Evaporation residue cross-section measurements for ${}^{48}\mathrm{Ti}$-induced reactions

Background: A significant research effort is currently aimed at understanding the synthesis of heavy elements. For this purpose, heavy ion induced fusion reactions are used and various experimental observations have indicated the influence of shell and deformation effects in the compound nucleus (CN) formation. There is a need to understand these two effects.

Purpose: To investigate the effect of proton shell closure and deformation through the comparison of evaporation residue (ER) cross sections for the systems involving heavy compound nuclei around the $Z_{\mathrm{CN}}=82$ region.

Methods: A systematic study of ER cross-section measurements was carried out for the ${}^{48}\mathrm{Ti}+{}^{142,150}\mathrm{Nd}, {}^{144}\mathrm{Sm}$ systems in the energy range of $140–205\mathrm{MeV}$. The measurement has been performed using the gas-filled mode of the hybrid recoil mass analyzer present at the Inter University Accelerator Centre (IUAC), New Delhi. Theoretical calculations based on a statistical model were carried out incorporating an adjustable barrier scaling factor to fit the experimental ER cross section. Coupled-channel calculations were also performed using the ccfull code to obtain the spin distribution of the CN, which was used as an input in the calculations.

Results: Experimental ER cross sections for ${}^{48}\mathrm{Ti}+{}^{142,150}\mathrm{Nd}$ were found to be considerably smaller than the statistical model predictions whereas experimental and statistical model predictions for ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ were of comparable magnitudes.

Conclusion: Though comparison of experimental ER cross sections with statistical model predictions indicate considerable non-compound-nuclear processes for ${}^{48}\mathrm{Ti}+{}^{142,150}\mathrm{Nd}$ reactions, no such evidence is found for the ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ system. Further investigations are required to understand the difference in fusion probabilities of ${}^{48}\mathrm{Ti}+{}^{142}\mathrm{Nd}$ and ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ systems.

Figure 1

Two-dimensional spectrum obtained from the TOF and energy loss ($\mathrm{\Delta }E$) signal for the ${}^{48}\mathrm{Ti}+{}^{150}\mathrm{Nd}$ system at $E_{\mathrm{c}.\mathrm{m}.}=157.83\mathrm{MeV}$.

Figure 2

Normalized angular distributions simulated by the ters code for (a) ${}^{48}\mathrm{Ti}+{}^{142}\mathrm{Nd}$, (b) ${}^{48}\mathrm{Ti}+{}^{150}\mathrm{Nd}$, and (c) ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ systems at measured energy ranges. These distributions were compared with the ${}^{48}\mathrm{Ti}+{}^{122}\mathrm{Sn}$ system to get the correction in ${\eta }_{\mathrm{HYRA}}$. Angular acceptance of HYRA is $9.5^{\circ }$ which is marked here by the vertical dashed line.

Figure 3

Statistical model predictions for ER angular distribution of (a) ${}^{48}\mathrm{Ti}+{}^{142}\mathrm{Nd}$, (b) ${}^{48}\mathrm{Ti}+{}^{150}\mathrm{Nd}$, and (c) ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ systems.

Figure 4

ER cross sections for ${}^{48}\mathrm{Ti}+{}^{142,150}\mathrm{Nd}, {}^{144}\mathrm{Sm}$ systems as a function of $E_{\mathrm{c}.\mathrm{m}.}$.

Figure 5

ER angular distribution comparison with fission (dashed lines) and fission suppression (dotted lines) at two energy points for (a, b) ${}^{48}\mathrm{Ti}+{}^{142}\mathrm{Nd}$, (c, d) ${}^{48}\mathrm{Ti}+{}^{150}\mathrm{Nd}$, and (e, f) ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ systems obtained using statistical model calculations.

Figure 6

Experimental ER cross sections (filled symbols) vs $E_{\mathrm{c}.\mathrm{m}.}$ plotted with the theoretical results (various lines) obtained from the statistical model calculations after varying $K_{\mathrm{f}}$ values for (a) ${}^{48}\mathrm{Ti}+{}^{142}\mathrm{Nd}$, (b) ${}^{48}\mathrm{Ti}+{}^{150}\mathrm{Nd}$, and (c) ${}^{48}\mathrm{Ti}+{}^{144}\mathrm{Sm}$ systems including the shell correction in the level density and the fission barrier.

Figure 7

Same as Fig. 6, but excluding the shell corrections.

Figure 8

Comparison of the best-fit values of $K_{\mathrm{f}}$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ using FRLDM fission barrier (a) including shell effects in the level density and fission barrier and (b) excluding shell corrections for ${}^{48}\mathrm{Ti}+{}^{142,150}\mathrm{Nd}, {}^{144}\mathrm{Sm}$ systems.