Oblate Deformation Research Articles

Prolate-oblate shape transition in heavy neutron-rich nuclei

A large amount of experimental information was obtained on heavy neutron-rich nuclei in the Hf-Hg region during the last decade. In the majority of the cases these nuclei were populated in relativistic energy fragmentation and studied via isomeric and β decays. In addition, deep-inelastic studies gave information to nuclei close to stability. The experimental data were used to establish the sign of quadrupole deformation, prolate or oblate. In the present paper this information is compared with two global theoretical calculations, one which is constrained to axial symmetry and one which considers triaxiality. The prolate-oblate transitional region was reached for (Z=76) Os and Ir (Z=77), as proved by the observation of oblate isomeric states in 197,198,199Os and 201Ir. For Ta (Z=73) and W (Z=74) isotopes no clear evidence of oblate deformation exists so far, with 192W and 189Ta being the most neutron-rich isotopes with spectroscopic information.

Geologic structure of Western Primorye: Structuring dynamics

The first data are reported on the structuring dynamics of Western Primorye. The analysis of the structural parageneses of the least studied macro- and mesolevels of the arrangement of the geologic space allowed us to distinguish three sequentially superposed structural patterns (parageneses), each of which was formed by its own stress field during separate geodynamic periods: the Late Proterozoic-Early Paleozoic, the Middle-Late Paleozoic, and the Mesozoic-Cenozoic. During the first two episodes of geodynamic activation (Late Proterozoic-Early Paleozoic), the main compression axis was oriented longitudinally. The first episode was characterized by the formation of a thrust-fold structural pattern. The second episode resulted in the superposition of the meridional riftogenic structures and, respectively, in the pull-apart normal-fault segmentation of the crystalline basement into mainly longitudinal blocks, which partially coincide with the previously distinguished terranes. During the latitudinal compression and oblate deformation that predominanted during the Middle-Late Paleozoic geodynamic period, the down-thrown and uplifted blocks were transformed into depressions and arches, respectively. The depressions were filled with Paleozoic sediments, while the primary rocks in the arches experienced granitization with the formation of two granitic complexes that joined terranes. The granites are characterized by shadow and shear-type fold and pseudofolded forms. The Mesozoic-Cenozoic period governed by NNW compression is divided into the Triassic-Jurassic, Early Cretaceous, and Tertiary tectonic episodes. During the Triassic-Jurassic period, the ENE-trending narrow arches and depressions were formed by warping. The arches accumulated granitized rocks, while the depressions were compensated for by the Early-Late Triassic sedimentary-volcanogenic sediments. All these processes led to the formation of structural complexes that joined and overlapped older complexes of meridional blocks (terranes) across the strike. Two subsequent Mesozoic-Cenozoic episodes manifested themselves in the discrete formation of coal-bearing depressions due to the NNW compression and ENE extension of the warping products.

Four-Quasiparticle High-K States in Neutron-Deficient Lead and Polonium Nuclei

Configuration-constrained potential energy surface calculations have been performed to investigate four-quasiparticle high-K configurations in neutron-deficient lead and polonium isotopes. A good agreement between the calculations and the experimental data has been found for the excitation energy of the observed Kπ = 19− state in 188Pb. Several lowly excited high-K states are predicted, and the large oblate deformation and low energy indicate high-K isomerism in these nuclei.

Deformation effect in the sub-barrier capture process

The role of prolate and oblate deformations of colliding nuclei in the sub-barrier capture process is studied within the quantum diffusion approach. The calculated and existing experimental capture cross sections are compared in the reactions ${}^{28}$Si + ${}^{198}$Pt and ${}^{40}$Ca + ${}^{194}$Pt with the heavy oblate nuclei. The possibility of the transition of heavy nucleus from the potential minimum with an oblate deformation of the ground state to the minimum with a prolate deformation during the capture process is discussed. The capture cross sections and mean angular momenta of the captured systems are predicted for the reactions ${}^{48}$Ca,${}^{36}$S + ${}^{194}$Pt, where the detection of this transition is possible.

