Superdeformed Research Articles

Systematic study of the superdeformed bands in the framework of the asymmetric rotor model in A≈ 130–150 mass region

The superdeformed (SD) nuclei in the [Formula: see text]–150 mass region are examined for the first time within the Asymmetric Rotor Model (ARM) context. The asymmetry parameter [Formula: see text] is obtained by using the ARM expressions for the energy levels of nonaxially deformed nuclei (triaxial nuclei). The variation of kinematic moment of inertia [Formula: see text] and dynamic moment of inertia [Formula: see text] with [Formula: see text] is examined. Both appear to decline as [Formula: see text] increases. In addition, the variation of [Formula: see text] and the [Formula: see text] product with [Formula: see text] are also examined.

Nuclear softness in the variable moment of inertia model and its application to superdeformed bands in the mass region A ≈ 60 - 90

For superdeformed (SD) bands 58Ni (b1), 58Cu, 59Cu (b1), 61Zn, 62Zn, 65Zn, 68Zn, 84Zr, 86Zr (b1), 88Mo (b1, b2, b3) and 89Tc in the A ≈ 60 - 90 mass region, the nuclear softness (NS) parameter, σ, has been calculated using the VMINS3 model. The SD bands 58Ni (b1), 58Cu, 59Cu (b1), 62Zn, 65Zn, and 88Mo (b2, b3) have NS parameter values that are greater than those of the normal deformed bands, indicating smaller rigidity. The fluctuation of the NS parameter versus the gamma energy ratio, R, of SD bands in the A ≈ 60 - 90 mass region is one of the study's findings. The ratio of transition energies was used to calculate the band head spin, I0, by the Descartes method (the greatest technique to solve the quartic equation based on an auxiliary cubic equation) which was then confirmed by root mean square deviations. The estimated and observed transition energies are in good agreement.

Defect and doping properties of sliding ferroelectric γ-InSe for photovoltaic applications

Layered van der Waals (vdw) materials have been proposed as light-absorbing materials for photovoltaic applications. InSe is a layered vdw semiconductor with ultra-high carrier mobility, strong charge transfer ability, super deformability, thermoelectricity, and optoelectronic properties. Its γ phase, or γ-InSe, was greatly stabilized by doping recently, which also exhibits sliding ferroelectricity. In this study, we propose that γ-phase InSe (γ-InSe), which was recently synthesized in a high-quality bulk phase, could be an excellent light-absorbing material candidate. Based on the first-principles simulations, bulk γ-InSe is found to possess suitable bandgap, decent absorption, and low effective mass. The investigation of defect properties reveals the major defect types, defect levels, and deep-level defects that could possibly harm the efficiency, and the deep-level defects can be significantly suppressed under Se-rich conditions. In addition, γ-InSe is intrinsically n-type, which can be tuned into weak p-type by Zn and Cd doping. We also identify the defect types of Y and Bi doping, which have been experimentally used to adjust the mechanical property of γ-InSe, and find that Y interstices could play an important role in improving the stiffness of γ-InSe. Our study provides theoretical insights for photovoltaic and other photoelectronic applications based on this interesting ferroelectric layered vdw material.

Search for Super-Deformed Identical Bands in the A = 190 Mass Region on the Basis of Level Spin

The systematic study of Super-Deformed (SD) bands in the A=190 mass region has been performed. We observed a large number of pairs of SD bands, with different mass numbers, having transition energies nearly equal (within 3 keV) and having identical dynamic moments of inertia. The bands having nearly equal transitions energies and other parameters are called identical bands. We have performed detailed analysis and found 16 pairs of Super-Deformed Identical Bands (SDIBs) whose Eγ energies and moment of inertia are in good agreement with each other. The modified Variable Moment of Inertia (VMI) model is applied to 16 pairs of SDIBs to estimate the band spins by fitting the two parameters J0 and C. We found that out of 16 pairs, the band-head spin is consistent with moment of inertia and transition energies for four pairs. For another seven pairs, the transition energies and moment of inertia are identical, but originate from levels with different spins. The remaining five pairs have the identical energy but spins are either increasing or decreasing by one unit in the pair. Secondly, the NpNn scheme is applied to verify the existence of SDIBs. The parameters deduced from the NpNn scheme are also in good agreement for the mentioned case. The study indicates that each pair of conjugate nuclei have nearly identical spin, moment of inertia (dynamic) and gamma transition energy.

