Complete and incomplete fusion of ${}^7\mathrm{Li}$ projectiles on heavy targets

We present a detailed discussion of a recently proposed method to evaluate complete and incomplete fusion cross sections for weakly bound systems. The method is applied to collisions of ${}^7\mathrm{Li}$ projectiles on different heavy targets, and the results are compared with the available data. The overall agreement between experiment and theory is fairly good.

Figure 1

Schematic representation of the projectile, its fragments, the target, and the coordinates involved in the calculations.

Figure 2

Discretization of the continuum of ${}^7\mathrm{Li}$ [panel (a)] and ${}^7\mathrm{Li}$ [panel (b)]. The narrower bins in the resonances regions are represented in light blue.

Figure 3

Convergence of ${\sigma }_{\mathrm{CF}}$ with respect to ${\varepsilon }_{\max }$.

Figure 4

Convergence of ${\sigma }_{\mathrm{TF}}$ with respect to ${\varepsilon }_{\max }$.

Figure 5

Convergence of ${\sigma }_{\mathrm{CF}}$ with respect to $l_{\max }$.

Figure 6

Convergence of ${\sigma }_{\mathrm{TF}}$ with respect to $l_{\max }$.

Figure 7

CF cross sections calculated with different values of the spectroscopic amplitude.

Figure 8

Calculated CF cross sections for the ${}^7\mathrm{Li} + {}^{209}\mathrm{Bi}$ system (solid black line) in comparison with the data of Refs. [6, 7] (open circles).

Figure 9

Same as Fig. 8 but for the ${}^7\mathrm{Li} + {}^{197}\mathrm{Au}$ system. Here the data are from Refs. [20, 47].

Figure 10

Same as Fig. 8 but now the system is ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$. Here, the system is ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$, and the data are from Ref. [19].

Figure 11

Same as Fig. 8 but for the ${}^7\mathrm{Li}+{}^{198}\mathrm{Pt}$ system. Here the data are from Ref. [15].

Figure 12

(a) The imaginary potentials $W_{00}\left(R\right)$ and $W_{\mathrm{PT}}\left(R\right)$, shown on a logarithmic scale; (b) fusion cross sections at very low energies. The CF cross section of our method (solid green line), and the fusion cross sections of one-channel calculations with the potentials $V_{00}\left(R\right)-i{W}_{\mathrm{PT}}\left(R\right)$ (red dotted line) and $V_{00}\left(R\right)-i{W}_{00}\left(R\right)$ (black dot-dashed line) are compared with the CF data of Ref. [15]. See the text for details.

Figure 13

Theoretical fusion functions $F_{\mathrm{th}}^{00}$ [panel (a)] and $F_{\mathrm{th}}^{\mathrm{PT}}$ [panel (b)] in collisions of ${}^7\mathrm{Li}$ with the ${}^{209}\mathrm{Bi},{}^{197}\mathrm{Au},{}^{124}\mathrm{Sn}$, and ${}^{198}\mathrm{Pt}$ targets. See the text for details.

Figure 14

Experimental fusion functions $F_{\exp }^{00}$ [panel (a)] and $F_{\exp }^{\mathrm{PT}}$ [panel (b)] in collisions of ${}^7\mathrm{Li}$ with the ${}^{209}\mathrm{Bi},{}^{197}\mathrm{Au},{}^{124}\mathrm{Sn}$, and ${}^{198}\mathrm{Pt}$ targets. See the text for details.

Figure 15

Incomplete fusion cross sections for the ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ system calculated by our method in comparison with the ICF data of Refs. [6, 7].

Figure 16

${\mathrm{ICF}}_t$ and ${\mathrm{ICF}}_{\alpha }$ cross sections for the ${}^7\mathrm{Li}+{}^{197}\mathrm{Au}$ system calculated by our method, in comparison to the data of Palshetkar et al. [20, 47].

Figure 17

Same as the previous figure, but now the system is ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$, and the data are from Parkar et al. [19].

Figure 18

Same as the previous figure, but now the system is ${}^7\mathrm{Li}+{}^{198}\mathrm{Pt}$, and the data are from Shrivastava et al. [15].