Superheavy nuclei in a relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond $Z=82$ and $N=126$ within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts $N=172$ and $Z=120$ and $N=258$ and $Z=120$ as spherical doubly magic superheavy nuclei, whereas $N=184$ and $Z=114$ show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.

Figure 1

The change with the neutron number $N$ of the two-neutron separation energy $S_{2n}$, the two-neutron shell gap ${\delta }_{2n}$, and the neutron average pairing gap ${\Delta }_n$ for $Z=120$ isotopes obtained from spherical calculations with the relativistic parameter set G2. The proton average pairing gap ${\Delta }_p$ vanishes in the whole isotopic chain.

Figure 2

Same as Fig. 1 but for the relativistic parameter set G1.

Figure 3

Same as Fig. 1 but for the relativistic parameter set NL3.

Figure 4

Single-particle spectrum of neutrons in the vicinity of the Fermi level for the superheavy isotopes ${}^{292}120$, ${}^{304}120$, and ${}^{378}120$ computed with the relativistic interactions G1, G2, and NL3.

Figure 5

The change with the proton number $Z$ of the two-proton separation energy $S_{2p}$, the two-proton shell gap ${\delta }_{2p}$, and the proton ${\Delta }_p$ and neutron ${\Delta }_n$ average pairing gaps for $N=172$ isotones obtained from spherical calculations with the relativistic parameter sets G2 (left panels) and NL3 (right panels).

Figure 6

Same as Fig. 5 but for the isotones of $N=184$.

Figure 7

Same as Fig. 5 but for the isotones of $N=258$.

Figure 8

Single-particle spectrum of protons in the vicinity of the Fermi level for the superheavy isotones ${}^{286}114$ and ${}^{292}120$ (left panel), and ${}^{298}114$ and ${}^{304}120$ (right panel) computed with the relativistic interactions G2 and NL3.

Figure 9

The change of the total shell correction energy (sum of the neutron and proton contributions) with the neutron number $N$ for the isotopes of $Z=114$ and $Z=120$ in spherical calculations with the G2 and NL3 models.

Figure 10

The change of the total shell correction energy (sum of the neutron and proton contributions) with the proton number $Z$ for the isotonic chains of $N=172$, $N=184$, and $N=258$ neutrons in spherical calculations with the G2 and NL3 models.