Triaxial Bands Research Articles

In-beam spectroscopy of medium- and high-spin states inCe133

Medium and high-spin states in $^{133}$Ce were investigated using the $^{116}$Cd($^{22}$Ne, $5n$) reaction and the Gammasphere array. The level scheme was extended up to an excitation energy of $\sim22.8$ MeV and spin 93/2 . Eleven bands of quadrupole transitions and two new dipole bands are identified. The connections to low-lying states of the previously known, high-spin triaxial bands were firmly established, thus fixing the excitation energy and, in many cases, the spin parity of the levels. Based on comparisons with cranked Nilsson-Strutinsky calculations and tilted axis cranking covariant density functional theory, it is shown that all observed bands are characterized by pronounced triaxiality. Competing multiquasiparticle configurations are found to contribute to a rich variety of collective phenomena in this nucleus.

Exotic rotations and triaxiality in Nd nuclei

We have recently studied the Nd nuclei up to very high spins and identified a multitude of bands which are interpreted as the manifestation of a nucleus with stable triaxial shape, presenting various types of collective motion: tilted axis and principal axis rotation, wobbling motion, chiral bands. Seniority isomers built on nearly spherical shapes up to very high spins, surrounded by coexisting triaxial bands, have also been observed. The new results obtained from the systematics of the high-spin bands of Nd nuclei are discussed.

Shape evolution and magnetic rotation in 141Nd

The high-spin states in Nd-141 were investigated using the Zr-96(Ca-48, 3n) reaction and the EU-ROBALL array. The level scheme has been extended up to an excitation energy of around 16MeV and spin 81/2. Two new bands of dipole transitions and three bands presumably of quadrupole transitions were identified and their connections to low-lying states were established. Cranked Nilsson-Strutinsky and tilted axis cranking calculations are combined in the interpretation of the observed dipole bands. The high-spin bands with assigned quadrupole transitions are interpreted as triaxial bands, while the dipole bands appear in the calculations to exhibit a shape evolution from low-deformation triaxial to spherical shape. They can be classified as magnetic rotation, with transition probabilities that show the characteristic decrease with angular momentum caused by the shears mechanism.

Shell model structure of43Sand44Sre-examined

We report on a shell model study of ${}^{43}S$ and ${}^{44}S$. Quadrupole rotational invariants proposed by Kumar about 40 years ago allow us to estimate axial and triaxial deformation parameters from shell model calculations. Present results, showing the large impact of the triaxial degree of freedom on the low-lying structure of studied sulfur isotopes, resolve several inconsistencies in previous interpretations of experimental data. In ${}^{43}S$ the prolate ground-state band coexists with a triaxial band built on the 7/2${}_{1}^{\ensuremath{-}}$ isomer and an excited prolate structure built on the ${K}^{\ensuremath{\pi}}$ = 5/2${}^{\ensuremath{-}}$ deformed orbit originating from the $\ensuremath{\nu}{f}_{7/2}$ shell. In ${}^{44}S$ coexistence of two deformed bands built on mixed 0${}_{1,2}^{+}$ states is reported as well as a pseudo-$\ensuremath{\gamma}$-band and an excited triaxial structure for which a particle-hole neutron excitation couples to proton collectivity. Present results are in good global agreement with recent antisymmetrized molecular dynamics and beyond-mean-field calculations.

Multiple triaxial bands and abnormal signature inversion in [formula omitted

Excited states of the odd–odd nucleus 74As have been investigated via heavy ion fusion evaporation reaction Zn70(Li7,3n)As74 at beam energy of 30 MeV. The properties of the positive- and the negative- parity bands can be interpreted in terms of the Cranked Nilsson–Strutinsky (CNS) model calculations which show that the observed bands are built on the triaxial deformed shape. The inversion of the favored and unfavored signature branches observed in the positive-parity bands presents at high spins rather than normal signature inversion occurs at low spins. This phenomenon may be explained as the origin of unpaired band crossing in a highly rotating triaxial nucleus.

Switch from short-axis to intermediate-axis rotation in138Nd

It is pointed out that the triaxial bands in ${}^{138\ensuremath{-}140}$Nd and in the Lu/Er nuclei can be understood from the same shell structure effects. Two of the bands in ${}^{138}$Nd, interpreted as signature partners, exhibit a crossing at high spins with a signature splitting which is strongly reduced above the crossing. This behavior is unique among the yrast and close-to-yrast configurations, revealing the mechanism which induces a change of the rotation axis from short to intermediate in the triaxially deformed nucleus.

Interpretation of the large-deformation high-spin bands in selectA=158–168 nuclei

The high-spin rotational bands in 168Hf and the triaxial bands in Lu nuclei are analyzed using the configuration-constrained Cranked Nilsson-Strutinsky (CNS) model. Special attention is given to the up-sloping extruder orbitals. The relative alignment between the bands which appear to correspond to triaxial shape is also considered, including the yrast ultra-high spin band in 158Er. This comparison suggests that the latter band is formed from rotation around the intermediate axis. In addition, the standard approximations of the CNS approach are investigated, indicating that the errors which are introduced by the neglect of off-shell matrix elements and the cut-off at 9 oscillator shells (N_{max}=8) are essentially negligible compared to other uncertainties. On the other hand, the full inclusion of the hexadecapole degree of freedom is more significant; for example it leads to a decrease of the total energy of ~ 500 keV in the TSD region of 168Hf.