Deformation, breakup and motion of a perfect dielectric drop in a quadrupole electric field

A detailed nonlinear analysis of the deformation and breakup of a perfect dielectric (PD) drop, suspended in another perfect dielectric fluid, in the presence of a quadrupole electric field is presented using analytical (asymptotic) and numerical (boundary integral) methods. The quadrupole field is the simplest kind of an axisymmetric non-uniform electric field. A drop, when placed at the center of such a field, does not translate, thus allowing systematic investigation of the effect of non-uniformity of the electric field. The deformation of a drop under a quadrupole field for PD-PD systems exhibits several novel features as compared to that of a drop under a uniform electric field. The first order analysis predicts oblate deformation for a PD-PD system when the dielectric constant of the suspending medium is larger than that of the drop (Q = εi/εe < 1). This is in sharp contrast to uniform electric fields where oblate shapes are observed only in leaky dielectric systems. Prolate shapes are observed for Q > 1, and the deformation is larger than that for uniform fields for similar electric capillary numbers. The steady state shapes are defined by higher harmonics as compared to the uniform field. At large capillary numbers, prolate deformations (Q > 1) show breakup whereas oblate deformations (Q < 1) do not. Positive and negative dielectrophoresis is observed when the drop is placed off center, and its translation and simultaneous deformation under quadrupole fields is also investigated. The electro-hydrostatics is unaffected by the viscosity ratio. However, the breakup of the drop and the dielectrophoretic motion and deformation strongly depend upon the viscosity ratio.

Oblate-prolate deformation effect in capture reactions at sub-barrier energies

The role of prolate and oblate deformations of colliding nuclei in the sub-barrier capture process is studied within the quantum-diffusion approach. A comparison of the calculated and measured capture cross sections in the reactions ${}^{16}\mathrm{O},{}^{48}\mathrm{Ca}+{}^{154}\mathrm{Sm}$ and ${}^{74}\mathrm{Ge}+{}^{74}\mathrm{Ge}$ show that transitions during the capture process occur from the potential minimum with an oblate deformation of the ground state to the minimum with a prolate deformation of the nuclei ${}^{154}\mathrm{Sm}$ and ${}^{74}\mathrm{Ge}$. These transitions crucially influence the sub-barrier capture. The capture cross sections and mean-angular momenta are predicted for the reactions of ${}^{36}\mathrm{S}+{}^{170}\mathrm{Er},{}^{174}\mathrm{Yb}$.

Shell Evolution around and beyond $N=28$ Studied with Large-Scale Shell-Model Calculations

The evolution of the shell structure around N = 28 is described by the shell-model calculation using an effective interaction based on the monopole-based universal interaction. Performing shell-model calculations, we successfully describe the configuration mixing and deformation from which the shell evolution in this region is well clarified. The reduction of the proton spin-orbit splitting from N = 20 to 28 is dominated by the tensor force and is quantitatively reproduced well in terms of the distribution of the spectroscopic factors. This reduction also brings about a large oblate deformation in 42 Si. The location of the neutron 0g9/2 orbit in Ca isotopes is identified by their 3 − states.

Signatures of oblate deformation in the111Tc nucleus

Monoisotopic samples of exotic, neutron-rich ${}^{111}$Mo nuclei, produced in the deuteron-induced fission of ${}^{238}$U and separated using the IGISOL3 isotope separator, coupled to the JYFLTRAP Penning trap, were used to perform $\ensuremath{\beta}$- and $\ensuremath{\gamma}$-coincidence spectroscopy of ${}^{111}$Tc. New excited levels in ${}^{111}$Tc populated in ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay of ${}^{111}$Mo provide the first indication for an oblate deformation in the mass $A\ensuremath{\approx}110$ region. The wide spin range of levels populated in ${}^{111}$Tc following the decay of ${}^{111}$Mo indicates the existence of two $\ensuremath{\beta}$-decaying levels in ${}^{111}$Mo. The Q${}_{\ensuremath{\beta}}$ value of the ${}^{111}$Mo ${\ensuremath{\beta}}^{\ensuremath{-}}$ decay was determined experimentally for the first time.

Chaotic motion in axially symmetric potentials with oblate quadrupole deformation

By computing the Poincaréʼs surfaces of section and Lyapunov exponents, we study the effect of introducing an oblate quadrupole in the dynamics associated with two generic spherical potentials of physical interest: the central monopole and the isotropic harmonic oscillator. In the former case we find saddle points in the effective potential, in contrast to the statements presented by Guéron and Letelier in [E. Guéron, P.S. Letelier, Phys. Rev. E 63 (2001) 035201]. The results we show in the second case have application in nuclear or atomic physics. In particular, we find values of oblate deformation leading to a disappearance of shell structure in the single-particle spectrum.

