Shape Resonance Research Articles

Adiabatic Evolution and Shape Resonances

Motivated by a problem of one mode approximation for a non-linear evolution with charge accumulation in potential wells, we consider a general linear adiabatic evolution problem for a semi-classical Schrödinger operator with a time dependent potential with a well in an island. In particular, we show that we can choose the adiabatic parameter ε \varepsilon with ln ⁡ ε ≍ − 1 / h \ln \varepsilon \asymp -1/h , where h h denotes the semi-classical parameter, and get adiabatic approximations of exact solutions over a time interval of length ε − N \varepsilon ^{-N} with an error O ( ε N ) {\mathcal O}(\varepsilon ^N) . Here N > 0 N>0 is arbitrary. \center Résumé \endcenter Motivés par un problème d’approximation à un mode pour une évolution avec accumulation de charge dans des puits de potentiel, nous considérons un problème d’évolution linéaire pour un opérateur de Schrödinger avec un potentiel dépendant du temps avec un puits dans une île. En particular, nous montrons que nous pouvons choisir le paramètre adiabatique ε \varepsilon avec ln ⁡ ε ≍ − 1 / h \ln \varepsilon \asymp -1/h , où h h désigne le paramètre semi-classique, et obtenir des approximations adiabatiques de solutions exactes sur des intervalles de temps de longueur ε − N \varepsilon ^{-N} avec une erreur O ( ε N ) {\mathcal O}(\varepsilon ^N) . Ici N > 0 N>0 est arbitraire.

Integrating Vernier spectrum with Fano resonance for high sensitivity of an all-optical sensor

Vernier and Fano resonances are promising approaches for enhancing the sensitivity of an all-optical sensor. A theoretical analysis was performed to integrate a Fano-like resonance shape with a Vernier resonance by considering the presence of partially reflective end facets at a double microring resonator waveguide. The system was developed based on scattering matrix and optical transfer function. The all-pass racetrack microring resonator (ARMRR) and the double racetrack microring resonator (DRMRR) were compared with and without the end facet at the waveguide to analyze the dynamic change of the output resonance spectrum. The spectrum was analyzed based on the free spectral range and resonance pattern. The resonator systems were applied to a refractive index-based sensing protocol, which was operated by a resonance wavelength shift with a refractive index change. The sensitivity was optimized by varying the configuration parameters such as the radius of the ring, the distance between the end facet, and the coupling coefficients. Integrating Vernier spectrum with Fano resonance improved the sensitivity for ARMRR configuration by 5.16% and the sensitivity for DRMRR configuration by 6.31%. The recorded limit of detection (LOD) of the DRMRR was 3.30 × 10-5.

Observation of the p -wave shape resonance in atom-molecule collisions

Partial wave resonances are quasi-bound states that are formed by tunneling through the centrifugal barrier. Such states are important to collisions that deviate from the Langevin limit where direct collision path is suppressed due to quantum symmetry or a potential barrier. In such a case, quantum resonances play a major role in the dynamics at low temperatures where scattering process can be described mainly by the resonance contribution. Here we present the first observation of the lowest-lying partial wave resonance in the Penning ionization collisions between metastable neon and rovibrationally ground state HD molecules. We observe the resonance at an energy of $k_B\times$22mK taking advantage of the phase space correlation similar to atomic delta kick cooling. We show that the $p$-wave resonance position is particularly sensitive to the leading term of the van der Waals interaction. We also measure shape resonance at a higher angular momentum state, $l=6$, allowing us to disentangle and probe the short and the long parts of the intermolecular interaction.