Analysis of super-deformed bands in A∼150 mass region: The principal-axis cranking versus the variable moment of inertia

A systematic study of the super-deformed (SD) bands in [Formula: see text] mass region is carried out by using two different approaches, namely, the Principal-axis Cranking (PAC) and the Variable Moment of Inertia (VMI). Both these approaches not only support each other’s results but also their hand-in-hand calculations help us in establishing the prominent features, like the band-head spin, parity, quadrupole moment and excitation energy, of the observed SD bands. Since the rotational frequency in the PAC model depends on angular momentum, parity, and quadrupole moment, by identifying the most common rotational frequency between the calculations and the experimentally observed ones, the band-head spin, and parity are likely to be extracted. On the other hand, the VMI model calculations are quite simple and are capable of predicting the threshold limits of band-head spin, the quadrupole moment, and the excitation energy, which in turn are significantly useful for deciding an appropriate configuration assignment in the PAC model calculations of the existing as well as upcoming SD bands. Further, the VMI model calculations involve the variation of the moment of inertia with angular momentum, which in turn is quite helpful in understanding the mechanism of the observed identical SD bands between a pair of neighboring nuclei.

The description of nuclear superdeformed rotational bands in A∼190 region with pq formula

The nuclear superdeformed (SD) rotational bands in [Formula: see text] mass region were systematically analyzed with the two-parameter [Formula: see text] formula. The study of the observed transition energies by using the best-fitting method shows that the [Formula: see text] formula can provide excellent descriptions of the SD bands. The analysis of two types of moments of inertia ([Formula: see text] and [Formula: see text]) and bandhead moment of inertia ([Formula: see text]) also demonstrates the reliability of the [Formula: see text] formula in describing the SD bands. Finally, by using the [Formula: see text] formula, the unobserved transition energies for the lower and higher spin regions were predicted herein.

Representations of super deformation of Heisenberg-Virasoro type Lie conformal algebras

We introduce a class of Lie conformal superalgebra S(a, b), where a, b are complex parameters. These Lie conformal superalgebras can be viewed as the super deformation of Heisenberg-Virasoro type Lie conformal algebras. We classify the free conformal modules of rank over S(a, b) for all . Using a Cheng-Kac’s lemma, we also classify the finite irreducible conformal modules over S(a, b).

Beyond-mean-field study of Ar based on the Skyrme-Hartree-Fock model * *Supported by the National NaturalScience Foundation of China (11905165, 11775081,12175071, 11547044), the 111 Project (B17035), andthe Fundamental Research Funds for the Central Universities(JB160510, XJS18020).

We present the hypernuclear states of Ar obtained using the Skyrme-Hartree-Fock (SHF) model and a beyond-mean-field approach, including angular momentum projection (AMP) and the generator coordinate method (GCM). A comprehensive energy spectrum is given, which includes normally deformed (ND) and super deformed (SD) hypernuclear states with positive or negative parities. Energy levels corresponding to the configurations in which a hyperon occupies the s-, p-, or sd-shell orbitals are discussed. For the s-shell , we pay special attention to the ND and SD states corresponding to the configurations Ar s and Ar s , where Ar and Ar denote the ND and SD nuclear cores, respectively. The disagreements between different models over the separation energy of the SD state in previous studies are revisited. For the p-shell , four rotational bands are predicted, and the impurity effects are shown. Furthermore, two energy levels corresponding to the configurations Ar [101] and Ar [101] are obtained below the separation threshold of Ar+ within 0.5 MeV. For the sd-shell , three bound states are found near the separation threshold, and the mechanism behind these states are discussed.

Super- and hyperdeformation inZn60, Zn62, andGe64at high spins

Background: The observation of the superdeformed (SD) bands in $^{60,62}\mathrm{Zn}$ indicates that the particle number 30 is a magic particle number, where two- and four-neutron single particles are considered to be promoted to the intruder $1{g}_{9/2}$ shell. However, the SD-yrast band in $^{62}\mathrm{Zn}$ is assigned negative parity.Purpose: I investigate various SD configurations in the rapidly rotating $^{60,62}\mathrm{Zn}$ and $^{64}\mathrm{Ge}$, and attempt elucidating the different roles of the energy gaps at particle numbers 30 and 32.Method: I employ a nuclear energy-density functional method: the configuration-constrained cranked Skyrme-Kohn-Sham approach is used to describe the rotational bands near the yrast line.Results: The negative-parity SD bands appear higher in energy than the positive-parity SD-yrast band in $^{60}\mathrm{Zn}$ by about 4 MeV, which is indicative of the SD doubly magic nucleus. However, the energy gap in $^{64}\mathrm{Ge}$ is smaller $\ensuremath{\approx}2--3$ MeV, though the quadrupole deformation of the SD states in $^{64}\mathrm{Ge}$ is greater than that of $^{60}\mathrm{Zn}$. The present calculation predicts the occurrence of the hyperdeformed state in $^{60}\mathrm{Zn}$ and $^{64}\mathrm{Ge}$ at a high rotational frequency $\ensuremath{\approx}2.0\phantom{\rule{4pt}{0ex}}\mathrm{MeV}/\ensuremath{\hbar}$ due to the occupation of the ${h}_{11/2}$ shell.Conclusions: An SD-shell gap at particle number 30 and 32 appears at different deformations and the energy gap at particle number 32 is low, which make the SD structures of $^{62}\mathrm{Zn}$ unique, where the negative-parity SD states appear lower in energy than the positive-parity one.

