Magnetic Dipole Excitations Research Articles

On the low-energy electromagnetic dipole modes in 151,153,155Sm Nuclei

The recently observed low-energy magnetic dipole (M1) and electric dipole (E1) excitations in deformed 151,153,155Sm are theoretically analysed. Rotational Invariant (RI-) and Translational-Galilean Invariant (TGI-) Quasiparticle Nuclear Model (QPNM) are used in the calculation of M1 and E1 properties, respectively. Both theories consider monopole pairing between nucleons, and the deformed Woods-Saxon potential is used as the mean-field potential. Pyatov's symmetry restoration procedure is applied in these models to eliminate the spurious modes from the intrinsic nuclear excitations. Model calculations show that although E1 transitions dominate the low-energy dipole spectra of 151,153,155Sm, many low-lying M1 transitions exist in these nuclei. It is shown that the most significant contribution to E1 and M1 excitation comes from ΔK=±1 transitions. The theory satisfactorily reproduces the gross features of low-lying dipole modes determined from the Oslo Method analysis of the experimental spectra.

Anapole states and transverse displacement sensing based on the interaction between cylindrical vector beams and Au core-Si shell nanodisks.

Precise optical control at the nanoscale is crucial for advancing photonic devices and sensing technologies. Herein, we theoretically introduce what we believe to be a novel approach for nano-optical manipulation, employing Au core-Si shell nanodisks interacting with tightly focused cylindrical vector beams to achieve electric and magnetic anapole states. Our investigations unveil that the interplay between individual nanodisks and radially polarized beams (RPBs) located in the center of RPBs yields a position-dependent electric anapole state. Conversely, under illumination by azimuthally polarized beams (APBs), the electric anapole state exhibits independence from the nanodisk's positioning and is accompanied by significant magnetic dipole excitations. Furthermore, the interaction between APBs and nanodisk multimers enables the formation of a magnetic anapole state, marking an advancement in nano-optical control. This study further explores the application of the position-dependent electric anapole state for nanoscale transverse displacement sensing, which allows for precise determination of the nanodisk's position within a plane. These findings not only facilitate versatile control over anapole states but also set a foundation for integrated displacement sensing technologies on-chip.

Electric and magnetic toroidal dipole excitations in core-shell spheres

Electric and magnetic toroidal dipole excitations in core-shell spheres

Magnetic dipole excitations in magic nuclei with subtracted second random-phase approximation

Magnetic dipole excitations in magic nuclei with subtracted second random-phase approximation

Multiple magnetic dipole excitation in permittivity-asymmetric all-dielectric metamaterials induced by quasi-bound states in the continuum

Multiple magnetic dipole excitation in permittivity-asymmetric all-dielectric metamaterials induced by quasi-bound states in the continuum

Dipole responses in γ−soft 124–134Xe in the spectroscopic energy region

This study aimed to systematically investigate the low-lying dipole states of even–even 124–134Xe isotopes using the quasiparticle random phase approximation method. Where in all the studied xenon isotopes, electric and magnetic dipole responses were clearly predicted. The calculations predict mainly a scissors mode, while the strength of weakly deformed 132, 134Xe was small compared to moderately deformed 124–130Xe isotopes, where electric dipole excitations make their own contributions as well. The obtained results are consistent with the available experimental data. Since it was not possible to experimentally determine the parity of dipole states here through a comparison of our results with the experiment, we investigated the role of electric and magnetic dipole excitations in forming the spectrum. After comparing the obtained results with the experimentally derived ones, the natures of several observed spin- and parity-unknown excitations were determined.