Diverse collective excitations in159Erup to high spin

A spectroscopic investigation of the gamma decays from excited states in Er-159 has been performed to study the changing structural properties exhibited as ultrahigh spins (I > 60 (h) over bar) are approached. The nucleus of Er-159 was populated by the reaction Cd-116(Ca-48, 5n gamma) at a beam energy of 215 MeV, and the resulting gamma decays were studied using the Gammasphere spectrometer. New rotational bands and extensions to existing sequences were observed, which are discussed in terms of the cranked shell model, revealing a diverse range of quasiparticle configurations. At spins around 50 (h) over bar, there is evidence for a change from dominant prolate collective motion at the yrast line to oblate non-collective structures via the mechanism of band termination. A possible strongly deformed triaxial band occurs at these high spins, which indicates collectivity beyond 50 (h) over bar. The high-spin data are interpreted within the framework of cranked Nilsson-Strutinsky calculations. (Less)

Experimental characterisation of shear and compaction band mechanisms in porous sandstone by a combination of AE and 3D-DIC

Shear and compaction bands represent two fundamental failure modes in sandstones. The identification of these features in both the natural outcrops and the laboratory scale yields useful insights into the mechanisms of localised deformation. Several conventional and advanced experimental full-field methods have been developed in order to shed light into the processes involved, as well as qualify and quantify parameters such as the orientation of these localised bands. In this paper, we present results of two triaxial tests, investigating shear and compaction bands in porous sandstone, using analysis of Acoustic Emission recorded during deformation and 3D-volumetric Digital Image Correlation based on pre- and post deformation x-ray tomography images. (Less)

New shape minimum inYb160: Evidence for a triaxial, strongly deformed band

A high-spin rotational band was observed in the N=90 nucleus Yb-160 with moment of inertia and decay characteristics very similar to recently discovered sequences in Er-157,Er-158. These latter structures were discussed in terms of strongly deformed triaxial bands. Detailed cranked Nilsson-Strutinsky calculations were performed that predict that well-deformed triaxial structures are also expected at high spin in Yb-160. Within this interpretation the observed discontinuity in the dynamic moment of inertia around h omega=0.40-0.45 MeV can be explained as a crossing between i(13/2) neutron levels.

Lifetime measurement of the six-quasiparticle isomer in 140Nd and evidence for an isomer above the 19/2+ state in 139Nd

The lifetime of the recently discovered six-quasiparticle (6-qp) isomer in 140Nd has been measured using the 126Te(18O, 4n) reaction and the pulsed-beam technique at the Institut de Physique Nucleaire (IPN) Orsay. The deduced lifetime of the 6-qp isomer in 140Nd of 1.23(7)μs supports the 20+ spin-parity assignment to the isomeric state which is based on a spherical configuration that coexists with the triaxial bands observed in this spin range. Evidence for delayed components for the transitions below the 19/2+ state in 139Nd was observed, with an apparent half-life of 272(4)ns.

Evidence for particle–hole excitations in the triaxial strongly-deformed well of 163Tm

Two interacting, strongly-deformed triaxial (TSD) bands have been identified in the Z=69 nucleus {sup 163}Tm. This is the first time that interacting TSD bands have been observed in an element other than the Z=71 Lu nuclei, where wobbling bands have been previously identified. The observed TSD bands in {sup 163}Tm appear to be associated with particle--hole excitations, rather than wobbling. Tilted-axis cranking (TAC) calculations reproduce all experimental observables of these bands reasonably well and also provide an explanation for the presence of wobbling bands in the Lu nuclei, and their absence in the Tm isotopes.

Coexisting normal and triaxial superdeformed structures in 165Lu

High-spin states in 165Lu were populated in the 139La ( 30 Si,4n) reaction at a beam energy of 152 MeV and γ-ray coincidences were measured with the EUROBALL spectrometer array. Nine new rotational bands were discovered, known band structures were considerably extended and many inter-band transitions were found. Structures with normal deformation coexist with bands associated with the strongly deformed triaxial energy minima found in calculations. Three of these triaxial bands form a family of wobbling excitations with phonon quanta n w =0, 1 and 2. The wobbling mode is a unique signature of nuclear triaxiality. Configuration assignments are discussed for the observed band structures. An exchange of configuration between two of the new bands due to mixing is observed, resulting in different signature partnerships at low and high spins.

The origin of doublet bands observed in $A \sim 130$ nuclei

The results obtained with the GASP array in the \(A \sim 130\) mass region are reviewed, emphasizing the study of excited highly deformed bands and their decay out, the discovery of chiral doublet bands in the odd-odd Pr nuclei and of stable triaxial bands in Nd nuclei close to the N = 82 shell closure. The very recent studies of nuclei near the proton drip line are described. A discussion of the origin of the various doublet bands observed in odd-odd nuclei of the \(A \sim 130\) mass region is presented.