Formation of the CH/CD molecules through radiative association of C with H/D

ABSTRACT Reaction rate constants have been calculated for the formation of CH and CD molecules through radiative association of C and H/D atoms in their ground states. Quantum mechanical and semiclassical/classical methods were used to obtain the reaction cross-sections. Shape resonances and inverse pre-dissociation are accounted for with Breit–Wigner theory. The potential, permanent/transition dipole moment curves and experimental pre-dissociation widths are taken from the literature. The resulting reaction rate constants were fitted to the Kooij formula for use in astrochemical modelling. Our rate constant is 3.5 × 10−17 cm3 s−1 at 100 K and it peaks at 20 K, where it is 8.0 × 10−17 cm3 s−1. These values are larger than what has been obtained in earlier studies but not large enough to account for the interstellar abundance of CH.

Investigation of electron-induced scattering resonances using a multiconfigurational polarization propagator and a complex absorbing potential

We develop a method based on the polarization propagator (PP) combined with the complex absorbing potential (CAP) technique to study metastable resonances induced by electron impact. We use a CASSCF wavefunction corresponding to the ground state of the anion as the initial state for the PP. The perturbation of the Hamiltonian by the CAP allows for complex eigenvalues that represent the continuum states including the resonance buried in the continuum. The artifacts due to the CAP are eliminated using the Padé extrapolation method. We apply our method to study the 2P Be− atomic shape resonance, and 2Πg N2− and 2Π CO− molecular shape resonances. Our estimated resonance positions and widths for the resonances are in agreement with the previously reported values. Overall, this method is a powerful and computationally tractable tool for the study of resonances.

Photodissociation spectroscopy via a rovibrational resonance in intense UV pulses

Photodissociation dynamics via a rovibrational resonance in intense UV pulses is investigated theoretically, using a showcase ${\text{CH}}^{+}$ molecule promoted to the $\text{C}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ valence excited electronic state with a potential barrier, thus giving access to study shape resonance controlled by the pulse frequency. Simulations of the kinetic energy release (KER) and angular distribution of the photofragments (ADP) spectra show dramatic differences for the cases when the pulse is tuned on and off the rovibrational resonance. It shows that as the increasing pulse intensity for the transitions to shape resonance, the KER spectra develop into new and higher energy peaks overlying on the broadened background, which is explained by the involvement of other resonances with higher partial waves through electronic Rabi flopping between the ground and excited electronic states. Those nonlinear contribution increases drastically the probability of photofragmentation along the laser polarization in the ADP spectra. The coincident KER-ADP spectra reveal clearly the correlated dynamics in the vicinity of the dissociation barrier. The present work opens possibilities for the manipulation of ultrafast photodissociation dynamics with the help of resonance states in the continuum.

Resonances and mode shape imaging for characterizing the microstructure of complex metals

Resonant Ultrasound Spectroscopy (RUS) is a mature and reliable technique for measuring the elastic stiffness constants of anisotropic materials. In highly processed materials such as additively manufactured metal parts, the anisotropic stiffnesses arrive from microstructures that contain grains with preferred orientations, which can result from directionally dependent thermal or mechanical processes. The connection between elastic stiffnesses and microstructure suggest the potential for RUS being used as a tool to characterize microstructure. This presentation will highlight modeling and experimental measurements in this direction. The RUS model is developed from a micromechanical foundation and includes structure-property linkages between the microstructure’s orientation distribution function and the macroscopic elastic constitutive behavior. The micromechanical basis allows efficient creation of a complete catalog containing all possible resonant behavior (resonant frequencies and mode shapes) of polycrystalline samples as a function of the possible textures. The second part of the presentation will focus on connecting experimentally measured resonances and mode shapes to a particular catalog entry. The inclusion of mode shape imaging in the analysis is expected to offer additional detail and potential for expanded characterization beyond texture and elastic stiffnesses.

