally shown that even at first order, the incoherent sum of the nuclear breakup cross sections is more important than the incoherent sum of the Coulomb breakup cross sections for the two reactions.

Figure 1

(a) Different partial-wave differential breakup cross sections; (b) total, Coulomb, and nuclear breakup cross sections for the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ reaction. See text for the details. The experimental data are taken from Ref. [37].

Figure 2

(a) Different partial-wave differential breakup cross sections; (b) total, Coulomb, and nuclear breakup cross sections for the ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reaction. The experimental data are taken from Ref. [11].

Figure 3

Energy-distribution differential (a) total, (b) Coulomb, and (c) nuclear breakup cross sections, corresponding to different multipoles, for the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ reaction. The different curves are explained in the text.

Figure 4

Energy-distribution differential (a) total, (b) Coulomb, and (c) nuclear breakup cross sections, corresponding to different multipoles, for the ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reaction.

Figure 5

Angular-distribution differential (a) total, (b) Coulomb, and (c) nuclear breakup cross sections, corresponding to different multipoles for the ${}^{15}\mathrm{C}+{}^{208}\mathrm{Pb}$ reaction.

Figure 6

Angular-distribution differential (a) total, (b) Coulomb, (c) nuclear breakup cross sections, corresponding to different multipoles for the ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ reaction.