Triaxial Rotor Research Articles

High-spin structures in theXe129nucleus

High-spin states in the Xe-129 nucleus are studied with the reaction Sn-124(Be-9,4n) at a beam energy of 36 MeV. The level scheme is extended significantly. For the positive-parity band, the alpha = +1/2 and the alpha = -1/2 signature components are combined to form a complete band structure based on the 3/2(+) state with spin and parity up to 21/2(+). For the negative-parity band based on the 11/2(-) state, the alpha = +1/2 signature component is newly established and both the alpha = +1/2 and the alpha = -1/2 signature components also form a complete band structure up to the 35/2(-) state. The positive-and negative-parity bands are proposed to originate from nu d(3/2) 3/2(+)[402] and nu h(11/2)11/2(-)[505] Nilsson configurations, respectively. A backbending is observed in the negative-parity band, which originates from the alignments of two h(11/2) protons according to crank shell model calculations. Based on the total Routhian surface and quasiparticle triaxial rotor model calculations, the negative-parity band is interpreted as a triaxially deformed shape with gamma approximate to -30 degrees, while the positive-parity band is associated with. softness, in accordance with previous studies. In the high-spin states, three decoupled bands and one oblate band with gamma approximate to -60 degrees are newly identified. The systematics and other characteristics of these bands are discussed.

Investigation of chirality in the case of 102Rh

Excited states in 102Rh were populated in the fusion-evaporation reaction 94Zr(11B, 3n)102Rh at a beam energy of 36 MeV using the INGA spectrometer at IUAC, New Delhi. The angular correlations and the electromagnetic character of some of the gamma-ray transitions observed were investigated in details. A new chiral candidate sister band was found. Lifetimes of exited states in 102Rh were measured using the Doppler-shift attenuation technique and the derived reduced transition probabilities are compared to the predictions of the Two Quasiparticles Plus Triaxial Rotor model.

Evidence for Octupole Correlations in Multiple Chiral Doublet Bands.

Two pairs of positive-and negative-parity doublet bands together with eight strong electric dipole transitions linking their yrast positive- and negative-parity bands have been identified in ^{78}Br. They are interpreted as multiple chiral doublet bands with octupole correlations, which is supported by the microscopic multidimensionally-constrained covariant density functional theory and triaxial particle rotor model calculations. This observation reports the first example of chiral geometry in octupole soft nuclei.

Shape coexistence and the role of axial asymmetry in 72Ge

The quadrupole collectivity of low-lying states and the anomalous behavior of the $0^+_2$ and $2^+_3$ levels in $^{72}$Ge are investigated via projectile multi-step Coulomb excitation with GRETINA and CHICO-2. A total of forty six $E2$ and $M1$ matrix elements connecting fourteen low-lying levels were determined using the least-squares search code, gosia. Evidence for triaxiality and shape coexistence, based on the model-independent shape invariants deduced from the Kumar-Cline sum rule, is presented. These are interpreted using a simple two-state mixing model as well as multistate mixing calculations carried out within the framework of the triaxial rotor model. The results represent a significant milestone towards the understanding of the unusual structure of this nucleus.

Lifetime measurements in mass regions A=100 and A=130 as a test for chirality in nuclear systems

Two odd-odd nuclei from the A ~ 100 and A ~ 130 regions, namely ^102Rh and ^134Pr have been studied in search for chiral doublet bands via ^94Zr(^11B,3n)^102Rh and ^119Sn(^19F,4n)^134Pr reactions, respectively. Two nearly degenerate bands built on the pig_9/2 ⊗ vh_11/2 configuration have been identified in ^102Rh and on the pig_11/2 ⊗ vh_11/2 configuration for ^134Pr. Lifetimes of excited nuclear states were measured using Dopplershift attenuation method and recoil distance Doppler-shift method. The deexciting gamma rays were registered by the Indian National Gamma Array for ^102Rh and using the EUROBALL IV detector array with an inner Bismuth Germanate (BGO) ball for ^134Pr, respectively. Polarization and angular correlation measurements have been performed to establish the spin and parity assignments for these bands. The derived reduced transition probabilities are compared to the predicitons of the two quasiparticles + triaxial rotor and interacting boson fermion-fermion models.