Effect of helmholtz resonator shape on suppression of thermo-acoustic instability

In combustion chambers thermo-acoustic instabilities arise due to the coupling between the unsteady heat release and pressure fluctuations. The instabilities created cause serious structural vibration, flame blow out, increase in heat transfer and damage, thereby reducing the life span and performance of jet engines, gas turbines and industrial burners. Therefore, there is need to develop a simple technique for effective control of these instabilities. The present work involves experimental study of thermo-acoustic instabilities occurring in a Rijke tube and their suppression by using Helmholtz resonators of different shape (a passive method of suppression). The combustor model is replaced by Rijke tube which is an experimental setup extensively employed for research purpose. Rijke tube is provided with a co-axial pre-mixed gas burner as the source of heat which could be placed at any desired position. When a heat source with proper air to fuel ratio is placed at about one fourth of the tube length, 3rd mode of instability is obtained and a loud noise of frequency 681 Hz is produced. A comparative study of thermo-acoustic instability suppression using cylindrical, spherical and conical Helmholtz resonators has been performed. Spherical resonator has been found to be the most effective one imparting a maximum damping effect of 20 dB and an average damping effect of 10.5 dB.

Elastic Electron Scattering by Diborane(6) and Diborane(4) Molecules

We present integral, differential, and momentum transfer cross sections for elastic electron collisions with the two most stable isomers of the B2H4 molecule, hereafter referred to as isomer I (C2v symmetry) and isomer II (D2d symmetry), and with the B2H6 molecule (D2h symmetry). The isomer I of B2H4 and the B2H6 molecule are known for their electrodeficiency in the "three-center two-electron" (3c-2e) bond, a region in which a hydrogen atom occupies a bridged position between two non-hydrogen atoms. The cross sections were computed by using the Schwinger multichannel method implemented with norm-conserving pseudopotentials, and the scattering calculations were carried out in the static-exchange and static-exchange plus polarization levels of approximation for energies from 0.1 to 50 eV. We discuss the presence of shape resonances in the scattering cross sections. We also made a direct comparison among the cross sections of these three targets.

Next-to-leading order (NLO) perturbative effects in QCD sum-rule analyses of light tetraquark systems: A case study in the scalar-isoscalar channel

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar (JPC=0++) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions 0.52GeV<mσ<0.77GeV for the lightest scalar-isoscalar σ state are in good agreement with the four-quark interpretation of the f0(500), and the relative coupling strengths of the f0(980) and f0(500) to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the σ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians.

Metallic spherical heterotrimer systems for plasmonic-based improvement in hyper-Raman scattering

A unique combination between structural parameters of collinearly arranged spherical particles is proposed as an effective plasmonic substrate for ultrahigh enhancement in hyper-Raman scattering signals. The suggested spherical trimer systems are mainly composed from two identical nanoparticle separated by a third alike shape resonator of different size. All the interacting plasmonic element are made from gold, arranged in 1D array and illuminated by a longitudinally polarized light. The optical properties, spatial distribution of nearfields and the surface charge densities were calculated numerically by FDTD tool. The enhancement factor of the hyper-Raman scattering, and the associated Raman shift were calculated theoretically from the optical response of the trimer. The extinction spectra of the heterotrimers demonstrate the excitation of two plasmonic modes, the first coupled band excited at a longer wavelength and is attributed to the in-phase coupling between the dipole moments induced in each of the three spherical resonators, the other hybrid mode observed in the shorter wavelength region and is resulted from the coupling between the dark mode excited in the intermediate particle and the bright band monitored in the bordered particles. The nearfields associated with the excitation of the two plasmonic modes are strongly localized and highly enhanced at the same intercoupling regions (hot spots) which optically match the excitation wavelength and the second-order stock condition. Through careful selecting of the relative size of the coupled nanoparticles and their coupling separation, the enhancement factor of hyper-Raman scattering signal can reach as high as 1 × 1013.

Algebraic equation of motion approach for solving the Anderson model

Based on the algebraic equation of motion (AEOM) approach, we have studied the single-impurity Anderson model by analytically solving the AEOM of the f-electron one-particle Green function in the Kondo limit. The related spectral function satisfies the sum rule and shows that there is a well-known three-peak structure at zero temperature. In the low energy limit, we obtain the analytical formula of the Kondo temperature that is the same as the exact solution in form except for a prefactor. We also show that the shape of the Kondo resonance is the Lorentzian form and the corresponding weight is proportional to the spin-flip correlation function.

