Decay analysis of compound nuclei with masses $A\approx 30–200$ formed in reactions involving loosely bound projectiles

The dynamics of compound nuclei formed in the reactions using loosely bound projectiles are analyzed within the framework of the dynamical cluster-decay model (DCM) of Gupta and Collaborators. We have considered the reactions with neutron-rich and neutron-deficient projectiles, respectively, as ${}^7\mathrm{Li}$, ${}^9\mathrm{Be}$, and ${}^7\mathrm{Be}$, on various targets at three different $E_{\mathrm{lab}}$ energies, forming compound nuclei in the mass region $\mathrm{A}\sim 30–200.$ For these reactions, the contributions of light-particle (LP, $A\le 4$) cross sections ${\sigma }_{\mathrm{LP}}$, energetically favored intermediate-mass-fragment (IMF, $5\le A_2\le 20$) cross sections ${\sigma }_{\mathrm{IMF}}$, as well as the fusion-fission ff cross sections ${\sigma }_{\mathrm{ff}}$ constitute the ${\sigma }_{\mathrm{fus}}\left(={\sigma }_{\mathrm{LP}}+{\sigma }_{\mathrm{IMF}}+{\sigma }_{\mathrm{ff}}\right)$, i.e., the contributions of the emitted LPs, IMFs, and ff fragments are added for all the angular momenta up to the ${\ell }_{\max }$ value for the respective reactions. Interestingly, we find that the empirically fitted neck-length parameter $\mathrm{\Delta }{R}^{\mathrm{emp}}$, the only parameter of the DCM, is uniquely fixed to address ${\sigma }_{\mathrm{fus}}$ for all the reactions having the same loosely bound projectile at a chosen incident laboratory energy. It may be noted that, in DCM, the dynamical collective mass motion of preformed LPs, IMFs, and ff fragments or clusters, through the modified interaction potential barrier, are treated on parallel footing. The modification of the barrier is due to nonzero $\mathrm{\Delta }{R}^{\mathrm{emp}}$, and the values of corresponding modified interaction-barrier heights $\mathrm{\Delta }{V}_B^{\mathrm{emp}}$ for such reactions are almost of the same order, specifically at the respective ${\ell }_{\max }$ value.

Figure 1

The scattering potentials $V$ for the compound system ${}^{34}\mathrm{Cl}^{*}$ (formed in the reaction ${}^7\mathrm{Be}+{}^{27}\mathrm{Al}$) for exit channel ${}^6\mathrm{Li}+{}^{28}\mathrm{Si}$ at the two extreme $\ell$ values.

Figure 2

The fragmentation potentials $V$ for the compound system ${}^{34}\mathrm{Cl}^{*}$ formed in the reaction ${}^7\mathrm{Be}+{}^{27}\mathrm{Al}$ at different $\ell$ values with different choices of $\mathrm{\Delta }R\ne 0$ and $\mathrm{\Delta }R=0$.

Figure 3

The preformation factor $P_0$ for the compound system ${}^{34}\mathrm{Cl}^{*}$ formed in the reaction ${}^7\mathrm{Be}{+}^{27}\mathrm{Al}$ at incident energy $E_{\mathrm{lab}}\sim 17$ MeV with different choices of $\mathrm{\Delta }R\ne 0$ and $\mathrm{\Delta }R=0$ for (a) $\ell =0\hslash$ and (b) $\ell ={\ell }_{\max }$.

Figure 4

Variation of summed preformation factor $P_0$ with angular momentum $\ell$ for ${}^{34}\mathrm{Cl}^{*}$ decay into LPs and IMFs.

Figure 5

The fragmentation potentials $V\left(A_2\right)$ for the compound systems having mass $\mathrm{A}\sim 30$-70 formed in ${}^7\mathrm{Be}$ induced reactions at incident energy $E_{\mathrm{lab}}\sim 17$ MeV for (a) $\ell =0\hslash$ and (b) $\ell ={\ell }_{\max }$.

Figure 6

(a) The barrier height $V_B$ (MeV) for the nuclei induced by ${}^7\mathrm{Be}$ projectiles at $\ell =0\hslash$. (b) The first and second turning points of ${}^{34}\mathrm{Cl}^{*}$ and ${}^{72}\mathrm{As}^{*}$ formed in ${}^7\mathrm{Be}+{}^{27}\mathrm{Al}$ and ${}^7\mathrm{Be}+{}^{65}\mathrm{Cu}$ reactions at the respective ${\ell }_{\max }$ values.

Figure 7

Same as Fig. 4 but for summed penetration probability.

Figure 8

The calculated fusion cross section ${\sigma }_{\mathrm{fus}}$ for different reactions using different loosely bound projectile ${}^7\mathrm{Li}$, ${}^7\mathrm{Be}$, and ${}^9\mathrm{Be}$, compared with the experimental data.