Global properties of even-even superheavy nuclei in macroscopic-microscopic models

A systematic study of global properties of superheavy nuclei in the framework of macroscopic-microscopic method is performed. Equilibrium deformations, masses, quadrupole moments, radii, shell energies, fission barriers and half-lives are calculated using the following macroscopic models: Myers-Swiatecki liquid drop, droplet, Yukawa-plus-exponential, and Lublin-Strasbourg drop. Shell and pairing energies are calculated in Woods-Saxon potential with a universal set of parameters. The analysis covers a wide range of even-even superheavy nuclei from $Z=100$ to 122. Magic and semimagic numbers occurring in this region are indicated and their influence on the observables is discussed. The strongest shell effects appear at proton number $Z=114$ and at neutron number $N=184$. Deformed shell closures are found at $N=152$ and 162. Spontaneous fission half-lives are calculated in a dynamical approach where the full minimization of the action integral in a three-dimensional deformation space of β deformations is performed. The fission half-lives obtained this way are two orders of magnitude smaller than the ones resulting from static calculations. The agreement of theoretical results and experimental data is satisfying.

Figure 1

Statical (stat) and dynamical (dyn) fission barriers $V({\beta }_2)$ (MeV) (solid lines) and effective inertia $B_{\mathrm{eff}}$ ($\hslash /\mathrm{MeV}$) (dashed lines) as functions of elongation parameter ${\beta }_2$ calculated for ${}^{290}\mathrm{Dt}$ along statical and dynamical paths to fission discussed in the text. The left abscissa corresponds to the fission barrier and the right one to the mass parameter.

Figure 2

The region of superheavy nuclei considered in the present study.

Figure 3

Contour map of the Strutinsky shell energy ($E_{\mathrm{shell}}$) for considered nuclei calculated in the ground state. The LSD model is used for the macroscopic part of the energy. The distance between isolines is 1 MeV.

Figure 4

Mass deviation $\Delta M$ (in mega-electron volts) resulting the calculations of Lublin-Strasbourg drop and Woods-Saxon model vs. mass number A. σ denotes the rms error. Experimentally known masses and estimates were taken from Refs. 49, 50.

Figure 5

Electric charge quadrupole moments ($Q_{2,p}$) in barns as a function of neutron number N. The underlying equilibrium deformations were calculated by use of the MM method with the LSD macroscopic part.

Figure 6

Root-mean-square charge radii as functions of neutron number N for even-even transfermium nuclei ($Z=100-122$).

Figure 7

Neutron pairing gap parameters (${\Delta }_n$) in mega-electron volts resulting BCS calculations as a function of neutron number N. Each curve corresponds to one isotopic chain $Z=\mathrm{const}$.

Figure 8

α-decay energies ($Q_{\alpha }$) in mega-electron volts calculated in the LSD model as functions of neutron number N (left panel). Experimental values indicated by full circles come from Ref. 49. The right panel shows the differences $\Delta Q_{\alpha }=Q_{\alpha }(\mathrm{model})-Q_{\alpha }(\mathrm{LSD})$ in mega-electron volts where model corresponds to the MSD, DPT, and YpE. The symbols used for different isotopic chains are the same in all parts of the figure.

Figure 9

First barrier heights (in mega-electron volts) versus neutron number N for even-even nuclei with $Z=100-122$. The left panel shows the results of calculations with macroscopic content corresponding to LSD model. The right panel shows the model deviations defined as $\Delta V_{\mathrm{Bar}}=V_{\mathrm{Bar}}(\mathrm{model})-V_{\mathrm{Bar}}(\mathrm{LSD})$ where model corresponds to MSD, DPT, or YpE.

Figure 10

The decimal logarithms of spontaneous fission half-lives (in years) calculated dynamically in LSD model (left panel). The right panel shows the deviations $\Delta \log {}_{10}(T_{\mathrm{sf}}/y)=\log {}_{10}[T_{\mathrm{sf}}(\mathrm{model})/y]-\log {}_{10}[T_{\mathrm{sf}}(\mathrm{LSD})/y]$ where model corresponds to MSD, DPT, and YpE respectively.

Figure 11

Logarithms of α-decay half-lives $T_{\alpha }$ (in years) obtained according to Viola-Seaborg formula Eq. (14).

Figure 12

Partial probability of α-decay (in percentages) for SHE. The distance between isolines is 10%.