Gamma-ray spectroscopy of nuclei with large deformations

The large multidetector gamma-ray arrays (such as GAMMASPHERE, EUROBALL, and GASP) have played a central role in nuclear-structure studies during the past decade. In this paper I will discuss recent results from experiments on nuclei with very large deformations, including: the measurement of the spins, parities, and excitation energies of superdeformed bands in 152 Dy; the observation of extreme deformations in 108 Cd and the evidence for hyper-intruder states; the study of superdeformed nuclei around $A \sim 40$ , which provide an opportunity to test our microscopic understanding of collective excitations; and lifetimes of strongly deformed triaxial bands in 163 Lu. I will conclude with a brief discussion on the next generation gamma-ray detector array, GRETA.

Wobbling phonon excitations in strongly deformed triaxial nuclei

The wobbling mode is uniquely related to triaxiality and introduces a series of bands with increasing wobbling phonon number, $n_{\rm w}$ . The pattern of $\gamma$ -transitions between the wobbling excitations will be influenced by the presence of an aligned particle. Evidence for the wobbling mode was obtained recently, and even a two-phonon wobbling excitation has now been identified in 163 Lu. The similarity of the data in 163 Lu to new strongly deformed triaxial bands and connecting transitions in the neighbouring nuclei, 165 Lu and 167 Lu, establishes wobbling as a more general phenomenon in this region. The higher phonon wobbling excitations show some anharmonicity, but the characteristic large $\Delta n_{\rm w} = 1$ E2 strength is observed. The wobbling interpretation is based on the comparison of electromagnetic decay strength between bands to particle-rotor calculations in which an i 13/2 proton is coupled to a triaxial core.

Wobbling phonon excitations, coexisting with normal deformed structures in 163Lu

Wobbling is a rotational mode unique to a triaxial body. The Lu–Hf isotopes with N∼94 at high spin provide a possible region of nuclei with pronounced triaxiality. We have investigated 163Lu through the fusion-evaporation reaction 139La( 29Si,5 n) 163Lu with a beam energy of 152 MeV. Three excited bands decaying into the known, presumably triaxial, superdeformed (TSD) band built on the i 13/2 proton orbital are observed. The electromagnetic properties of the connecting transitions from the two strongest populated excited TSD bands have been investigated. New particle-rotor calculations in which one i 13/2 quasiproton is coupled to the core of triaxial shape produce a variety of bands, whose properties can clearly be interpreted either as “wobbling” or “cranking” motion of the core. Evidence for the assignment of the excited TSD bands as one, and possibly even two wobbling phonon modes built on the yrast TSD band in 163Lu is given. These triaxial bands coexist with bands built on quasiparticle excitations in the normal deformed (ND) minimum for which new data are also presented.

Stable triaxiality at the highest spins in138Ndand139Nd

The nuclei ${}^{138}\mathrm{Nd}$ and ${}^{139}\mathrm{Nd}$ have been studied at very high spins via the ${}^{48}\mathrm{Ca}{+}^{94}\mathrm{Zr}$ reaction. Several new rotational bands were observed, four in ${}^{138}\mathrm{Nd}$ and two in ${}^{139}\mathrm{Nd}.$ The ${J}^{(2)}$ moments of inertia calculated from the observed $\ensuremath{\gamma}$-ray energies are very small and almost constant, indicating that these bands are triaxial. Cranked Nilsson-Strutinsky calculations reproduce the general behavior of the bands, supporting this interpretation and suggesting an approximately constant $\ensuremath{\gamma}$ value of $\ensuremath{\sim}+35\ifmmode^\circ\else\textdegree\fi{}$ over a large spin range up to the highest observed spins. These bands and a few similar bands in other nuclei of the $N\ensuremath{\approx}80$ region are a unique example of almost undisturbed triaxial bands.

Lifetime measurements of a triaxial band in133Ce

Lifetimes of states within a triaxial band belonging to the $\ensuremath{\gamma}$-soft nucleus ${}^{133}\mathrm{Ce}$ have been determined through a Doppler-broadened line shape analysis. A value, ${Q}_{t}\ensuremath{\approx}2.2$ $e\mathrm{b},$ has been found for the transition quadrupole moment which is considerably smaller than that of superdeformed structures ${(Q}_{t}\ensuremath{\approx}7.4$ $e\mathrm{b})$ in this mass region. The results are discussed in terms of deformation self-consistent calculations based on the total Routhian surface formalism.

Lifetime measurements of a triaxial band in133Ce

The Doppler shift attenuation method has been used to determined the transition quadrupole moment of a triaxial band belonging to the γ-soft nucleus,133Ce. Doppler broadened lineshape (DBLS) analysis has revealed the magnitude of theQ t value, to be ∼ 2.4 eb. This contribution provides new information of (i) the transition quadrupole moment of this band (ii) the life-times of in-band and sidefeeding transition and (iii) the relative deformations of coexisting nuclear shapes.