Four-body dynamics in ${}^6\text{Li}$ elastic scattering

We analyze ${}^6\text{Li}$ elastic scattering in a wide range of incident energies ($E_{\mathrm{in}}$), assuming the $n+p+\alpha +\mathrm{target}$ four-body model and solving the dynamics with the four-body version of the continuum-discretized coupled-channels method (CDCC). Four-body CDCC reproduces the experimental data well with no adjustable parameter for ${}^6\text{Li}+{}^{209}\text{Bi}$ scattering at $E_{\mathrm{in}}=24$–50 MeV and ${}^6\text{Li}+{}^{208}\text{Pb}$ scattering at $E_{\mathrm{in}}=29$–210 MeV. In the wide $E_{\mathrm{in}}$ range, ${}^6\text{Li}$ breakup is significant and provides repulsive corrections to the folding potential. In ${}^6\text{Li}$ elastic scattering, as an interesting property, ${}^6\text{Li}$ is mainly broken up into two particles $d$ and $\alpha$, and hardly into three particles $n$, $p$, and $\alpha$. We investigate what causes this $d\alpha$ dominance.

Figure 1

Three sets of Jacobi coordinates ${\mathbf{\xi }}_c=\{{\mathit{r}}_c,{\mathit{y}}_c\}$ in the $n+p+\alpha$ three-body system. Each set is identified by a label $c$.

Figure 2

Calculated eigenenergies of ${}^6\text{Li}$ for $I^{\pi }=1^{+}$, $2^{+}$, and $3^{+}$ from the $np\alpha$ threshold (${\varepsilon }_{\mathrm{th}}^{\left(np\alpha \right)}=0$ MeV). The $d\alpha$ threshold (${\varepsilon }_{\mathrm{th}}^{\left(d\alpha \right)}=-2.2$ MeV) is also shown by the dotted line. The numbers of pseudostates up to ${\varepsilon }_{\max }=10$ MeV are shown in the parentheses.

Figure 3

Elastic cross sections (normalized by the Rutherford cross section) for ${}^6\text{Li}+{}^{209}\text{Bi}$ scattering at 32.8–50 MeV in (a) the linear scale and (b) the logarithmic scale. The solid lines represent the results of full four-body CDCC calculations, whereas the dotted lines show the results of 1ch calculations with no breakup effect. The symbols are experimental data taken from Refs. [30, 31, 32].

Figure 4

Same as Fig. 3, but $E_{\mathrm{in}}=24,28$, and 29.9 MeV.

Figure 5

Total reaction cross section ${\sigma }_{\mathrm{R}}$ as a function of $E_{\mathrm{in}}$. The solid and dotted line represents the calculation with and without the channel coupling effects. The derived cross section based on the optical model analysis [32] is also shown.

Figure 6

Elastic cross sections (normalized by the Rutherford cross section) for ${}^6\text{Li}+{}^{208}\text{Pb}$ scattering at 29–210 MeV as a function of the transfer momentum $q$. The solid lines represent the results of full four-body CDCC calculations, whereas the dotted lines denote the results of 1ch calculations. The experimental data are taken from Refs. [34, 35, 36].

Figure 7

Elastic $S$-matrix elements for ${}^6\text{Li}+{}^{208}\text{Pb}$ scattering (a) at $E_{\mathrm{in}}=39$ MeV and (b) at $E_{\mathrm{in}}=210$ MeV. The open circles stand for the results of full CDCC calculations, and the closed squares correspond to the results of 1ch calculations.

Figure 8

Elastic cross sections (normalized by the Rutherford cross section) for ${}^6\text{Li}+{}^{208}\text{Pb}$ scattering at $E_{\mathrm{in}}=39$ and 210 MeV. The solid line represents the result of full four-body CDCC calculations, whereas the dotted line denotes the results of 1ch calculations with no breakup channel. In the dot-dashed line, the model space $P_{d\alpha }$ is switched off from the solid line.

Figure 9

Same as Fig 8, but in the dashed line the model space $P_{np\alpha }$ is switched off from the solid line.

Figure 10

Distribution of $d\alpha$ probability in excitation spectrum. The closed circles (open squares) correspond to the $d\alpha$-dominant states ($np\alpha$-dominant states); see text for details. The threshold energies of ${\varepsilon }_{\mathrm{th}}^{\left(d\alpha \right)}=-2.2$ MeV and ${\varepsilon }_{\mathrm{th}}^{\left(np\alpha \right)}=0$ MeV are also shown as the dotted line for reference.

Figure 11

Coulomb-breakup effects on ${}^6\text{Li}+{}^{209}\text{Bi}$ elastic cross section at 28–50 MeV. The solid and dashed lines show the results of CDCC calculations without and with Coulomb breakup. The symbols are experimental data taken from Refs. [30, 31, 32].

Figure 12

The $N+N+\alpha$ three-cluster model and its coordinates.