Microscopic analysis of low-energy spin and orbital magnetic dipole excitations in deformed nuclei

A low-energy magnetic dipole $(M1)$ spin-scissors resonance (SSR) located just below the ordinary orbital scissors resonance (OSR) was recently predicted in deformed nuclei within the Wigner function moments (WFM) approach. We analyze this prediction using fully self-consistent Skyrme quasiparticle random phase approximation (QRPA) method. Skyrme forces SkM*, SVbas, and SG2 are implemented to explore SSR and OSR in $^{160,162,164}\mathrm{Dy}$ and $^{232}\mathrm{Th}$. Accuracy of the method is justified by a good description of $M1$ spin-flip giant resonance. The calculations show that isotopes $^{160,162,164}\mathrm{Dy}$ indeed have at 1.5--2.4 MeV (below OSR) ${I}^{\ensuremath{\pi}}K={1}^{+}1$ states with a large $M1$ spin strength ($K$ is the projection of the total nuclear moment to the symmetry $z$ axis). These states are almost fully exhausted by $pp[411\ensuremath{\uparrow},411\ensuremath{\downarrow}]$ and $nn[521\ensuremath{\uparrow},521\ensuremath{\downarrow}]$ spin-flip configurations corresponding to $pp[2{d}_{3/2},2{d}_{5/2}]$ and $nn[2{f}_{5/2},2{f}_{7/2}]$ structures in the spherical limit. So the predicted SSR is actually reduced to low-orbital ($l=2,3$) spin-flip states. Following our analysis and in contradiction with WFM spin-scissors picture, deformation is not the principle origin of the low-energy spin $M1$ states but only a factor affecting their features. The spin and orbital strengths are generally mixed and exhibit interference: weakly destructive in SSR range and strongly constructive in OSR range. In $^{232}\mathrm{Th}$, the $M1$ spin strength is very small. Two groups of ${I}^{\ensuremath{\pi}}={1}^{+}$ states observed experimentally at 2.4--4 MeV in $^{160,162,164}\mathrm{Dy}$ and at 2--4 MeV in $^{232}\mathrm{Th}$ are mainly explained by fragmentation of the orbital strength. Distributions of nuclear currents in QRPA states partly correspond to the isovector orbital-scissors flow but not to the spin-scissors one.

Discerning nuclear pairing properties from magnetic dipole excitation

Pairing correlation of Cooper pair is a fundamental property of multi-fermion interacting systems. For nucleons, two modes of the Cooper-pair coupling may exist, namely of $$S_{12}=0$$ with $$L_{12}=0$$ (spin-singlet s-wave) and $$S_{12}=1$$ with $$L_{12}=1$$ (spin-triplet p-wave). In nuclear physics, it has been an open question whether the spin-singlet or spin-triplet coupling is dominant, as well as how to measure their role. We investigate a relation between the magnetic-dipole (M1) excitation of nuclei and the pairing modes within the framework of relativistic nuclear energy-density functional (RNEDF). The pairing correlations are taken into account by the relativistic Hartree-Bogoliubov (RHB) model in the ground state, and the relativistic quasi-particle random-phase approximation (RQRPA) is employed to describe M1 transitions. We have shown that M1 excitation properties display a sensitivity on the pairing model involved in the calculations. The systematic evaluation of M1 transitions together with the accurate experimental data enables us to discern the pairing properties in finite nuclei.

Relativistic nuclear energy density functional approach to magnetic-dipole excitation

Magnetic-dipole (M1) excitations of 18O and 42Ca nuclei are investigated within a relativistic nuclear energy density functional framework. In our last work [1], these nuclei are found to have unique M1 excitation and its sum rule, because of their characteristic structure: the system consists of the shell-closure core plus two neutrons. For a more systematic investigation of the M1 mode, we have implemented a framework based on the relativistic nuclear energy density functional (RNEDF). For benchmark, we have performed the RNEDF calculations combined with the random-phase approximation (RPA). We evaluate the M1 excitation of 18O and 42Ca, whose sum-rule value (SRV) of the M1 transitions can be useful to test the computational implementation [1]. We also apply this RNEDF method to 208Pb, whose M1 property has been precisely measured [2, 3, 4, 5]. Up to the level of the M1 sum rule, our result is in agreement with the experiments, except the discrepancy related with the quenching factors for g coefficients.