First spectroscopy of 66Se and 65As: Investigating shape coexistence beyond the [formula omitted] line

We report on the first γ spectroscopy of 66Se and 65As from two-neutron removal at intermediate beam energies. The deduced excitation energies for the first-excited states in 66Se and 65As are compared to mean-field-based predictions within a collective Hamiltonian formalism using the Gogny D1S effective interaction and to state-of-the-art shell-model calculations restricted to the pf5/2g9/2 valence space. The obtained Coulomb-energy differences for the first excited states in 66Se and 65As are discussed within the shell-model formalism to assess the shape-coexistence picture for both nuclei. Our results support a favored oblate ground-state deformation in 66Se and 65As. A shape transition for the ground state of even–odd As isotopes from oblate in 65As to prolate in 67,69,71As is suggested.

High-spin structure and multiphononγvibrations in very neutron-richRu114

High-spin levels of the neutron-rich $^{114}\mathrm{Ru}$ have been investigated by measuring the prompt $\ensuremath{\gamma}$ rays in the spontaneous fission of $^{252}\mathrm{Cf}$. The ground-state band and one-phonon $\ensuremath{\gamma}$-vibrational band have been extended up to 14${}^{+}$ and 9${}^{+}$, respectively. Two levels are proposed as the members of a two-phonon $\ensuremath{\gamma}$-vibrational band. A back bending (band crossing) has been observed in the ground-state band at $\ensuremath{\hbar}\ensuremath{\omega}\ensuremath{\approx}$ 0.40 MeV. Using the triaxial deformation parameters, the cranked shell model calculations indicate that this back bending in $^{114}\mathrm{Ru}$ should originate from the alignment of a pair of ${h}_{11/2}$ neutrons. Triaxial projected shell model calculations for the $\ensuremath{\gamma}$-vibrational band structures of $^{114}\mathrm{Ru}$ are in good agreement with the experimental data. However, when using the oblate deformation parameters, both of the above-calculated results are not in agreement with the experimental data.

Spin, quadrupole moment, and deformation of the magnetic-rotational band head inPb193

The spectroscopic quadrupole moment of the ${T}_{1/2}=9.4(5)$ ns isomer in $^{193}\mathrm{Pb}$ at an excitation energy ${E}_{\mathrm{ex}}=(2585+x)$ keV is measured by the time-differential perturbed angular distribution method as $|{Q}_{s}|=2.6(3)$ $e$ b. Spin and parity ${I}^{\ensuremath{\pi}}=27/{2}^{\ensuremath{-}}$ are assigned to it based on angular distribution measurements. This state is the band head of a magnetic-rotational band, described by the $1{i}_{13/2}$ subshell with the $(3{s}_{1/2}^{\ensuremath{-}2}1{h}_{9/2}1{i}_{13/2}){}_{{11}^{\ensuremath{-}}}$ proton excitation. The pairing-plus-quadrupole tilted-axis cranking calculations reproduce the measured quadrupole moment with a moderate oblate deformation ${\ensuremath{\epsilon}}_{2}=\ensuremath{-}0.11$, similar to that of the ${11}^{\ensuremath{-}}$proton intruder states, which nuclei in the region. This is the first direct measurement of a quadrupole moment and thus of the deformation of a magnetic-rotational band head.

Fusion of deformed nuclei:C12+C12

The $S$ factor and the fusion cross-section values for the $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction are evaluated in the framework of a simple barrier-penetration model, which takes into account quadrupole and hexadecapole surface deformations of $^{12}\mathrm{C}$. The calculated values agree well with corresponding experimental data at off-resonances energies. It is shown that the strong oblate quadrupole deformation of $^{12}\mathrm{C}$ induces the increasing of both the $S$ factor and the fusion cross-section values at subbarrier energies. The $S$ factor and the fusion cross section for the $^{12}\mathrm{C}+^{12}\mathrm{C}$ reaction are slightly reduced at low energy due to the influence of the hexadecapole deformation.

On the character of three 8+ states in 192Pb

Three low-lying 8+ states have been identified in 192Pb . A newly observed cascade of $ \gamma$ -rays built directly on the 8+ 1 state is compared to the previously identified, weakly rotational band above the 11- $ \pi$ i 13/2 , h 9/2 isomer in the same nucleus, and to analogous structures in 194Pb . The similarity of all four structures lends support to the suggestion that the 8+ 1 configurations are of a similar oblate deformation to the 11- isomers. The excitation energies of all three 8+ states in 192Pb and 190Pb are compared to systematics. The possibility that one of the 8+ states in 192Pb is associated with a prolate shape is discounted.

