Formation and decay of ${}^{200}\mathrm{Pb}{}^{*}$ using different incoming channels

Entrance channel effect is studied in the dynamics of ${}^{200}\mathrm{Pb}{}^{*}$ formed in ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$, ${}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$, and ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er}$ reactions over a wide range of excitation energies using the dynamical cluster-decay model (DCM) and Wong model. The effect of deformations up to ${\beta }_2$ along with optimum orientation is investigated in both formalisms. The fusion cross section is studied using the Wong model, which overestimates experimental data for ${}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$ and ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er}$ reactions and underestimates the data at few energies for ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$. However with the use of the extended $\ell$-summed Wong model, the overestimation is taken care and the cross sections are fitted nicely. The Wong-based calculations suggest that there might be some noncompound nucleus contribution at few energies for the ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$ channel, as the underestimation of the cross section persists even after the inclusion of deformation effects. This lead us to conclude that the formation of ${}^{200}\mathrm{Pb}{}^{*}$ compound nucleus depends on the choice of the incoming channel. In addition to this, the decay path of ${}^{200}\mathrm{Pb}{}^{*}$ is investigated using DCM. Although the overall decay pattern of compound nucleus ${}^{200}\mathrm{Pb}{}^{*}$ seems similar for all the chosen reactions, some signatures of variation are observed in fission and in the intermediate mass fragment region for the deformed fragmentation process. It is to be noted that with the inclusion of deformation, the decay pattern changes from symmetric to asymmetric, thereby suggesting that the deformation and orientation of decaying fragment are equally important in the formation as well as in the decay process of proton magic nuclear system ${}^{200}\mathrm{Pb}{}^{*}$. Prediction of the evaporation residue and fission cross sections at higher as well as at lower incident energies is also worked out. In addition to this, the dynamics of neighboring nuclei ${}^{192}{\mathrm{Pb}}^{*}$ and ${}^{202}{\mathrm{Pb}}^{*}$ is also analyzed.

Figure 1

Comparison of experimental data with the calculated fusion cross section using the Wong formula and its extended version, the $\ell$-summed extended Wong model, for the ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er}\to {}^{200}{\mathrm{Pb}}^{*}\mathrm{reaction}$ with (a) spherical and (b) deformed choice of nuclei.

Figure 2

Same as Fig. 1 but for the ${}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}\to {}^{200}{\mathrm{Pb}}^{*}$ reaction.

Figure 3

Same as Fig. 1 but for the ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}\to {}^{200}{\mathrm{Pb}}^{*}$ reaction.

Figure 4

Deduced ${\ell }_{\max }$ values as a function of $E_{\mathrm{c}.\mathrm{m}.}$ for three incoming channels, i.e., ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er},{}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$, and ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$ with (a) spherical and (b) deformed (up to ${\beta }_2$) fragmentation.

Figure 5

Total interaction potential ${\mathrm{V}}_T$ (MeV) as a function of R (fm), for three incoming channels, i.e., ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er},{}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$, and ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$. (a) Corresponds to spherical nuclei without temperature and angular momentum effects and (b) and (c) at $E_{\mathrm{c}.\mathrm{m}.}$ $\approx$ 110 MeV (T $\ne$ 0 and $\ell$ $\ne$ 0) for spherical and ${\beta }_2$ deformations, respectively.

Figure 6

Fragmentation potential V (MeV) as a function of fragment mass $A_2$ at fixed $E_{\mathrm{c}.\mathrm{m}.}$ for three entrance channels with (a) spherical and (b) deformed choice of fragmentation. (For ${\ell }_{\max }$ see Table 1.)

Figure 7

Preformation probability $P_0$ as a function of fragment mass $A_2$ for three different incoming channels for (a) spherical and (b) deformed choice of nuclei. (For ${\ell }_{\max }$ see Table 1.)

Figure 8

Neck-length parameter $\Delta R$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ for spherical choice of nuclei of CN ${}^{200}\mathrm{Pb}{}^{*}$ formed by using three entrance channels. Filled and open symbols mark calculations with DCM and predicted values of $\Delta$R by polynomial fitting of order three, respectively, for (a) ER and (b) fission cross section.

Figure 9

Preformation probability $P_0$ as a function of fragment mass $A_2$ plotted at $E_{\mathrm{c}.\mathrm{m}.}$ = 98 MeV and 128 MeV for (a) ${}^{30}\mathrm{Si}+{}^{170}\mathrm{Er}$, (b) ${}^{19}\mathrm{F}+{}^{181}\mathrm{Ta}$, and (c) ${}^{16}\mathrm{O}+{}^{184}\mathrm{W}$ reactions.

Figure 10

Barrier-lowering parameter $\Delta V_B$ as a function of $E_{\mathrm{c}.\mathrm{m}.}$ for highest contributing fragments at $\ell$ = ${\ell }_{\max }$ (a) ER and (b) fission.

Figure 11

Preformation probability $P_0$ (upper panel) and experimental mass yield (lower panel), plotted as a function of fragment mass $A_2$.

Figure 12

(a) Penetrability P at $\ell ={\ell }_{\max }$ and (b) the $\ell$-summed $P_0^{\ell }{P}_{\ell }$ as a function of fragment mass $A_2$ for two incoming channels.

Figure 13

Average total kinetic energy $\langle \mathrm{TKE}\rangle$ and available experimental data plotted as a function of fragment mass $A_2$.