Pairing Vibrations Research Articles

Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals. II. Low-energy excitation spectra of triaxial nuclei

Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals. II. Low-energy excitation spectra of triaxial nuclei

A creative wide-frequency and large-amplitude vibration isolator design method based on magnetic negative stiffness and displacement amplification mechanism

Negative stiffness vibration isolation devices have attracted significant attention and research interest for their ability to enhance the low-frequency vibration isolation performance of passive vibration isolators. However, their narrow linear negative stiffness region has hindered their broader application. To address this limitation, a novel design method for vibration isolators is proposed, integrating the permanent magnetic negative stiffness device (NSD) with the displacement amplification mechanism (DAM). The paper begins by presenting a specific vibration isolator design method and analyzing the kinematic relationship. Next, a single-degree-of-freedom (SDOF) nonlinear equivalent model of the vibration isolator is established using the pseudo-rigid-body model (PRBM) approach. Numerical simulations are then conducted to obtain the transmissibility of the isolator. Furthermore, two isolators—one with the displacement amplification effect and another without—are manufactured, and experimental investigations are carried out. The experimental results confirm that the incorporation of the displacement amplification mechanism effectively expands the linear negative stiffness region of the negative stiffness magnet pair, enabling wide-frequency and large-amplitude vibration isolation. Notably, these experimental findings align well with the simulation results. In summary, this paper proposes a creative design method for wide frequency and large amplitude vibration isolators, and proves it through theoretical analysis and experimental validation.

Design and simulation of gear transmission system based on metamaterial

In this research, we integrate a three-dimensional micro-/nano-lattice structure metamaterial with conventional helical gears using a composite method to reduce the vibration. A comprehensive six-degree-of-freedom nonlinear dynamics model is constructed to analyze the vibration characteristics of the resulting mechanical metamaterial gear pair. The model incorporates crucial factors such as meshing damping, error excitation, bearing support stiffness, and time-varying meshing stiffness using the dynamic–static method. The results demonstrate the good damping effect of the designed mechanical metamaterial on gear pair vibrations. This research provides theoretical insights for reducing vibrations in gear transmission systems by using mechanical metamaterial.

Higgs response and pair condensation energy in superfluid nuclei

Abstract The pairing correlation in nuclei causes a characteristic excitation, known as the pair vibration, which is populated by the pair transfer reactions. Here we introduce a new method of characterizing the pair vibration by employing an analogy to the Higgs mode, which emerges in infinite superconducting/superfluid systems as a collective vibrational mode associated with the amplitude oscillation of the Cooper pair condensate. The idea is formulated by defining a pair-transfer probe, the Higgs operator, and then describing the linear response and the strength function to this probe. We will show that the pair condensation energy in nuclei can be extracted with use of the strength sum and the static polarizability of the Higgs response. In order to demonstrate and validate the method, we perform numerical analysis for Sn isotopes based on the quasi-particle random phase approximation to the Skyrme–Hartree–Fock–Bogoliubov model. We discuss the possibility of applying this new scheme to pair-transfer experiments.

Excited states of zero seniority based on a pair condensate

We study the excited states of zero seniority for various like-particle systems interacting by pairing forces and by general two-body interactions. We consider two types of excitations, generated from a ground state described by a pair condensate. One type is obtained by breaking a pair from the ground state condensate and replacing it by "excited" collective pairs built on time-reversed single-particle orbits. The second type of zero seniority excited states is described by a condensate of identical excited pairs. The structure of these excited states is analysed for the picked fence model and for the valence neutrons of $^{108}$Sn. For a state-depending pairing interaction, the first type of excited states agree well with the J=0 states which are known in $^{108}$Sn. At the same time, these states can be also associated unambiguously with those exact states which are the closest in energy to the experimental levels. The states corresponding to the excited pair condensate appear at low energies, around the energy of the second excited state of the first type, and they do not have a simple correspondence with exact eigenstates. However, at a much higher excitation energy there is an exact state which is similar in structure to an EPC state. It is shown that this EPC state has the features of a giant pairing vibration.