Mode localization in metastructure with T-type resonators for broadband vibration suppression

This paper proposes a design scheme of a plate-type metastructure integrated with mistuned T-type resonators for broadband vibration suppression. We focus on the effect mechanism of mode localization of the resonators on the bandgap of the metastructure under simply supported boundary conditions. The mathematical model is formulated to accurately predict its dynamic behaviors based on the Hamilton’s principle. The explicit bandgap edge expressions considering the mistuning factor are developed based on the modal analysis approach using the assumption of an infinite number of resonators. It is found that the bandwidths of the bandgaps targeted at a natural frequency of the metastructure depend not only on the mass ratio of the T-type resonator but also on the mistuning factors. With the influence of mistuning parameters on mode localization feature (i.e., the phenomena of the frequency veering and the exchange of mode shapes) of the T-type resonator theoretically and experimentally examined, the formation mechanism of broaden bandgaps of the metastructure is revealed. A coupling broad bandgap and double bandgaps can be generated by designing appropriate mistuning parameters. In particular, the phenomena of the bandgap boundaries veering and bandgap near-coupling can be formed through the interaction of double bandgaps to improve the performance of vibration suppression. The present work demonstrates that the proposed mode-localization-based metastructure can provide some insights and potential applications for broadband and multi-frequency vibration suppression of engineering structures.

Silver‐Mediated Squaric Acid Reduction as a Facile, Ambient‐temperature and Seedless Route to Tunable Bimetallic Au/Ag Nanostars and Nanosnowflakes

AbstractBimetallic Au/Ag nanoparticles were successfully synthesized using a facile and reproducible method involving rapid, room‐temperature mixing of aqueous solutions of HAuCl4 and AgNO3 in the presence of squaric acid as both the reducing agent and surface capping ligand. Variation in the initial Au : Ag molar ratio yielded a tunable anisotropic shape and affiliated surface plasmon resonance. The nanoparticles displayed excellent stability in water for at least 10 weeks and showed robust catalytic activity in the borohydride‐assisted reduction of the model substrate 4‐nitrophenol.

Temperature stability of individual plasmonic Au and TiN nanodiscs

Refractory plasmonic materials are of interest for high-temperature plasmonic applications due to their increased thermal stability when compared to gold and silver. Titanium nitride (TiN) has been highlighted as a promising refractory material, offering both strong plasmonic and thermal performance. In this work, we analyze the stability of both the structural and optical response of individual plasmonic nanodiscs of various diameters subjected to elevated temperature conditions in air. Using cathodoluminescence spectroscopy, we trace the resonance spectra and shape modifications of the same single TiN and Au discs annealed at increasing temperatures up to 325 °C. TiN discs display greater morphological stability, but the optical properties of both materials deteriorate from 200 °C, although the mechanisms of degradation are different. The results are essential for optimizing nanostructured materials for high temperature nanophotonic applications.

Transfer matrix modeling and experimental verification of forked piezoelectric actuators

Piezoelectric actuators with forked substructures are popular in practical applications. However, there is still a lack of effective modeling methods for forked piezoelectric actuators whose essential substructures converge on the same interface. The critical problem is establishing the transfer conditions between the state vectors distributed on the interface for the forked piezoelectric actuators. To ease these issues, the transfer matrix method is adopted to create forked transfer conditions and to achieve the modeling of the forked piezoelectric actuators in this paper. The forked transfer conditions, including the velocity and force relationships at the interface, are first created. The velocity relationships between state vectors are built by the method of relative velocity, and the force components acting on the interface are equilibrant. Then, a piezoelectric actuator with forked substructures is designed, and its electromechanical coupling model is developed as a case study to confirm the created forked transfer condition. Finally, an actuator prototype is manufactured to verify the proposed forked transfer conditions and the correctness of the developed transfer matrix model of the whole system. The computational and measured vibration characteristics, including resonant frequencies and vibration shapes, agree with each other. Results powerfully demonstrate that the forked connection can transform the vibration direction and realize the amplitude amplification. This modeling method can analyze the vibration characteristics of other similar piezoelectric actuators with the forked substructures.