The Behavior of Moments of Inertia and Energy Staggering in Superdeformed Nuclei.

Three pairs of signature partners' transition energies of Thallium (Tl) odd mass superdeformed (SD) nuclei's (A ~ 191-195), were fitted with the experimental one using the Bohr-Mottelson four-parameter collective rotational model. We chose the Bohr-Mottelson four-parameter rotational energy formula because it has been reported that it has excellent compatibility with the γ-ray transition energies. The four model parameters were extracted using a suitable search program. Harris's method was used to calculate the superdeformed rotational bands' (SDRBs) bandhead spins. The values of the adopted parameters, which were obtained using a simulated fitting search software, were used to measure the rotational frequency, dynamic J(2), and kinematic J(1) moments of inertia to the transition energies. When compared to the experimental values, there is a great deal of agreement J(2) and J(1) have been studied as a function of increasing rotational frequency. The suggested staggering function was used to investigate the ΔI= 1 energy staggering in Tl odd mass SD nuclei.

Gross features of the spectrum of the 36Ar nucleus

Samples of the spectrum of the [Formula: see text]Ar nucleus are known in different energy windows. In addition to the ground-state (GS) region, the superdeformed (SD) state is observed, too, and there is a good candidate for the hyperdeformed (HD) one, as well. They are populated in different reactions. We intend to describe the gross features of the spectra of different energies, deformations and reactions in a unified way. We apply the multiconfigurational dynamical symmetry (MUSY). The SU(3) quantum numbers of the shape isomers from previous studies pave the way for this description. The MUSY reproduces the gross features of the spectra to a reasonable approximation. The energy spectrum of the three valleys (GS, SD, HD) indicates that the multiconfigurational symmetry is valid to a good approximation, and different cluster configurations coexist in the shape isomers.

Properties of superdeformed bands in A < 100 mass region within the variable moment of inertia model

The variable moment of inertia (VMI) model has been used to study the properties of superdeformed (SD) bands in A < 100 mass region. The experimental γ-ray (E γ ) transitions energies are least square fitted to obtain the model parameters such as band head moment of inertia, (J 0), and stiffness constant, (C). The observed E γ transition energies obtained using the VMI formula are in excellent agreement with the experimental values. In the paper, we have studied the dynamic moment of inertia (J (2)) and its variation with rotational frequency (ℏ ω). We also studied the ΔI = 2 staggering phenomena in SD bands of 61Zn(SD), 62Zn(SD1), 80Sr(SD1), 81Sr(SD1), 82Sr(SD), 83Sr(SD), 84Zr(SD), 86Zr(SD1), 86Zr(SD4), 87Nb(SD2), 89Tc(SD) and 91Tc(SD) nuclei. The VMI model brings very comprehensive interpretation for spin assignment and to study the properties of SD bands in light mass region nuclei.

Super deformability and thermoelectricity of bulk γ-InSe single crystals* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11674040, 11604032, 51472036, 51672270, and 11904039), the Fundamental Research Funds for the Central Universities, China (Grant No. 106112016CDJZR308808), and Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDB-SSW-SLH016).