Wobbling geometry in a simple triaxial rotor**Supported by President's Undergraduate Research Fellowship (PURF), Peking University, Major State 973 Program of China (2013CB834400), National Natural Science Foundation of China (11175002, 11335002, 11375015, 11345004, 11461141002), National Fund for Fostering Talents of Basic Science (NFFTBS) (J1103206) and Research Fund for the Doctoral Program of Higher Education (20110001110087)

The spectroscopic properties and angular momentum geometry of the wobbling motion of a simple triaxial rotor are investigated within the triaxial rotor model. The obtained exact solutions of energy spectra and reduced quadrupole transition probabilities are compared to the approximate analytic solutions from the harmonic approximation formula and Holstein-Primakoff formula. It is found that the low lying wobbling bands can be well described by the analytic formulae. The evolution of the angular momentum geometry as well as the K-distribution with respect to the rotation and the wobbling phonon excitation are studied in detail. It is demonstrated that with the increase of the wobbling phonon number, the triaxial rotor changes its wobbling motions along the axis with the largest moment of inertia to the axis with the smallest moment of inertia. In this process, a specific evolutionary track that can be used to depict the motion of a triaxial rotating nucleus is proposed.

Transverse wobbling in ^{135}pr.

A pair of transverse wobbling bands is observed in the nucleus ^{135}Pr. The wobbling is characterized by ΔI=1, E2 transitions between the bands, and a decrease in the wobbling energy confirms its transverse nature. Additionally, a transition from transverse wobbling to a three-quasiparticle band comprised of strong magnetic dipole transitions is observed. These observations conform well to results from calculations with the tilted axis cranking model and the quasiparticle rotor model.

Triaxial rotor in the SU(3) limit of the interacting boson model

A mapping from a triaxial rotor Hamiltonian to that of the SU(3) limit description in the interacting boson model (IBM) is established, which is achieved by the SU(3) realization of the triaxial rotor. A detailed comparison between the triaxial dynamics generated from the quadrupole-deformed rotor and those from the IBM image is made. The results indicate that the mapping can be well realized. A preliminary test for $^{128}\mathrm{Ba}$ further confirms the finite-$N$ effect of the mapping. It thus provides an alternative way to understand the triaxiality in the finite-$N$ system and additional insight into understanding the SU(3) IBM theory from microscopic point of view via the SU(3) shell model.

Different collectivity in the two signatures of the i13/2 stemming band in 167Yb

Six lifetimes have been determined in the 5/2+ [642] band from vi13/2 parentage in 167Yb by means of Recoil distance Doppler-shift (RDDS) measurements carried out at the Cologne FN tandem. The deduced transition strengths and the level scheme are reasonably described by Particle plus triaxial rotor model (PTRM) calculations except for the behavior of the quadrupole collectivity in the two signatures of the 5/2+[642] band. In that band, the quadrupole collectivity of the favored signature is appreciably larger than this of the unfavored signature. The effect increases with increasing the spin. Naturally, the rigid PTRM cannot explain these features, but the structure of its wave functions suggests a possible solution. It is associated with the enhanced contribution of low-Ω orbitals from vi13/2 parentage in the favored signature compared to the unfavored one. This could selectively increase the deformation of the favored signature band members and give rise to a dynamic shape coexistence taking place between the two signatures which needs quantitative explanation by future theoretical work.

