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

W. Zhang·J. Meng·S. Q. Zhang·L. S. Geng·H. Toki
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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 $δ_{2p}$ and $δ_{2n}$, 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 $Δ_{p}$ and $Δ_{n}$, $Z$=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 $α$-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 $^{292}_{172}$120 and $^{304}_{184}$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.

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W. Zhang, J. Meng, S. Q. Zhang, L. S. Geng, H. Toki. 2004-03-07. Magic numbers for superheavy nuclei in relativistic continuum Hartree-Bogoliubov theory. https://doi.org/10.1016/j.nuclphysa.2005.02.086

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