R. A. Gherghescu

Valleys due to Pb and Sn on the potential energy surface of superheavy and lighter α-emitting nuclei

The strong shell effects of the magic nuclei 208Pb, 132Sn and 102Sn are the origin of valleys on the potential energy surfaces (PES) of the superheavy nucleus 294118 and of the alpha emitters 212Po and 106Te. We use the most advanced asymmetric two-centre shell model allowing us to obtain shell and pairing corrections which are added to the Yukawa plus exponential model deformation energy. For the first time the alpha valley of a nucleus (106Te) calculated by using the macroscopic–microscopic method is clearly seen on a PES. The α-decay half-lives calculated within fission theories (analytical superasymmetric fission model, universal curve, semiempirical formula based on fission theory) are very close to the experimental ones. The increased deviations in the neighbourhood of magic numbers of nucleons, present in other frequently used relationships (e.g. Viola–Seaborg formula), are smoothed out by the semiempirical formula based on fission theory.

Simple relationships for α-decay half-lives

The universal curve for α-decay and cluster radioactivities based on the fission approach of these decay modes is compared with the universal decay law derived using α-like R-matrix theory for a total of 534 α-emitters in four groups: even–even, even–odd, odd–even and odd–odd. The standard deviations of calculated half-lives from the experimental ones are comparable in the two cases. Large absolute values of deviations from experimental data which are found in the neighborhood of magic numbers of neutrons 126, 162 and 172, and magic numbers of protons 82 and 108 are explained by a part of shell effects which are not taken into account.

Nuclear inertia and the decay modes of superheavy nuclei

Superheavy nuclei produced up to now decay mainly by α emission and spontaneous fission. For atomic numbers larger than 121 cluster decay has a good chance to compete. While calculated α decay half-lives are in agreement with experimental data within one order of magnitude and cluster decay experiments are also very well accounted for, the discrepancy between theory and experiment can be as high as ten orders of magnitude for spontaneous fission. We analyze some ways of improving the accuracy: using a semiempirical formula for α decay and changing the parameters of analytical superasymmetric fission and of the universal curve for cluster decay. For spontaneous fission we act on nuclear dynamics based on potential barriers computed by the macroscopic–microscopic method and employing various nuclear inertia variation laws. Applications are illustrated for 284Cn and Z = 118–124 even–even parent nuclei. Communicated by Steffen Bass

Deformation energy of superheavy nuclei

We study the nuclear deformation energy of superheavy nuclei by using the macroscopic - microscopic method. Nuclear shape is determined by three independent shape coordinates: separation distance between the fragment centres; mass asymmetry, and neck radius. The Yukawa-plus-exponential model gives the macroscopic energy. Shell and pairing (microscopic) corrections are calculated on the basis of a superasymmetric two-centre shell model. Various spherical magic numbers in the region of superheavy nuclei are obtained by changing the strength of the spin - orbit coupling in the two-centre shell model. A complete set of and values have been obtained leading to magic numbers up to 126 for protons and 184 for neutrons (including Z = 114, 120 and N = 172). Potential energy surfaces for nuclei , , and are plotted versus the separation distance and mass asymmetry. Compact shapes, typical for synthesis by fusion reactions or cold fission, are assumed.

Liquid-drop stability of a superdeformed prolate semi-spheroidal atomic cluster

Analytical relationships for the surface and curvature energies of oblate and prolate semi-spheroidal atomic clusters have been obtained. By modifying the cluster shape from a spheroid to a semi-spheroid (including the flat surface of the end cup) the most stable shape was changed from a sphere to a superdeformed prolate semi-spheroid. Potential energy surfaces vs. deformation and the number of atoms, N, illustrate this property independent of N.

Spontaneous fission of the superheavy nucleus

The decimal logarithm of spontaneous fission half-life of the superheavy nucleus

^{286}

^{286}

Fl

Fl experimentally determined is

Potential energy surfaces for cluster emitting nuclei

\log_{10} T_f^{exp} (s) = -0.632

BINARY AND TERNARY EMISSION FROM SUPERHEAVY NUCLEI

. We present a method to calculate the half-life based on the cranking inertia and the deformation energy, functions of two independent surface coordinates, using the best asymmetric two center shell model. In the first stage we study the statics. At a given mass asymmetry up to about