Fusion barrier distributions in ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ reactions from quasi-elastic and fusion excitation function measurements

Fusion barrier distributions have been obtained from the measurement of the quasi-elastic scattering excitation functions at a backward angle in the reactions of ${}^{6,7}\mathrm{Li}$ with ${}^{209}\mathrm{Bi}$. Comparisons have been carried out among barrier distributions, obtained from quasi-elastic scattering by considering elastic + inelastic and elastic + inelastic + [breakup(BU) and/or transfer] and also from fusion excitation function measurements. It has been observed that representations of barrier distributions obtained from elastic + inelastic + [breakup(BU) and/or transfer] and from fusion excitation functions are in good agreement showing the importance of the inclusion breakup channels for the correct fusion barrier representations in the ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ reactions. The observed discrepancy in the resultant barrier distributions with and without including breakup and/or transfer has been interpreted in terms of the capture barrier distribution. The results obtained from the continuum discretized coupled channels calculations also follow the fusion barrier distributions which have been obtained from the fusion excitation functions measurements. It has been observed that the inclusion of direct breakup $\alpha$ with the elastic and inelastic channels in quasi-elastic scattering play an important role in explaining consistently the fusion barrier distributions for both the ${}^{6,7}\mathrm{Li}+{}^{209}\mathrm{Bi}$ systems.

Figure 1

A typical two-dimensional spectrum of $\Delta E$ versus $E_{\mathrm{tot}}$ for ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ at $E_{\mathrm{lab}}$ = 34 MeV and ${\theta }_{\mathrm{lab}}$ = 140${}^{\circ }$.

Figure 2

Quasi-elastic excitation function at 140${}^{\circ }$ for the ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ system. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The dotted line indicates the results of coupled channels calculations using a bare potential. The continuous line shows the results from the CDCC calculation which includes elastic + direct breakup (BU).

Figure 3

Quasi-elastic excitation function at 140${}^{\circ }$ for the ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ system. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The dotted line indicates the results of Coupled Channels calculations using bare potential. The continuous line shows the results from CDCC calculation which includes elastic + ${}^7\mathrm{Li}$-inelastic + direct breakup (BU).

Figure 4

Fusion barrier distributions for the ${}^6\mathrm{Li}+{}^{209}\mathrm{Bi}$ system at 140${}^{\circ }$. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The data points shown by unfilled circles are taken from Ref. [14]. The dotted line indicates the results of coupled channels calculations using a bare potential. The continuous line shows the results from CDCC calculation which includes elastic + direct breakup (BU).

Figure 5

Fusion barrier distributions for the ${}^7\mathrm{Li}+{}^{209}\mathrm{Bi}$ system at 140${}^{\circ }$. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The data points shown by unfilled circles are taken from Ref. [14]. The dotted line indicates the results of coupled channels calculations using a bare potential. The continuous line shows the results from the CDCC calculation which includes elastic + ${}^7\mathrm{Li}$-inelastic + direct breakup (BU).

Figure 6

Transmission or capture probability ($T_{\circ }$) as a function of $E_{\mathrm{c}.\mathrm{m}.}$ in the reaction of ${}^6\mathrm{Li}$ with ${}^{209}\mathrm{Bi}$. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The data points shown by unfilled circles are taken from Ref. [14].

Figure 7

Transmission or capture probability ($T_{\circ }$) as a function of $E_{\mathrm{c}.\mathrm{m}.}$ in the reaction of ${}^7\mathrm{Li}$ with ${}^{209}\mathrm{Bi}$. The filled circles (black) show the data points with elastic + inelastic and crosses (red) show the data points with elastic + inelastic + BU and/or transfer. The data points shown by unfilled circles are taken from Ref. [14]