Evidence for nuclear shape coexistence in180Hg

Theγ decay in the radiative fusion reaction⁹⁰Zr+⁹⁰Zr→¹⁸⁰Hg+xγ has been observed in an array of NaI detectors. States up to 6⁺ in the yrast sequence of¹⁸⁰Hg are tentatively assigned and suggest the coexistence of weakly oblate and strongly prolate nuclear shapes. The difference in potential energy between the two inferred shapes has dropped to about 200 keV, continuing the downward trend observed in the heavier even isotopes^188–182Hg.     

Decay of high-spin isomers in Os nuclei by barrier penetration

A decay scheme for the 130±20 ns high-spin isomer in ¹⁸²Os has been established. The excitation energy of the isomer is 7049±1 keV and it has I^π = 25⁽⁺⁾. A 2.4% decay directly to the yrast 24⁺ level at 5988 keV is observed. In ¹⁸⁴Os a 20±5 ns isomer is observed at 2366±1 keV excitation energy with I^π = 10⁺. Again, direct transitions into the yrast 8⁺ and 10⁺ levels are observed. Contrary to previous speculations, there is no compelling evidence for stable triaxial shapes in the structure of the levels through which the isomers decay. The abnormally short half-lives observed, as well as the unusual decay patterns, are best understood in terms of a γ-soft nuclear potential. Motion in the γ-direction allows the isomer to decay via barrier penetration from an axially symmetric prolate shape with the angular momentum along the nuclear symmetry axis (deformation aligned state) via oblate shapes to another prolate shape with the angular momentum perpendicular to the nuclear symmetry axis (rotation-aligned state).     

Nuclear reorientation effects for the 26Mg, 28Si(12C, 12C′) reactions at E = 41 MeV

Angular distributions for elastic and inelastic scattering of 41 MeV ¹²C from ²⁶Mg and ²⁸Si have been measured. Corresponding angular distributions from coupled-channels calculations show significant differences depending on whether a prolate or an oblate intrinsic shape is assumed. The ²⁶Mg and ²⁸Si data are best described by calculations with prolate and oblate shapes, respectively, in agreement with previous Coulomb excitation rorientation measurements. The Hendrie scaling procedure fails to accurately predict the measured nuclear β₂ deformation for ²⁶Mg.     

Evidence for shape coexistence in186Pt

High-spin states in¹⁸⁶Pt have been populated by the¹⁸⁸Os (α, 6n) reaction and were investigated with the OSIRIS spectrometer. A shape coexistence at high spins was established in the nucleus¹⁸⁶Pt, which lies on the border between light prolate and heavy oblate Pt nuclei. Two bands corresponding to predominantly prolate shapes and one band of predominantly oblate shape have been observed. For prolate shapes a (π h _9/2)² alignment and for oblate shapesa (vi _13/2)² alignment has been found.     

Shape-excited states of28Si

The Hartree-Fock (HF) minima for the nucleus²⁸Si were obtained for the prolate, oblate and spherical shapes using the interaction obtained by Preedom and Wildenthal. The interaction gives rise to large energy separation between the prolate and the oblate shapes. The spherical solution is just 2 MeV above the lowest HF (oblate) minimum. The spectrum projected from the oblate HF state is in good agreement with the experimental spectrum. The transition probabilities for the different energy levels also agree reasonably well. The configuration mixing calculations performed on the basis of states projected from the three shapes indicate that there is no significant mixing of different projected states. The second 0 ₂ ⁺ state, thus obtained, corresponds to the third 0 ₃ ⁺ state in the experimental spectrum and stems dominantly from the spherical HF state. It is seen that the structure of the energy levels of²⁸Si, especially the second 0 ₂ ⁺ level is very sensitive to the two body interaction. The results are compared with those obtained using the renormalised interaction of Kuo.     

Nuclear deformations in the pairing-plus-quadrupole model (III). Static nuclear shapes in the rare-earth region

The potential energy of deformation (β, γ), is calculated with the pairing-plus-quadrupole model for nuclei with N=82–126, Z=50–82. There is a sudden onset of deformation in the N=86–90 region, and the static nuclear shape, the lowest minimum of the potential function, changes from spherical to prolate. The disappearance of deformation in the Z=74–80 region is more gradual, and the static shape changes from prolate to asymmetric to oblate to spherical. The energy of zero-point motion is calculated, and it is concluded that all the stable deformed shapes of the region are prolate. Proton and neutron energy gaps, intrinsic quadrupole moments, moments of inertia and gyromagnetic ratios of the doubly even nuclei of the rare-earth region are calculated and compared with the experimental data.     

