Three-body description of direct nuclear reactions: Comparison with the continuum discretized coupled channels method

The continuum discretized coupled channels (CDCC) method is compared with the exact solution of the three-body Faddeev equations in momentum space. We present results for (i) elastic and breakup observables of $d+$${}^{12}\mathrm{C}$ at $E_d=56$ MeV, (ii) elastic scattering of $d+$${}^{58}\mathrm{Ni}$ at $E_d=80$ MeV, and (iii) elastic, breakup, and transfer observables for ${}^{11}\mathrm{Be}$$+p$ at $E_{{}^{11}\mathrm{Be}}/A=38.4$ MeV. Our comparative studies show that in the first two cases, the CDCC method is a good approximation of the full three-body Faddeev solution, but for the ${}^{11}\mathrm{Be}$ exotic nucleus, depending on the observable or the kinematic regime, it may miss some of the dynamic three-body effects that appear through the explicit coupling to the transfer channel.

Figure 1

Screening function $w_R(r)/w(r)$ as function of the distance between the two charged particles $r$ for characteristic values of the parameter $n$ in Eq. (1): $n=1$ (dashed-dotted curve) corresponds to Yukawa screening, $n=4$ (solid curve) is the choice of this paper, and $n\to \infty$ (dotted curve) corresponds to a sharp cutoff.

Figure 2

Elastic cross section for deuterons on ${}^{12}\mathrm{C}$ at $E_d=56\mathrm{MeV}$: the solid line corresponds to exact three-body results and the dash-dotted line to CDCC. The result of a single channel cluster folding (dotted) is also shown. The experimental data are from Ref. [22].

Figure 3

Semi-inclusive differential cross section vs proton scattering angle for the breakup of deuterons on ${}^{12}\mathrm{C}$ at $E_d=56\mathrm{MeV}$: the solid line corresponds to the exact three-body results and the dash-dotted line to CDCC. The dotted line corresponds to the three-body exact result in the absence of the Coulomb force. The experimental data are from Ref. [36].

Figure 4

Exclusive differential cross section vs proton energy for the breakup of deuterons on ${}^{12}\mathrm{C}$ at $E_d=56\mathrm{MeV}$, ${\theta }_n={15}^{°}$, and ${\theta }_p>0$: the solid line corresponds to exact three-body results and the dash-dotted line to CDCC. The experimental data are from Ref. [36].

Figure 5

Same as Fig. 4, but for ${\theta }_p<0$.

Figure 6

Elastic cross section for deuterons on ${}^{58}\mathrm{Ni}$ at $E_d=80\mathrm{MeV}$: the solid line corresponds to the exact three-body results and the dash-dotted line to CDCC results. The experimental data at $80\mathrm{MeV}$ (diamonds) are from Ref. [23], and those at $79\mathrm{MeV}$ (triangles) are from Ref. [24]. The dotted line is the CDCC calculation suppressing the coupling to the deuteron continuum (see text).

Figure 7

${}^1\mathrm{H}$(${}^{11}\mathrm{Be}$,${}^{11}\mathrm{Be}$$)p$ elastic cross section at $E_{\mathrm{Lab}}/A=38.4\mathrm{MeV}.$ The solid line corresponds to exact three-body results while the dash-dotted line to CDCC. The dashed line corresponds to an optical potential fit to the corresponding ${}^{10}\mathrm{Be}$$\text{−}p$ data of Ref. [25] shown by the triangles. The diamonds correspond to ${}^{11}\mathrm{Be}$$\text{−}p$ elastic data of Ref. [25].

Figure 8

Transfer reaction ${}^1\mathrm{H}$(${}^{11}\mathrm{Be}$,${}^{10}\mathrm{Be}$$)d$ cross section at $E_{\mathrm{Lab}}/A=38.4\mathrm{MeV}$. The thick solid line corresponds to the exact three-body result, while the dotted line corresponds to the same calculation multiplied by 0.7. The thin solid line is the exact calculation with a partial-wave independent $n\text{−}$${}^{10}\mathrm{Be}$ interaction. The latter is to be compared with the CDCC-TR${}^{*}$ calculation (dashed line), as explained in the text. The experimental data are from Ref. [39] at $E_p=35.3\mathrm{MeV}.$

Figure 9

Semi-inclusive differential cross section for the reaction ${}^1\mathrm{H}$(${}^{11}\mathrm{Be}$,${}^{10}\mathrm{Be}$$)\mathit{pn}$, at $E_{\mathrm{Lab}}/A=38.4\mathrm{MeV}$, vs ${}^{10}\mathrm{Be}$ center of mass energy. The thick solid line corresponds to exact three-body results, the dashed line to CDCC-TR${}^{*}$, the dash-dotted line and the thin solid line to CDCC-BU with $l_{max}=8$ and $l_{max}=6$, respectively.

Figure 10

Same as Fig. 9, but showing ${}^{10}\mathrm{Be}$ angular distribution after energy integration.