Shape evolution in self-conjugate nuclei, and the transitional nucleusSe68

We report on the first measurement of the absolute transition strength $B(E2;{0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+})$ in the self-conjugate nucleus $^{68}\mathrm{Se}$. It is found that the ${0}_{1}^{+}\ensuremath{\rightarrow}{2}_{1}^{+}$ transition displays a strength similar to that for the triaxial $^{64}\mathrm{Ge}$ nucleus, in sharp contrast to the much stronger collectivity observed for the oblate $^{72}\mathrm{Kr}$ nucleus. Shape evolution along the $N=Z$ line from zinc to strontium is analyzed through beyond-mean-field calculations using the D1S force. Over this narrow mass region the nuclear structure shows clear-cut transition from prolate to oblate and back to prolate, with $^{68}\mathrm{Se}$ standing as pivotal between triaxial and oblate deformations.

Further examination of prolate-shape dominance in nuclear deformation

The observed almost complete dominance of prolate over oblate deformations in the ground states of deformed even-even nuclei is related to the splitting of high center dot surface orbits in the Nilsson diagram: on the oblate side the occurrence of numerous strongly avoided crossings which reduce the fanning out of the low Lambda orbits, while on the prolate side the same interactions increase the fanning out. It is further demonstrated that the prolate dominance is rather special for the restricted particle number of available nuclei and is not generic for finite systems with mean-field potentials resembling those in atomic nuclei.

Weakly deformed oblate structures in76198Os122

Gamma rays de-exciting isomeric states in the neutron-rich nucleus 76198Os122 have been observed following relativistic projectile fragmentation of a 1 GeV per nucleon Pb208 beam. The ground-state band has properties compatible with oblate deformation. The evolution of the structure of Os isotopes characterized by sudden prolate-oblate shape change is discussed and contrasted with the smooth change known in the Pt chain.Received 23 January 2009DOI:https://doi.org/10.1103/PhysRevC.79.031305©2009 American Physical Society

Nuclear structure of 189Tl states studied via $ \beta^{{+}}_{}$ /EC decay and laser spectroscopy of 189m+gPb

The $ \beta^{{+}}_{}$ /EC decay of 189m, gPb has been studied at the ISOLDE facility using nuclear spectroscopy and in-source laser spectroscopy. A level scheme of 189Tl has been built from $ \gamma$ - $ \gamma$ coincidence relationships and information on the feeding of some excited levels of 189Tl provided by the hyperfine spectra obtained from laser ionization. The half-lives of both the 13/2+ and 3/2- 189Pb isomers have been estimated to be T 1/2 = 50±3 s and T 1/2 = 39±8 s, respectively. Calculations have been performed for different oblate and prolate nuclear deformations using an axial-rotor coupled to one-quasiparticle model, a structure has been suggested for the low-lying levels of the 189Tl nucleus.

Erratum: High-spin states inAu191,193andPt192: Evidence for oblate deformation and triaxial shapes [Phys. Rev. C 76, 044315 (2007)

Erratum: High-spin states inAu191,193andPt192: Evidence for oblate deformation and triaxial shapes [Phys. Rev. C 76, 044315 (2007)

Revised spin-parity assignment and a new interpretation of the high-spin isomer in 151Er

The high-spin isomer in 151Er ( Ex = 10.3 MeV, T1/2 = 420 ns) has been studied by the 116Sn ( 40Ar , 5n) 151Er reaction at 197MeV. From the \( \gamma \gamma\) coincidence relations, a new transition with an energy of 1514keV was found. This finding requires the revision of the spin-parity assignment from previous 67/2- to 61/2+ or 65/2- . The 61/2+ assignment is the one which was predicted by the deformed independent particle model as an isomer with a large oblate deformation ( \( \beta\) = - 0.17) of the \(\ensuremath[\nu(f_{7/2}h_{9/2} i_{13/2}) \pi(h^4_{11/2})]_{61/2^+}\) configuration. The isomerism may be attributed to the sudden shape change of the isomer from the nearly spherical shape of the lower-spin yrast states to the oblate shape.