Relative population of oblate and prolate structures in189Au

High spin states of¹⁸⁹Au were populated via the¹⁷⁴Yb (¹⁹F, 4n reaction at 86, 90, 95 and 100 MeV beam energies. The study of the relative population of oblate and prolate structures shows a striking disappearance of the prolate band relative to the oblate ones as the beam energy goes from 86 to 100 MeV.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Angular momentum dependence of giant dipole vibrations in hot dysprosium nuclei

The spin dependence of the giant dipole resonance built on excited states in ¹⁵⁶Dy has been studied with a new technique using Ge-BGO spectrometers. The observed structure of the GDR and the measured γ-ray anisotropies are consistent with a change in nuclear shape from prolate to oblate with increasing spin. No evidence is found for centroid shifts nor for superdeformed shapes at high temperature.     

Properties of the quasiparticle excitations in 207Pb and 209Pb from an extrapolation of the optical-model potential

A previously developed dispersion relation approach is used to calculate the shell-model potential in the case of neutrons in ²⁰⁸Pb, in the energy domain (-50 MeV, 0). This potential contains a dispersive contribution besides a Hartree-Fock type component, and thereby includes correlation and polarization effects. The shell-model and the Hartree-Fock type potentials are assumed to have Woods-Saxon shapes with diffuseness a_v = 0.70 fm; the energy dependence of their depths and radii is calculated. The energy dependence of the shell-model potential is characterized by the effective mass, whose dependence upon radial distance and neutron energy is determined. The effective mass is a sensitive function of energy, in contrast to its Hartree-Fock type component which is nearly independent of energy. Attention is drawn to the fact that the effective mass in nuclear matter cannot be straightforwardly identified with the effective mass at the nuclear centre. The effective mass presents a sharp peak at the nuclear surface near the Fermi energy and a dip at the surface for energies 10 to 20 MeV away from the Fermi energy. The spectroscopic factors of single-particle excitations in ²⁰⁷Pb and ²⁰⁹Pb are calculated from the difference between the effective mass and its Hartree-Fock type component. The predicted values of the valence single-particle wave functions at large radial distances are in fair agreement with experimental values deduced from analyses of sub-Coulomb pickup reactions. It is shown that the dispersive contribution increases the level density parameter by about 25%, in agreement with previous microscopic or semi-phenomenological models; the calculated level density parameter is in good agreement with the empirical value.     

Triple point of nuclear deformations

We show that the second-order phase transition between spherical and deformed shapes of atomic nuclei is an isolated point following from the Landau theory of phase transitions. This point can occur only at the junction of two or more first-order phase transitions which explains why it is associated with one special type of structure and requires the recently proposed first-order phase transition between prolate and oblate nuclear shapes. Finally, we suggest the first empirical example of a nucleus located at the isolated triple-point.     

Reaction dependence of nuclear decay linewidths

Various light- and heavy-ion reactions, 20 < E < 100 MeV, have been used to study the reaction dependence of α-decay widths for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV). Although slight differences (< 20 %) are found for the observed line shapes (Γ), the resonance widths inferred (Γ_R) are self-consistent and indicate little if any reaction dependence (< 10 %). Near a decay threshold one may expect Γ < Γ_R by 20 % or more, however, and thus care must be taken in comparing decay widths inferred from nuclear reactions with those from scattering resonances. Reduced formal α-decay widths of γ_λ² = 680 ± 100 keV (s = 4.8 fm) and γ_λ² = 350 ± 50 keV(s = 5.4 fm), corresponding to θ_λ² = 0.50 and θ_λ² = 0.49 are deduced for ⁸Be¹(2 ⁺ , 2.9 MeV) and ¹⁶O¹(1^?, 9.6 MeV) using the nuclear-reaction Γ_R values and a particular set of α-nucleus potentials.     

Relative population of the oblate and prolate structures in187Au

The population of the oblate and the prolate structures in¹⁸⁷Au has been studied using the “Château de Cristal” set-up through the¹⁷²Yb(¹⁹F, 4n) reaction at 90, 95 and 100 MeV beam energy. γ — γ, γ-Fold and γ -Sum energy coincidence measurements were performed, γ-ray intensity measurements showed that as the beam energy increases the prolate system is less populated than the oblate one. Fold and Sum-energy associated with oblate and prolate structures showed a different behaviour with increasing beam energy. Two mechanisms are suggested to explain these results.     

Elastic and inelastic scattering of 12C ions at intermediate energies

Elastic and inelastic scattering of ¹²C ions on ¹²C and ²⁰⁸Pb targets have been measured at the incident energies per nucleon E / A = 120 MeV/u and E / A = 200 MeV/u. Optical-model analysis is reported and nuclear surface transparency effects are discussed, together with the nuclear potential-energy dependence. The transparency region extends down to a radial internuclear distance of about 3 fm for the ¹²C-¹²C system and 8 fm for the ¹²C-²⁰⁸Pb system. A decrease of the imaginary potential with increasing incident energy is deduced for the two systems. Anomalous collapse of the real potential in the surface region is observed for ¹²C-²⁰⁸Pb system at 200 MeV/u. DWBA analysis of data on the 2⁺, 4.4 MeV state of ¹²C is reported and trends for the energy dependance of mean-field excitations are deduced.     

