Background: Synthesis of a doubly magic spherical nucleus beyond ${}_{82}^{208}$Pb${}_{126}$ is a key question in contemporary nuclear physics. Such nuclei can exist solely because of shell stabilization. As the formation cross section of super heavy elements is prohibitively low, attempts have been made to understand stabilizing effects of closed proton ($Z$) and neutron ($N$) shells in the vicinity of ${}_{82}^{208}$Pb${}_{126}$.

Purpose: The present work attempts to elucidate the stabilizing effect of shell closure, in general, and the same of $Z=82$, in particular.

Methods: The evaporation residue (ER) excitation function and ER-gated $\gamma$-multiplicity distribution have been measured for the reaction ${}^{31}$P + ${}^{170}$Er at a laboratory energy range of 134–172 MeV. The measurements have been carried out using the HYbrid Recoil mass Analyzer (HYRA) in gas-filled mode and a $4\pi$ spin spectrometer consisting of 29 NaI(Tl) detectors. Results of the present reaction have been compared with those of the reaction ${}^{30}$Si + ${}^{170}$Er. Statistical model calculation has been performed for both the systems.

Results: The two reactions, induced by ${}^{30}$Si and ${}^{31}$P projectiles, resulted in compound nuclei (CN) ${}^{200}$Pb ($Z=82$) and ${}^{201}$Bi ($Z=83$), respectively. To reproduce experimental ER cross sections, the liquid drop fission barrier ($B_{\mathrm{f}}$) had to be scaled in the statistical model calculation. The scaling factor ($K_{\mathrm{f}}$) varies from $0.75$ to $1.05$ and $0.90$ to $1.05$ for ${}^{30}$Si and ${}^{31}$P induced reactions, respectively. No significant differences have been found between $\gamma$-multiplicity distribution and the distribution moments of the two systems.

Conclusions: No clear signature has been observed in favor of extra stability of the ERs with closed proton shell ($Z=82$) as $K_{\mathrm{f}}$ values of the two systems match within errors. More exclusive measurements and comparison between more systems forming CN/ER around $Z=82$ are desirable.

• Received 17 August 2013

DOI:https://doi.org/10.1103/PhysRevC.88.034606