Збудження парних коливань у надплинних ядрах

Excitation of monopole pairing vibrations in superfluid nuclei in the two-neutron transfer reaction is studied within a kinetic model based on the semiclassical time-dependent Hartree - Fock - Bogolyubov theory. Using the anomalous (correlated) density response function, the monopole pairing mode and the amplitude of the dynamic variation of the pairing gap associated with this mode are obtained. It is shown that the pairing correlations give a coherent contribution to the spectroscopic factor for the excitation of monopole pairing vibrations in the two-neutron transfer reaction in superfluid nuclei. The contribution is determined by the distribution of neutron levels near the Fermi energy and does not exceed a few percent of the spectroscopic factor for the transfer of two neutrons to the ground state. This estimate is in agreement with experimental data for the ratio of the cross-section for excitation of the 0+-state in the (p, t)-reaction in the energy region of the monopole pairing mode, which is equal to the double pairing gap, to the cross section for excitation of the ground state in superfluid nuclei.

Study of gear pair vibration caused by random manufacturing errors

Study of gear pair vibration caused by random manufacturing errors

Stochastic model of the gearbox pair vibration

The model of vibration signal of gearbox pair in the form of periodically correlated non-stationary random process is considered. It is shown that hidden periodicities in biperiodic correlated random process mean and covariance function, characterizing the vibrations of gearbox pair can be detected using the component and least square methods. Seven particular cases of the bi-rhythmic hidden periodicity for different modulation modes are analyzed.

Methods of Hidden Periodicity Discovering for Gearbox Fault Detection.

It is shown that the models of gear pair vibration, proposed in literature, are particular cases of the bi-periodically correlated random processes (BPCRPs), which describe its stochastic recurrence with two periods. The possibility of vibration and analysis within the framework of BPCRP approximation, in the form of periodically correlated random processes (PCRPs), is grounded and the implementation of vibration processing procedures using PCRP techniques, which are worked out by the authors, is given. Searching for hidden periodicities of the first and the second orders was considered as the main issue of this approach. The estimation of the non-stationary period (basic frequency) allowed us to carry out a detailed analysis of the deterministic part, the covariance structure of the stochastic part, and to form, using their parameters, the sensitive indicators for fault detection. The results of the processing of the wind turbine gearbox vibration signals are presented. The amplitude spectra of the deterministic oscillations and the time changes of the stochastic part power for different fault stages are analyzed. The most efficient indicators, which are formed using the amplitude spectra for practical applications, are proposed. The presented approach was compared with known in literature cyclostationary analysis and envelope techniques, and its advantages are shown.

Interplay between pairing and triaxial shape degrees of freedom in Os and Pt nuclei

The effect of coupling between pairing and quadrupole triaxial shape vibrations on the low-energy collective states of $\gamma$-soft nuclei is investigated using a model based on the framework of nuclear energy density functionals (EDFs). Employing a constrained self-consistent mean-field (SCMF) method that uses universal EDFs and pairing interactions, potential energy surfaces of characteristic $\gamma$-soft Os and Pt nuclei with $A\approx190$ are calculated as functions of the pairing and triaxial quadrupole deformations. Collective spectroscopic properties are computed using a number-nonconserving interacting boson model (IBM) Hamiltonian, with parameters determined by mapping the SCMF energy surface onto the expectation value of the Hamiltonian in the boson condensate state. It is shown that, by simultaneously considering both the shape and pairing collective degrees of freedom, the EDF-based IBM successfully reproduces data on collective structures based on low-energy $0^{+}$ states, as well as $\gamma$-vibrational bands.

Coupling of pairing and triaxial shape vibrations in collective states of γ -soft nuclei

In addition to shape oscillations, low-energy excitation spectra of deformed nuclei are also influenced by pairing vibrations. The simultaneous description of these collective modes and their coupling has been a long-standing problem in nuclear structure theory. Here we address the problem in terms of self-consistent mean-field calculations of collective deformation energy surfaces, and the framework of the interacting boson approximation. In addition to quadrupole shape vibrations and rotations, the explicit coupling to pairing vibrations is taken into account by a boson-number non-conserving Hamiltonian, specified by a choice of a universal density functional and pairing interaction. An illustrative calculation for $^{128}$Xe and $^{130}$Xe shows the importance of dynamical pairing degrees of freedom, especially for structures built on low-energy $0^+$ excited states, in $\gamma$-soft and triaxial nuclei.