Indium selenide, a III–V group semiconductor with layered structure, attracts intense attention in various photoelectric applications, due to its outstanding properties. Here, we report super deformability and thermoelectricity of γ-InSe single crystals grown by modified Bridgeman method. The crystal structure of InSe is studied systematically by transmission electron microscopy methods combined with x-ray diffraction and Raman spectroscopy. The predominate phase of γ-InSe with dense stacking faults and local multiphases is directly demonstrated at atomic scale. The bulk γ-InSe crystals demonstrate surprisingly high intrinsic super deformative ability which is highly pliable with bending strains exceeding 12.5% and 264% extension by rolling. At the meantime, InSe also possesses graphite-like features which is printable, writable, and erasable. Finally, the thermoelectric properties of γ-InSe bulk single crystals are preliminary studied and thermal conductivity can be further reduced via bending-induced defects. These findings will enrich the knowledge of structural and mechanical properties’ flexibility of InSe and shed lights on the intrinsic and unique mechanical properties of InSe polytypes.

A novel magneto-mechanical metamaterial cell structure with large, reversible and rapid two-way shape alteration

Smart mechanical metamaterials based on various types of stimuli-sensitive materials break through the limitations of traditional metamaterials and exhibit many attractive properties. The development of multi-functional mechanical metamaterials capable of multi-mode, reversible, large deformations and remote controllability remains a challenge. In this work, we designed and prepared several magneto-mechanical metamaterial unit cells based on magnetoactive soft materials using 3D printing technology. A novel cell structure of cuboctahedron was fabricated and examined deeply which was elongated or contracted along the central magnetic field direction under different external magnetic fields. Experiment and simulation results shown that the special metamaterial structure design enables the magneto-active unit cells to achieve super deformation characteristics that it does not originally possess. The rapid two-way large deformation of the cuboctahedron cell was achieved with a quite remarkable deformation up to 85%, and it could quickly return to the original shape of the cell when the magnetic field was removed. Besides of these capabilities, as an application example, we further demonstrated the multi-modal shape of shrinkage and elongation of the cell structure in a biomimetic blood vessel, to show the effectiveness of the prototype smart stent for particle transport in a remotely controllable manner. The developed magneto-mechanical metamaterial certainly can be extended to various functionalized application, such as soft robots, healthcare and flexible electronics.

Description of Superdeformed Bands of the Isotones $$\boldsymbol{N=113}$$ for Nuclear Mass Region $$\boldsymbol{A\sim 190}$$

Electric quadrupole $$\gamma$$ -ray transition energies $$E_{\gamma}$$ , rotational frequencies $$\hbar\omega$$ and dynamic $$J^{(2)}$$ and kinematic $$J^{(1)}$$ moments of inertia have been calculated for yrast and excited superdeformed (SD) bands in Hg, Tl, Pb isotonic ( $$N=113$$ ) nuclei by using two-parameter power-law formula. The model parameters and the bandhead spins were determined using a $$\chi^{2}$$ fit by random minimization via Monte Carlo simulation technique with a uniform distribution of random numbers. The calculated results of $$E_{\gamma}$$ agreed with the experimental data published in National Nuclear Data Center (nndc) very well, and present assigned spins of the studied superdeformed rotational bands (SDRB’s) are consistent with the spins suggested by other previous formulae. The majority of the studied SD bands displayed the same large, smooth increase in $$J^{(2)}$$ by increasing $$\hbar\omega$$ . A saturation of $$J^{(2)}$$ at higher values of $$\hbar\omega$$ was observed for the two bands (1, 2) in $${}^{195}$$ Pb due to the Pauli blocking of the quasineutron alignment in the presence of quasiproton alignment. The studied SD bands exhibited staggering in their transition energies. Five pairs of signature partner SDRBs exhibited an $$\Delta I=1$$ staggering effect in their transition energies, namely $${}^{193}$$ Hg (SD1, SD2), $${}^{193}$$ Hg (SD3, SD4), $${}^{194}$$ Tl (SD1, SD2), $${}^{195}$$ Pb (SD1, SD2), and $${}^{195}$$ Pb (SD3, SD4). To investigate this $$\Delta I=1$$ staggering, we extracted the difference between the average transition $$I+2\to I$$ and $$I\to I-2$$ energies in one band and the transition $$I+1\to I-1$$ energies in the signature partner. Also, a $$\Delta I=2$$ staggering exists in three SD bands of odd–odd $${}^{194}$$ Tl. This $$\Delta I=2$$ staggering effect was determined by calculating the energy difference between two consecutive $$\gamma$$ -ray transitions as a function of rotational frequency after subtracting a smooth reference expressed in the notation of Cederwall.