Microscopy of an ultranarrow Feshbach resonance using a laser-based atom collider: A quantum defect theory analysis

We employ a quantum defect theory framework to provide a detailed analysis of the interplay between a magnetic Feshbach resonance and a shape resonance in cold collisions of ultracold $^{87}\mathrm{Rb}$ atoms as captured in recent experiments using a laser-based collider [M. Chilcott et al., Phys. Rev. Research 3, 033209 (2021)]. By exerting control over a parameter space spanned by both collision energy and magnetic field, the width of a Feshbach resonance can be tuned over several orders of magnitude. We apply a quantum defect theory specialized for ultracold atomic collisions to fully describe of the experimental observations. While the width of a Feshbach resonance generally increases with collision energy, its coincidence with a shape resonance leads to a significant additional boost. By conducting experiments at a collision energy matching the shape resonance and using the shape resonance as a magnifying lens, we demonstrate a feature broadening to a magnetic width of 8 G compared to a predicted Feshbach resonance width much less than $0.1$ mG.

Recent Progress in Low-Energy Electron Elastic-Collisions with Multi-Electron Atoms and Fullerene Molecules

We briefly review recent applications of the Regge pole analysis to low-energy 0.0 ≤ E ≤ 10.0 eV electron elastic collisions with large multi-electron atoms and fullerene molecules. We then conclude with a demonstration of the sensitivity of the Regge pole-calculated Ramsauer–Townsend minima and shape resonances to the electronic structure and dynamics of the Bk and Cf actinide atoms, and their first time ever use as novel and rigorous validation of the recent experimental observation that identified Cf as a transitional element in the actinide series.

Autoionization decay and radiative decay for doubly excited 1Po resonance states in H− and Ps− ions

The autoionization decay (AD) and radiative decay (RD) for doubly excited 1Po resonance states in H− and Ps− are studied using correlated exponential wavefunctions based on the variational methods. To trace the resonance poles from Ps− to H−, the nuclear mass is varied from one unit to infinitely heavy. Resonance positions, widths related to AD rates, oscillator strengths, the ratios of oscillator strengths between the Feshbach and shape resonances (FSR), RD rates for the lowest two FSR in the 1Po spectrum, are reported. Few results are new, and others are comparable with the available theoretical and experimental data.

Shape Resonances in DNA: Nucleobase Release, Reduction, and Dideoxynucleoside Products Induced by 1.3 to 2.3 eV Electrons.

Understanding the details of DNA damage caused by high-energy particles or photons is complicated by the multitude of reactive species, arising from the ionization and dissociation of H2O, DNA, and protein. In this work, oligonucleotides (ODNs) are irradiated with a beam of low-energy electrons of 1.3 to 2.3 eV, which can only induce damage via the decay of shape resonances into various dissociative electron attachment channels. Using LC-MS/MS analysis, the major products are the release of nonmodified nucleobases (NB; Cyt ≫ Thy ∼ Ade > Gua). Additional damage includes 5,6-dihydropyrimidines (dHT > dHU) and eight nucleosides with modified sugar moieties consisting of 2',3'- and 2',5'-dideoxynucleosides (ddG > ddA ∼ ddC > ddT). The distribution of products is remarkably different in a 16-mer ODN compared to that observed previously with thymidylyl-(3'-5')-thymidine. This difference is explained by electron delocalization occurring within a sufficiently long strand, the DEA theory of O'Malley, and recent time-dependent density functional theory calculations.