Comprehensive analysis of large $\alpha$ yields observed in ${}^6\mathbf{Li}$-induced reactions

Background: Large $\alpha$ yields have been reported over the years in reactions with ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ projectiles. Previous theoretical analyses have shown that the elastic breakup (EBU) mechanism (i.e., projectile breakup leaving the target in its ground state) is able to account only for a small fraction of the total $\alpha$-inclusive breakup cross sections, pointing toward the dominance of nonelastic breakup (NEB) mechanisms.

Purpose: We aim to provide a systematic study of the $\alpha$-inclusive cross sections observed in nuclear reactions induced by ${}^6\mathrm{Li}$ projectiles. In addition to estimating the total $\alpha$ singles' cross sections, it is our goal to evaluate angular and energy distributions of these $\alpha$ particles and compare them with experimental data, when available.

Method: We compute separately the EBU and NEB components of the inclusive breakup cross sections. For the former, we use the continuum-discretized coupled-channels (CDCC) method, which treats this mechanism to all orders. For the NEB part, we employ the model proposed by Ichimura et al. [Phys. Rev. C 32, 431 (1985)], within the distorted-wave Born approximation (DWBA).

Results: Overall, the sum of the computed EBU and NEB cross sections is found to reproduce very well the measured singles' cross sections. In all cases analyzed, we find that the inclusive breakup cross section is largely dominated by the NEB component.

Conclusions: The presented method provides a global and systematic description of inclusive breakup reactions induced by ${}^6\mathrm{Li}$ projectiles. It provides also a natural explanation of the previously observed underestimation of the measured $\alpha$ yields by CDCC calculations. The method used here can be extended to other weakly bound projectiles, including halo nuclei.

Figure 1

Coordinates used in the nonelastic breakup calculations.

Figure 2

Angular distribution of $\alpha$ particles produced in the reaction ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$ at the incident energies indicated by the labels. The dotted, dashed, and solid lines correspond to the NEB (IAV model), EBU (CDCC), and their sum (TBU), respectively. Experimental data are from Refs. [19, 20]. See text for details.

Figure 3

Elastic scattering of ${}^6\mathrm{Li}+{}^{144}\mathrm{Sm}$ at 22.1 (top) and 35.1 MeV (bottom). The solid and dashed lines are, respectively, the CDCC calculation and the optical model calculation with the optical potential from Ref. [23]. Experimental data are from Ref. [25].

Figure 4

Angular distribution of $\alpha$ particle production of the reaction ${}^6\mathrm{Li}+{}^{159}\mathrm{Tb}$ at the incident energies indicated by the labels. The dashed, dotted, and solid lines are EBU calculated with CDCC, NEB calculated with finite-range DWBA, and their sum (TBU), respectively. The experimental data are taken from Ref. [24].

Figure 5

Elastic scattering of ${}^6\mathrm{Li}+{}^{118}\mathrm{Sn}$ at different incident energies. The solid and dashed lines are, respectively, the CDCC calculation and the optical model calculation with the optical potential from Ref. [27]. Experimental data are from Ref. [27].

Figure 6

Angular distribution of $\alpha$ particles produced in the reaction ${}^6\mathrm{Li}+{}^{118}\mathrm{Sn}$ at the incident energies indicated by the labels. The dotted, dashed, and solid lines correspond to the NEB (IAV model), EBU (CDCC), and their sum (TBU), respectively. Experimental data are from Ref. [27].

Figure 7

Elastic scattering of ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ at an incident energy of 18 MeV. The solid and dashed lines are, respectively, the CDCC calculation and the optical model calculation with the optical potential from Ref. [23]. Experimental data are from Ref. [28].

Figure 8

Angular distribution of $\alpha$ particles produced in the reaction ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$ at an incident energy of 21.5 MeV. The dashed, dotted, and solid lines are, respectively, the EBU (CDCC), NEB(IAV model), and their sum. Experimental data are taken from Ref. [29].

Figure 9

Experimental and calculated inclusive $\alpha$ energy spectra for $E_{\mathrm{lab}}=21.5$ MeV, at selected scattering angles. The dashed, dotted, and solid lines are respectively the EBU (CDCC), NEB (IAV model), and their sum. Experimental data are taken from Ref. [29].

Figure 10

Elastic scattering of ${}^6\mathrm{Li}+{}^{58}\mathrm{Ni}$ at several energies indicated by the labels. The solid and dashed lines are, respectively, the CDCC calculation and the optical model calculation with the optical potential from Ref. [27]. Experimental data are from Ref. [27].

Figure 11

Angular distribution of $\alpha$ particles produced in the reaction ${}^6\mathrm{Li}+{}^{58}\mathrm{Ni}$ at the incident energies indicated by the labels. The dashed, dotted, and solid lines are, respectively, the EBU, NEB, and their sum (TBU). Experimental data are from Ref. [27].

Figure 12

Top: NEB cross section as a function of the $d-{}^{208}\mathrm{Pb}$ relative energy in the c.m. frame for the reaction ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$. The vertical dotted line indicates the energy of the Coulomb barrier for the $d+{}^{208}\mathrm{Pb}$ reaction. The solid line is the reaction cross section for $d+{}^{208}\mathrm{Pb}$, arbitrarily normalized. Bottom: same as in top panel but for the ${}^6\mathrm{Li}+{}^{58}\mathrm{Ni}$ system.

Figure 13

Contour plots for the double differential cross section (upper panels) and the angle-integrated energy differential cross section as a function of the outgoing $\alpha$ energy in the c.m. frame (lower panels) for the reactions (a) ${}^6\mathrm{Li}+{}^{208}\mathrm{Pb}$, (b) ${}^6\mathrm{Li}+{}^{159}\mathrm{Tb}$, (c) ${}^6\mathrm{Li}+{}^{118}\mathrm{Sn}$, and (d) ${}^6\mathrm{Li}+{}^{59}\mathrm{Co}$. The vertical lines indicate the breakup threshold for the $d$ + target system ($E_x=0$).

Figure 14

Inclusive breakup $\alpha$ cross sections involving ${}^6\mathrm{Li}$ projectile with several targets as a function of $E_{\mathrm{c}.\mathrm{m}.}/V_{\mathrm{B}}$.

Figure 15

Ratios of calculated EBU over TBU (= EBU + NEB) for different systems. See text for details.

Figure 16

Ratios of calculated TBU (= EBU + NEB) $\alpha$ cross sections over the reaction cross section for the systems and energies analyzed in this work. See the text for details.