Confirmation of Giant Pairing Vibration evidence in $$^{\mathrm {12,13}}$$C($$^{\mathrm {18}}$$O,$$^{\mathrm {16}}$$O)$$^{\mathrm {14,15}}$$C reactions at 275 MeV

The Giant Pairing Vibration (GPV) is a correlated two-nucleon excitation mode in atomic nuclei predicted long time ago. It is expected to be excited in two-nucleon transfer reactions, similarly to the pairing vibrations feeding the ground states of even-even nuclei near shell-closure. Recent experiments have provided evidence for this mode in $$^{\mathrm {14}}$$ C and $$^{\mathrm {15}}$$ C nuclei populated via $$^{\mathrm {12}}$$ C, $$^{\mathrm {13}}$$ C( $$^{\mathrm {18}}$$ O, $$^{\mathrm {16}}$$ O) $$^{\mathrm {14}}$$ C, $$^{\mathrm {15}}$$ C two-neutron transfer reactions at 84 MeV beam energy. In the present paper, new data show the persistence of the same structures in the energy spectra of $$^{\mathrm {14}}$$ C and $$^{\mathrm {15}}$$ C populated by the same reactions at a higher bombarding energy of 275 MeV. The extracted centroid, width, spin-parity and transition probability fully agree with the previous observation thus giving a robust confirmation that the GPV mode is populated in such transfer reactions.

Matter Density in a Simple Core-Plus-Particle Model

In this paper we give formulae for three-particle corrections to the matter density of spherical fermionic quantum systems with an odd number of particles in their ground and excited states. The corrections add to the spherical shape due to pairing vibrations and also infer deformation. In order to achieve trackable results we performed a series of approximations which do not allow for considering more elaborate effects. The results can be applied to both atomic nuclei and small electronic systems such as atomic or molecular clusters.

Pairing vibrations in the interacting boson model based on density functional theory

We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number non-conserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially-symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for $^{122}$Xe, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^+$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.

Isovector pair correlations in analytically solvable models

The eigensolutions of the collective Hamiltonian with different potentials suggested for description of the isovector pair correlations are obtained, analyzed and compared with the experimental energies. It is shown that the isovector pair correlations in nuclei around [Formula: see text]Ni can be described as anharmonic pairing vibrations. The results obtained indicate the presence of the [Formula: see text]-particle type correlations in these nuclei and the existence of the interaction different from isovector pairing which also influences on the isospin dependence of the energies.

Coupling of shape and pairing vibrations in a collective Hamiltonian based on nuclear energy density functionals

The quadrupole collective Hamiltonian, based on relativistic energy density functionals, is extended to include a pairing collective coordinate. In addition to quadrupole shape vibrations and rotations, the model describes pairing vibrations and the coupling between shape and pairing degrees of freedom. The parameters of the collective Hamiltonian are determined by constrained self-consistent relativistic mean-field plus Bardeen-Cooper-Schrieffer (RMF+BCS) calculations in the space of intrinsic shape and pairing deformations. The effect of coupling between shape and pairing degrees of freedom is analyzed in a study of low-energy spectra and transition rates of four axially symmetric $N=92$ rare-earth isotones. When compared to results obtained with the standard quadrupole collective Hamiltonian, the inclusion of dynamical pairing increases the moment of inertia, lowers the energies of excited $0^+$ states and reduces the E0-transition strengths, in better agreement with data.

Gamma-ray spectra in the positron-annihilation process of molecules at room temperature

In this study, a fully self-consistent method was developed to obtain the wave functions of the positron and electrons in molecules simultaneously. The wave function of a positron at room temperature, with a characteristic energy of approximately 0.04 eV [1], was used to analyse the experimental results of its annihilation in helium, neon, hydrogen, and methane molecules. The interactions between the positron and molecule provide a significant correction in the gamma-ray spectra of the annihilating electron–positron pairs. It was also observed that high-order correlations offered almost no correction in the spectra, as the interaction between the low-energy positron and electrons cannot drive the electrons into excited electronic states. More accurate studies, which consider the coupling of the positron–electron pair states and vibration states of nuclei, must be undertaken.