Candidates for Twin Chiral Bands inRh102

Excited states in 102Rh, populated in the fusion-evaporation reaction Zr94(11B,3n)102Rh at a beam energy of 36 MeV, were studied using the Indian National Gamma Array spectrometer at Inter University Accelerator Center, New Delhi. The angular correlations and the electromagnetic character of some of the gamma-ray transitions observed were investigated in detail. A new chiral candidate sister band was found. Lifetimes of exited states in both chiral candidate bands of 102Rh were measured for the first time in the A∼100 mass region by means of the Doppler-shift attenuation technique. The derived reduced transition probabilities are compared to the predictions of the two quasiparticles plus triaxial rotor model. Both experimental results and calculations do not support the presence of static chirality in 102Rh.

Transverse wobbling: A collective mode in odd-Atriaxial nuclei

The wobbling motion of a triaxial rotor coupled to a high-j quasiparticle is treated semiclassi- cally. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively, whether the quasiparticle angular momentum is oriented parallel or perpendicular to the rotor axis with the largest moment of inertia. Simple analytical expressions for the wobbling frequency and the electromagnetic E2 and M1 transition probabilities are derived assuming rigid alignment of the quasiparticle with one of the rotor axes and harmonic oscillations (HFA). Transverse wobbling is characterized by a decrease of the wobbling frequency with increasing angular momentum. Two examples for transverse wobbling, 163Lu and 135Pr, are studied in the framework of the full triax- ial particle-rotor model and the HFA. The signature of transverse wobbling, decreasing wobbling frequency and enhanced E2 inter-band transitions, is found in agreement with experiment.

Low-lying bands with different quadrupole deformation in155Dy

To investigate the interplay between collective and single particle degrees of freedom in odd nuclei, Recoil distance Doppler-shift and Doppler-shift attenuation lifetime measurements were carried out for levels in 155Dy in coincidence detection of gamma-rays. 26 lifetimes were determined using the Differential decay curve method. Particle plus triaxial rotor model (PTRM) calculations were performed to compare the experimental level scheme and transition strengths with theoretical ones in order to get information on the quadrupole deformation (є,γ) of the bands. As a result, different quadrupole deformations for the one-quasineutron bands at low and medium spins are deduced.

Angular correlation between proton and neutron rotors

A brief review is given on the controversy and its solution about the fact that the angular momentum vector of protons and that of neutrons in well-deformed nuclei at low total angular momenta have a strong correlation that they are oriented in opposite directions. In a simple two-rotor model in 2-dimensional space, this fact is explained as originating from the quantum mechanical uncertainty relation between the angle and the angular momentum for the relative rotation of the two rotors. As the second topic, a more realistic model consisting of two triaxial rotors in 3-dimensional space coupled with a QQ interaction is employed to investigate a possible shears-band-like collective rotation predicted by T. Otsuka, in which the angle at which the angular momentum of protons and that of neutrons intersect changes continuously from 180° at spin zero toward 0° at high spins within the same rotational band. The probability distributions of the angle between the two angular momenta and the angle between the longest principal axes of two rotors are calculated to examine the participation of the scissors mode in the evolution of the ground rotational band versus spin.

Plunger lifetimes and electromagnetic transition strengths in odd 167Yb

Abstract Nine lifetimes have been determined for the first time in the 5 / 2 − [ 523 ] and 5 / 2 + [ 642 ] bands of 167Yb by means of Recoil distance Doppler-shift measurements carried out at the Cologne FN tandem. For the data analysis, a dedicated version of the Differential decay curve method was used. The newly deduced transition strengths and the level scheme are reasonably described by the Particle plus triaxial rotor model (PTRM) calculations except for the behavior of the quadrupole collectivity in the two signatures of the 5 / 2 + [ 642 ] band. The stretched B(E2)ʼs in the favored signature are appreciably larger than those in the unfavored signature. The effect increases with spin. In the PTRM calculations, the wave functions of the favored signature levels contain larger contribution of low-Ω orbitals from ν i 13 / 2 parentage than those of the unfavored levels. This could selectively increase the deformation of the favored signature band members. If so, rotation and Coriolis interaction would give rise to a dynamic shape coexistence taking place between the two signatures.