Wetting layer and size effects on the nonlinear optical properties of semi oblate and prolate Si0.7Ge0.3/Si quantum dots

Semi oblate and semi prolate are among the most probable self-organized nanostructures shapes. The optoelectronic properties of such nanostructures are not just manipulated with the height and lateral size but also with the wetting layer element. The practical interest of derivatives of germanium and silicon has a great important role in optoelectronic devices. This study is a contribution to the analysis of linear and nonlinear optical properties of Si_0.7Ge_0.3/Si. In the framework of the effective mass approximation, we solve numerically the Schrödinger equation relative to one particle confined in Si_0.7Ge_0.3/Si semi prolate and semi oblate quantum dots by using the finite element method and by taking into consideration the effect of the wetting layer. The energy spectrum of the lowest states and the dipolar matrix for the fourth allowed transitions are determined and discussed. We also calculate the detailed optical properties, including absorption coefficients, refractive index changes, second and third harmonic generation as a function of the quantum dot sizes. We found that with the change in the size of prolate and oblate quantum dots, there is a shift in the resonance peaks for the absorption coefficient and refractive index. It is due to the modification in the energy levels with changing size. The study proves a redshift in the second harmonic generation and third harmonic generation coefficients with an increase in the height/radius of the oblate/prolate quantum dot, respectively. We also demonstrated the variation of wavefunction inside the quantum dot with the change in wetting layer thickness.     

Mixing of prolate and oblate shapes by tunneling in <Emphasis Type="Italic">γ</Emphasis> direction

The equation is derived, similar to the Bohr-Mottelson one, which describes the rotation and vibrations of the nuclear ellipsoid of inertia. Using it we considered the dynamics of nonrotating nuclei, whose energy landscape has minima corresponding to prolate and oblate shapes, connected by the collective path, along which the triaxiality parameter γ varies from γ = 0 to π/3. Peculiarities of the barrier tunneling in γ direction are considered with the aid of the modified WKB approximation. The electric-monopole-transition strength between the levels of the ground 0⁺ doublet of the nuclei with mixed prolate-oblate shapes is calculated. The results are consistent with the experimental data for Kr isotopes. The text was submitted by the authors in English.     

Microscopic study of yrast bands and backbending anomaly in 78-82Kr isotopes

The yrast spectra of ^78-82Kr are studied by using the projected shell model (PSM) approach. The energy states are obtained by taking oblate as well as prolate quadrupole deformations for ^78-82Kr. The structure of yrast states and backbending phenomena are investigated. The theoretical results predict low-lying states in ^{78, 82}Kr to be oblate and coexistence of oblate-prolate shapes for ⁸⁰Kr. The B(E2) transition probabilities and g-factors are obtained and compared with the available experimental data.     

Collectivity and configuration mixing in 186,188Pb and 194Po

Lifetimes of prolate intruder states in 186Pb and oblate intruder states in 194Po have been determined by employing, for the first time, the recoil-decay tagging technique in recoil distance Doppler-shift lifetime measurements. In addition, lifetime measurements of prolate states in 188Pb up to the 8+ state were carried out using the recoil-gating method. The B(E2) values have been deduced from which deformation parameters |beta2|=0.29(5) and |beta2|=0.17(3) for the prolate and the oblate bands, respectively, have been extracted. The results also shed new light on the mixing between different shapes.     

Theory study of shapes in <Superscript>187,189</Superscript>Tl nuclei

The nuclear shapes of ^187,189Tl were investigated theoretically in this work. The total routhian surface (TRS) calculations were performed for N=106 and 108 isotopes of thallium (Z=81). The single-particle energies were obtained from the deformed Woods-Saxon potential, with the Lipkin-Nogami (LN) treatment of pairing. It is found that the collective oblate rotation coexists with the high-K prolate rotation. Superdeformed prolate rotation is included in this calculation. Supported by the National Natural Science Foundation of China (Grant Nos. 10575036 and 10675046) and the Natural Science Foundation of Zhejiang Province of China (Grant Nos. Y605476 and Y604027)     

Shape coexistence in117I

The ¹¹⁷Inucleus has been investigated in a high-spin γ-spectroscopic study using the NORDBALL detector array. The observed level structures are interpreted as resulting from coexisting collective prolate and oblate as well as non-collective oblate shapes.