Fusion of ${}^7\mathrm{Li}$ with ${}^{205}\mathrm{Tl}$ at near-barrier energies

The complete and incomplete fusion cross sections for the ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ reaction were measured at near barrier energies by the online characteristic $\gamma$-ray detection technique. The complete fusion (CF) cross sections at energies above the Coulomb barrier were found to be suppressed by $\sim 26\%$ compared to the coupled channel calculations. Reduced fusion cross sections for the present system at energies normalized to the Coulomb barrier were also found to be systematically lower than those with strongly bound projectiles forming a similar compound nucleus. The suppression observed in CF cross sections is found to be commensurate with the measured total incomplete fusion (ICF) cross sections. In the ICF cross sections, $t$-capture is found to be dominant than $\alpha$-capture at all the measured energies. The systematic study of available CF, ICF, and total fusion data with the ${}^7\mathrm{Li}$ projectile is performed.

Figure 1

$\gamma$-ray add-back spectrum from all the clover detectors obtained in ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ system at $E_{\text{beam}}=38$ MeV. The $\gamma$ lines from the possible evaporation residues (${}^{208,209}\mathrm{Po}$) following CF are labeled. Also the $\gamma$ lines following the $\alpha$-capture channel (${}^{207,208}\mathrm{Bi}$) and $t$-capture channel (${}^{206,207}\mathrm{Pb}$) are marked.

Figure 2

ER cross sections for $3n$ (${}^{209}\mathrm{Po}$) and $4n$ (${}^{208}\mathrm{Po}$) channels following CF are shown as a triangle and circle, respectively. The results of the statistical model calculations for the corresponding ERs are shown by dashed dot dot ($3n$) and long dashed ($4n$) lines.

Figure 3

Complete fusion cross section (filled circles) for the ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ system compared with coupled (dashed lines) and uncoupled (dotted lines) results from ccfull calculations. Solid lines were obtained by multiplying the coupled results by a factor of 0.74.

Figure 4

Reduced cross sections as a function of reduced energy for the present system (filled circles) along with two other systems ${}^{12}\mathrm{C}+{}^{198}\mathrm{Pt}$ (hollow square [33]) and ${}^{18}\mathrm{O}+{}^{192}\mathrm{Os}$ (hollow triangle [34]). Dashed line is the result of coupled channel calculations for ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ system. Solid line is obtained by multiplying the coupled results by a factor of 0.74.

Figure 5

Measured residue cross sections for (a) $t$-capture and (b) $\alpha$-capture in the ${}^7\mathrm{Li}+{}^{205}\mathrm{Tl}$ system. The lines are the predictions from statistical model calculations for the corresponding residues. (c) total $t$-capture and $\alpha$-capture cross sections are compared. (See text for details.)

Figure 6

Systematic behavior of (a) CF, (b) $t$-capture, (c) $\alpha$-capture, (d) Total ICF ($=t$-capture $+\alpha$-capture), and (e) TF (=$\mathrm{CF}+\mathrm{ICF}$) cross sections as a function of reduced energy with ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ [19], ${}^{159}\mathrm{Tb}$ [30], ${}^{197}\mathrm{Au}$ [54], ${}^{198}\mathrm{Pt}$ [49], ${}^{209}\mathrm{Bi}$ [40], and ${}^{205}\mathrm{Tl}$ (present data) systems.

Figure 7

Measured fusion function $F\left(x\right)$ for (a) CF, (b) $t$-capture, (c) $\alpha$-capture, (d) Total ICF ($=t$-capture $+\alpha$-capture), and (e) TF (= $\mathrm{CF}+\mathrm{ICF}$) for ${}^7\mathrm{Li}+{}^{124}\mathrm{Sn}$ [19], ${}^{159}\mathrm{Tb}$ [30], ${}^{197}\mathrm{Au}$ [54], ${}^{198}\mathrm{Pt}$ [49], ${}^{209}\mathrm{Bi}$ [40], and ${}^{205}\mathrm{Tl}$ (present data) systems in linear scale. The solid and dashed lines represent the UFF and UFF multiplied by a factor ‘$a$’. The value of ‘$a$’ is 0.70, 0.26, 0.08, and 0.34 for CF, $t$-capture, $\alpha$-capture, and total ICF, respectively (see text for details).