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Superdeformed (SD) states in ⁴⁰Ar have been studied using the deformed-basis antisymmetrized molecular dynamics and the generator coordinate method (GCM). GCM basis wave functions were obtained by the energy variation with a constraint on the quadrupole deformation parameter β, while other quantities such as triaxiality γ were optimized by the energy variation. An SD band is obtained just above the ground state band. The SD band involves a K^π = 2⁺ side band due to the triaxiality. The calculated quadrupole electric transition strengths of the SD band reproduce well the experimental values. Triaxiality is significantly important to understand low-lying states.

Following the semiclassical formalism of Strutinsky et al.,¹¹ we have obtained the complete eigenvalue spectrum for a particle enclosed in an infinitely high spheroidal cavity. Our spheroidal trace formula also reproduces the results of a spherical billiard in the limit η → 1.0. Inclusion of repetition of each family of the orbits with reference to the largest one significantly improves the eigenvalues of the sphere and an exact comparison with the quantum mechanical results is observed up to the second decimal place for kR₀ ≥ 7. The contributions of the equatorial, planar (in the axis of symmetry plane) and non-planar (three-dimensional) orbits are obtained from the same trace formula by using the appropriate conditions. The resulting eigenvalues compare very well with the quantum mechanical eigenvalues at normal deformation. It is interesting that the partial sum of equatorial orbits leads to eigenvalues with maximum angular momentum projection, while the summing of planar orbits leads to eigenvalues with L_z = 0 except for L = 1. The remaining quantum mechanical eigenvalues are observed to arise from the three-dimensional (3D) orbits. Very few spurious eigenvalues arise in these partial sums. This result establishes the important role of 3D orbits even at normal deformations.

Recently, long-lived high spin super- and hyperdeformed isomeric states with unusual radioactive decay properties have been discovered. Based on these newly observed modes of radioactive decay, consistent interpretations are suggested for previously unexplained phenomena seen in nature. These are the Po halos, the low-energy enhanced 4.5 MeV α-particle group proposed to be due to an isotope of a superheavy element with Z=108, and the giant halos.

We consider a semiclassical model of light nuclei, where the nucleus has a crystal-like shape and is built solely from α-particles. We analyze the role of linear configurations in this model, which correspond to super-deformed nuclei. The strong deformed shape for the doubly even nuclei from ¹²C to ²⁴Mg has been determined according to this model. The obtained results show a good agreement with the experimental data.

Evidence for the possible existence of a superheavy nucleus with atomic mass number A = 292 and abundance of about 1×10^-12 relative to ²³²Th has been found in a study of natural Th using inductively coupled plasma-sector field mass spectrometry. The measured mass is different from any species with molecular mass of 292, but it matches the predictions for the mass of an isotope with atomic number Z = 122 or a nearby element. Its deduced half-life of t_1/2 ≥ 10⁸ y suggests that a long-lived isomeric state exists in this isotope. The possibility that it might belong to a new class of long-lived high spin super- and hyperdeformed isomeric states is discussed.

In this work, we review a few structural properties in finite nuclei and nuclear matter that are sensitive to differences in the symmetry energy, and discuss mechanisms that can enhance the sensitivity to differences in the symmetry energy with the relativistic mean-field model. Emphasis has been placed on the establishment of the relationship between the deexcitation energy of superdeformed secondary minima and the density dependence of the symmetry energy.

Based on the observation of the long-lived isotopes of roentgenium, ²⁶¹Rg and ²⁶⁵Rg(Z = 111, t_1/2≥10⁸y) in natural Au, an experiment was performed to enrich Rg in 99.999% Au. 16 mg of Au were heated in vacuum for two weeks at a temperature of 1127°C(63°C above the melting point of Au). The content of ¹⁹⁷Au and ²⁶¹Rg in the residue was studied with high resolution inductively coupled plasma-sector field mass spectrometry (ICP-SFMS). The residue of Au was 3×10^-6 of its original quantity. The recovery of Rg was a few percent. The abundance of Rg compared to Au in the enriched solution was about 2×10^-6, which is a three to four orders of magnitude enrichment. It is concluded that the evaporation rate of Rg from an Au matrix in vacuum at 63°C above the Au melting point is lower than that of Au. This experiment reinforces our first observation of Rg in a terrestrial material. As before it is concluded that a long-lived isomeric state exists in ²⁶¹Rg and that it probably belongs to a new class of isomeric states, namely high spin (K-type) super- or hyperdeformed isomeric states.

The collective features of superdeformed nuclei have been investigated in self-consistent cranked Nilsson plus quasiparticle random-phase approximation. The analysis supports the octupole collectivity of some low-lying excited bands observed recently and, moreover, shows that the onset of supederformation changes considerably the E1 and E2 strength distribution and greatly enhances the collectivity of the low-lying scissors mode.