Article

# Magic nuclei in superheavy valley

Modern Physics Letters A (Impact Factor: 1.2). 01/2012; 27(30):1250173. DOI: 10.1142/S0217732312501738

Source: arXiv

**ABSTRACT**

An extensive theoretical search for the proton magic number in the superheavy

valley beyond $Z=$82 and corresponding neutron magic number after $N=$126 is

carried out. For this we scanned a wide range of elements $Z=112-130$ and their

isotopes. The well established non-relativistic Skryme-Hartree-Fock and

Relativistic Mean Field formalisms with various force parameters are used.

Based on the calculated systematics of pairing gap, two neutron separation

energy and the shell correction energy for these nuclei, we find $Z=$120 as the

next proton magic and N=172, 182/184, 208 and 258 the subsequent neutron magic

numbers.

valley beyond $Z=$82 and corresponding neutron magic number after $N=$126 is

carried out. For this we scanned a wide range of elements $Z=112-130$ and their

isotopes. The well established non-relativistic Skryme-Hartree-Fock and

Relativistic Mean Field formalisms with various force parameters are used.

Based on the calculated systematics of pairing gap, two neutron separation

energy and the shell correction energy for these nuclei, we find $Z=$120 as the

next proton magic and N=172, 182/184, 208 and 258 the subsequent neutron magic

numbers.

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**ABSTRACT:**We calculate the ground state properties of recently synthesized superheavy nuclei starting from $Z$=105-120. The nonrelativistic and relativistic mean field formalisms is used to evaluate the binding energy, charge radius, quadrupole deformation parameter and the density distribution of nucleons. We analyzed the stability of the nuclei based on the binding energy and neutron to proton ratio. We also studied the bubble structure of the nucleus which reveals about the special features of the superheavy nucleus. - [Show abstract] [Hide abstract]

**ABSTRACT:**The ground state and first intrinsic excited state of superheavy nuclei with Z = 120 and N = 160–204 are investigated using both nonrelativistic Skyrme–Hartree–Fock (SHF) and the axially deformed relativistic mean field (RMF) formalisms. We employ a simple BCS pairing approach for calculating the energy contribution from pairing interaction. The results for isotopic chain of binding energy (BE), quadrupole deformation parameter, two neutron separation energies and some other observables are compared with the finite range droplet model (FRDM) and some recent macroscopic–microscopic calculations. We predict superdeformed ground state solutions for almost all the isotopes. Considering the possibility of magic neutron number, two different modes of α-decay chains 292120 and 304120 are also studied within these frameworks. The Qα-values and the half-life for these two different modes of decay chains are compared with FRDM and recent macroscopic–microscopic calculations. The calculation is extended for the α-decay chains of 292120 and 304120 from their excited state configuration to respective configuration, which predicts long half-life (in seconds). - [Show abstract] [Hide abstract]

**ABSTRACT:**Relativistic energy-consistent pseudopotentials for the superheavy elements with nuclear charges 119 and 120 replacing 92 electrons of a [Xe]4f (14)5d(10)5f (14) core were adjusted to relativistic multi-configuration Dirac-Coulomb-Breit finite nucleus all-electron reference data including lowest-order quantum electrodynamic effects, i.e., vacuum polarization and electron self-energy. The parameters were fitted by two-component multi-configuration Hartree-Fock calculations in the intermediate coupling scheme to the total valence energies of 131 to 140 relativistic states arising from 31 to 33 nonrelativistic configurations covering also anionic and highly ionized states, with mean absolute errors for the nonrelativistic configurations below 0.01 eV. Primitive basis sets for one- and two-component calculations with errors below 0.02 and 0.03 eV to the Hartree-Fock limit, respectively, as well as general contractions of these basis sets with double- to quadruple-zeta quality were obtained. Atomic highly correlated test calculations using the Fock-space coupled-cluster method yield for valence excitation energies and ionization potentials mean absolute errors of 26 cm(-1) and 59 cm(-1), respectively. Correlated and uncorrelated molecular test calculations show deficiencies below 0.005 Å for the bond lengths and 3 N m(-1) for the force constants.