Communication—Controllable Deformation of Composite Graphite Electrodes during Electrochemical Process

A large and controllable deformation of a cantilever consisting of a MCMB (MesoCarbon MicroBeads) graphite layer on a Cu foil is reported. In the charging process, the insertion of lithium ions causes the expansion of the MCMB layer and generates stress due to the deformation mismatch between the MCMB layer and Cu foil. By controlling the amount of Li ions and thickness ratio, the initially flat MCMB graphite/Cu electrode can bend into circular shape reversibly. A theoretical mechanical model is proposed to analyze the bending deformation. This super deformation driven by electrochemical reactions may be used for real-time control devices.

Plasmon-based optical sensors for high-sensitivity surface deformation detection of silver and gold

Surface deformation is a common phenomenon in many situations, and can be caused by stress, temperature variation, environmental variation, etc. With the developing of nanotechnology, biological and chemical properties of nano materials are generally in association with its surface condition. High-sensitivity methods of sensing super tiny surface deformations become necessary. In this work, a high sensitive surface deformation sensor is proposed by one-dimensional photonic crystal. Results show that Tamm plasmon polaritons are generated in this configuration and the reflection spectrum is dramatically influenced by the surface deformation of the silver and gold films. The variation rate of reflection light intensity reaches 20% when the surface deformation of is 1 nm. And the variation rate reaches 13% per nanometer for gold surfaces. Since the detecting precision of light intensity is greatly high, the theoretical precision of this device can reach picometer magnitude. Meanwhile, this configuration also can realize mapping surface deformation distribution through scanning method. The simulation results reveal the proposed configuration can distinguish 1 nm surface deformation of silver surfaces.

Signature-dependent triaxiality for shape evolution from superdeformation in rapidly rotating 40Ca and 41Ca

Abstract We investigate the possible occurrence of highly elongated shapes near the yrast line in $^{40}$Ca and $^{41}$Ca at high spins on the basis of the nuclear energy-density functional method. Both the superdeformed (SD) yrast configuration and the yrare configurations on top of the SD band are described by solving the cranked Skyme–Kohn–Sham equation in the three-dimensional coordinate space representation. It is suggested that some of the excited SD bands undergo band crossings and develop to hyperdeformation (HD) beyond $J \simeq 25 \hbar$ in $^{40}$Ca. We find that the change of triaxiality in response to rotation plays a decisive role in the shape evolution towards HD, and that this is governed by the signature quantum number of the last occupied orbital at low spins. This mechanism can be verified in an experimental observation of the positive-parity SD yrast signature-partner bands in $^{41}$Ca, one of which ($\alpha=+1/2$) undergoes crossings with the HD band, while the other ($\alpha=-1/2$) shows smooth evolution from collective rotation at low spins to non-collective rotation with an oblate shape at termination.

Moments of Inertia of SDIBs in A = 190 Mass Region using VMI Model

A lot of identical bands are known at present in the Normal Deformed (ND) region. In our study of the occurrence and properties of identical bands in Super-Deformed (SD) nuclei we first applied the modified Variable Moment of Inertia (VMI) model to extract the band-head spin of Super-Deformed bands. The calculated transition energies, level spins and dynamic moment of inertia are systematically examined. Then, in the framework of theoretical model several identical bands are identified. The kinematic and dynamic moment of inertia have been calculated for the six pairs of Super-Deformed Identical Bands (SDIBs) which was not reported earlier in the literature. Thus, the results are significant. In all the cases J(2) is significantly higher than J(1) over a large range of frequency.

On the question of spin assignment and quantized alignment in the A~ 100-140 superdeformed mass region

The structure of the superdeformed (SD) mass region, A~ 100-140 is re-studied by using a direct approach based on the rotational energy formula E (I, K). To determine the lowest spin (If) and the K-value of the considered SD bands; namely, 104Pd(b1), 132Ce(b1), 134Nd(b1), 136Nd(b2), 142Sm(b1), 148Eu(b1, b2), 131Ce(b1, b2), 133Ce(b1, b2), 133Pr(b1, b3), 137Sm(b1) and 143Eu(b1), we study the dependence of the dynamic, (2) and static, (1) , moments of inertia on the rotational frequency (ℏω). Using a search method, the higher order inertial parameters A and B of such method were determined by fitting the proposed transition energies with their observed ones. The calculated transition energies are strongly dependent on the identified spins. It was found that, when an accurate bandhead spin (I0) is assigned, a good agreement is achieved between the calculated and observed transition energies. The results for the spin are in satisfactory agreement with other theoretical results and available experimental data. A good agreement between the calculated and corresponding experimental transition energies of the SD bands is obtained which supports our methodology. The incremental alignment and also the angular momentum alignment, for the identical SD bands exist among the considered ones, have been studied and the results verified well Stephens’s law of alignment.