Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory

Abstract

The magic proton and neutron numbers are searched in the superheavy region with proton number $Z$=100 - 140 and neutron number $N$= ($Z$+30) - (2$Z$+32) by the relativistic continuum Hartree-Bogoliubov (RCHB) theory with interactions NL1, NL3, NLSH, TM1, TW99, DD-ME1, PK1, and PK1R. Based on the two-nucleon separation energies $S_{2p}$ and $S_{2n}$, the two-nucleon gaps ${\delta }_{2p}$ and ${\delta }_{2n}$, the shell correction energies $E_{shell}^p$ and $E_{shell}^n$, the pairing energies $E_{pair}^p$ and $E_{pair}^n$, and the pairing gaps ${\Delta }_p$ and ${\Delta }_n$, $Z$=120, 132, and 138 and $N$=172, 184, 198, 228, 238, and 258 are suggested to be the magic numbers within the present approach. The $\alpha$-decay half-lives are also discussed. In addition, the potential energy surfaces of possible doubly magic nuclei are obtained by the deformation-constrained relativistic mean field (RMF) theory, and the shell effects stabilizing the nuclei are investigated. Furthermore, the formation cross sections of ${}_{172}^{292}$120 and ${}_{184}^{304}$120 at the optimal excitation energy are estimated by a phenomenological cold fusion reactions model with the structure information extracted from the constrained RMF calculation.

37 pages, 14 figures

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