Pairing properties of the double- β emitter Cd116

The pairing properties of the neutrinoless double-$\beta$ decay candidate $^{116}$Cd have been investigated. Measurements of the two-neutron removal reactions on isotopes of $^{114,116}$Cd have been made in order to identify 0$^+$ strength in the residual nuclei up to $\approx$3 MeV. No significant $L=0$ strength has been found in excited states indicating that the Bardeen-Cooper-Schrieffer (BCS) approximation is a reasonable basis to describe the neutrons in the ground state. This approximation avoids complications in calculations of double-$\beta$ decay matrix elements that use the quasiparticle random-phase approximation (QRPA) techniques. However this is not the case for the protons, where pair vibrations are prevalent and the BCS approximation is no longer valid, complicating the use of traditional QRPA techniques for this system as a whole.

Influence of simultaneous time-varying bearing and tooth mesh stiffness fluctuations on spur gear pair vibration

This work investigates the influence of time-varying roller bearing stiffness on gear-bearing system vibration. An isolated bearing model established by a finite element/contact mechanics approach is introduced to analyze the variation of bearing stiffness due to the continuous change of roller circumferential locations. Then, dynamic gear-bearing models with constant and time-varying bearing stiffness are built by analytical and finite element methods. Comparisons are conducted among the dynamic response of the different gear-bearing models to verify their accuracy and to indicate the special features introduced by the time-varying bearing stiffness. Additional resonances (or parametric instabilities) are caused by the time-varying bearing stiffness, and modulation between the mesh frequency and the bearing ball pass frequency is observed in the dynamic response. Theoretical explanations of the parametric instabilities of the system with simultaneous mesh and bearing stiffness fluctuations are derived using perturbation analysis and verified with Floquet theory.

Vibration and noise characteristics of a gear reducer under different operation conditions

Gear system is characterized by high efficiency, compact structure, and transmission ratio stability, and it has been extensively applied in various industrial equipment. This paper presents a novel preliminary estimate method for gear reducer noise radiation and vibration characteristics, and systematic researches on radiation characteristics of gear reducer are made. In the noise analysis process, the influence of time-varying mesh stiffness, error excitation, and tooth flank contact feature are comprehensively considered, the linear vibration model and nonlinear vibro-impact model for transmission system is set up, and then the dynamic load of the gearbox is obtained by solving the model. The dynamic load of bearing is taken as an excitation, the finite element method/boundary element method is adopted to analyze vibration and noise radiation characteristics of the gear reducer. The time domain response and field point noise spectrum at sound field are obtained, and the influence of harmonic components in excitation on vibration noise radiation of gearbox are discussed. The dynamic characteristics and sound radiation characteristics of gear reducer under different operating conditions are calculated, the change pattern of frequency component of the bearing dynamic load and noise radiation based on operating condition are obtained, and some interesting conclusions are observed from research that the gearbox produce the linear vibration and noise under the heavy load condition. Meanwhile, the nonlinear vibro-impact and noise is appeared under light load condition. The distribution of the gearbox radiated nose is uniform in various conditions, but noise takes sub-harmonic components as fundamental frequency and more peaks in the noise spectrum are observed. With the increase of the rotary speed, the noise tallies with the trend described by Kato formula except that under the gear system resonance speed. The impact force between teeth flanks shall be on the increase with the increase of rotary speed, and gear pair vibration experiencing a course from irregular vibration to regular periodic rattle vibration. With the increase of load, the noise of reducer changes with load as the variation of logarithmic function. For the noise in the process with load on the increase from no-load (the load is 0), the gear reducer vibration condition experienced both sides collision, single-side collision, and normal meshing in three stages. The radiated nose is increased gradually, but the abrupt change happened in critical positions between both sides collision and single-side collision as well as single-side collision and normal meshing in the process. The conclusions of this paper will offer theoretical basis for reducer to reduce vibration and noise.