Triaxial rotor model for the study of the nuclear structure and transition between different symmetries in nuclei for A = 120-200 mass region

The rigid triaxial rotor model used to search the dependence of ROT(E)/ 1 (2 ) E + and SF(E)/ 1 (2 ) E + on the mixing effect of asymmetric parameter (γ) and mixing angle (τ). The dependence of γ and deformation parameter (β) on the energy ratio (R4/2) is discussed. It can be found that the calculated energy, B(E2) values have reasonable agreement with the experimental energy, B(E2) values and B(E2) ratios.

Collective and noncollective states in116Sb

Excited states of ${}^{116}$Sb were investigated using in-beam $\ensuremath{\gamma}$-ray spectroscopy techniques with the ${}^{114}$Cd(${}^{7}$Li, $5n$) reaction. About 25 new states and 35 new transitions were added into the level scheme of ${}^{116}$Sb. The previously known two rotational bands based on the $\ensuremath{\pi}{g}_{9/2}^{}{}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{h}_{11/2}$ and $\ensuremath{\pi}{g}_{9/2}^{}{}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}{d}_{5/2}$ configurations have been extended up to (16)${}^{\ensuremath{-}}$ and (13)${}^{+}$ states, respectively. A new $\ensuremath{\Delta}I=1$ band was identified, and interpreted in terms of the triaxial particle rotor model calculations.

Description of the candidate chiral doublet bands in 98Tc

The candidate chiral doublet bands in 98Tc with configuration πg9/2 ⊗ νh11/2 are studied theoretically for the first time via the triaxial particle rotor model. The main properties of the doublet bands including the energy spectra and electromagnetic transitions are calculated for different triaxiality parameter γ, and the data in 98Tc can be well described by the calculations with γ = 38°. Based on the analysis of angular momentum components, it is found that the chiral rotational geometry in 98Tc deviates from the ideal chiral picture.

The relationship between the interacting boson model and the algebraic version of Bohrʼs collective model in its triaxial limit

Abstract Recent developments and applications of an algebraic version of Bohrʼs collective model, known as the algebraic collective model (ACM), have shown that fully converged calculations can be performed for a large range of Hamiltonians. Examining the algebraic structure underlying the Bohr model (BM) has also clarified its relationship with the interacting boson model (IBM), with which it has related solvable limits and corresponding dynamical symmetries. In particular, the algebraic structure of the IBM is obtained as a compactification of the BM and conversely the BM is regained in various contraction limits of the IBM. In a previous paper, corresponding contractions were identified and confirmed numerically for axially-symmetric states of relatively small deformation. In this paper, we extend the comparisons to realistic deformations and compare results of the two models in the rotor–vibrator limit. These models describe rotations and vibrations about an axially symmetric prolate or oblate rotor, and rotations and vibrations of a triaxial rotor. It is determined that most of the standard results of the BM can be obtained as contraction limits of the IBM in its U ( 5 ) – SO ( 6 ) dynamical symmetries.

Bohr Hamiltonian with a finite well for triaxial nuclei

The effect of the potential well size on the spectra and B(E2) transition rates of the Z(5) solution of the Bohr Hamiltonian, corresponding to triaxial shapes, has been studied. Convergence to the Z(5) solution is obtained for large well sizes. The results are compared to the infinite well, the harmonic oscillator and the rigid triaxial rotor results. The relevance of this solution to the prolate to oblate shape/phase transition in neutron-rich nuclei in the W–Os–Pt region is discussed.

The Influence of Triaxiality Parameter γ on the Chiral Doublet Bands with (πg9/2)−1 (νh11/2)2 Configuration

The chiral doublet bands with three-quasiparticle configuration (πg9/2)−1 (νh11/2)2 are studied by the fully quantal triaxial particle rotor model. The energy spectra and B(M1)/B(E2) ratios of the doublet bands with different triaxiality parameter γ are systematically analyzed. It is found that γ is a sensitive parameter for the properties of these doublet bands.