Magnetic dipole excitations based on the relativistic nuclear energy density functional

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies.

Pygmy dipole resonance in the well-deformed even–even 152–162Gd

The electric dipole E1 strength in the well-deformed even–even 152–162Gd was calculated using a model based on translational and Galilean invariant quasi-particle random phase approximation (QRPA), where for the first time the highly-fragmented E1 strength has been predicted below the particle threshold energy. The predicted concentration of the electric dipole excitations exhausts less than 2% of the energy weighed sum rules (EWSR) below 20 MeV in rather good agreement with the experimental data for neighbor nuclei. Through cross sections, transition probabilities, and other properties, the electric dipole response was investigated in 152–162Gd for a wide range of excitation energies from 5 to 20 MeV. The calculation that was performed with the elimination of effects associated with deformation revealed that the effects associated with neutron excess play a more significant role in the formation of the pygmy dipole resonance (PDR) strength when compared to the effects associated with a changing deformation. The calculations indicate the presence of magnetic dipole excitations with summed M1 strengths in the energy region between 5 and 8 MeV was less than 10% of the total dipole strength in the same energy region. We also took into account a recent experimental study of 156Gd in our discussion and paid particular attention to this isotope.

Role of residual interaction in the relativistic description of M1 excitation

Magnetic dipole (M1) excitation is the leading mode of multi-nucleon excitations induced by the magnetic field, and is a phenomenon of the spin–orbit splitting and residual interactions involved. In this work, we investigate the effects of the residual interactions on the M1 excitation from a novel perspective, the framework of relativistic nuclear energy-density functional. The relativistic Hartree–Bogoliubov model is utilized to determine the nuclear ground state properties, while the relativistic quasi-particle random-phase approximation is employed for the description of M1-excitation properties. From the analysis of M1 mode in the Ca isotope chain, role of the isovector–pseudovector residual interaction is discussed. For open-shell nuclei, the pairing correlation also plays a noticeable role in the M1 mode. The experimental data on M1 mode is expected to provide a suitable reference to improve and optimize the theoretical models to describe the residual interactions.

Magnetic dipole excitation and its sum rule in nuclei with two valence nucleons

Background: Magnetic dipole (M1) excitation is the leading mode of nuclear excitation by the magnetic field, which couples unnatural-parity states. Since the M1 excitation occurs mainly for open-shell nuclei, the nuclear pairing effect is expected to play a role. As expected from the form of operator, this mode may provide the information on the spin-related properties, including the spin component of dineutron and diproton correlations. In general, the sum rule for M1 transition strength has not been derived yet. Purpose: To investigate the M1 excitation of the systems with two valence nucleons above the closed-shell core, with pairing correlation included, and to establish the M1 sum rule that could be used to validate theoretical and experimental approaches. Possibility to utilize the M1 excitation as a tool to investigate the pairing correlation in medium is also discussed. Method: Three-body model, which consists of a rigid spherical core and two valence nucleons, is employed. Interactions for its two-body subsystems are phenomenologically determined in order to reproduce the two-body and three-body energies. We also derive the M1 sum rule within this three-body picture. Conclusion: The introduced M1 sum rule can be utilized as a benchmark for model calculations of M1 transitions in the systems with two valence nucleons. The total sum of the M1 transition strength is related with the coupled spin of valence nucleons in the open shell, where the pairing correlation is unnegligible. The three-body-model calculations for 18 O, 18 Ne, and 42 Ca nuclei demonstrate a significant effect of the pairing correlations on the low-lying M1 transitions. Therefore, further experimental studies of M1 transitions in those systems are on demand, in order to validate proposed sum rule, provide a suitable probe for the nuclear pairing in medium, as well as to optimize the pairing models.

Enhanced Four-Wave Mixing in Doubly Resonant Si Nanoresonators

Frequency conversion is one of the main applications of nonlinear optical processes in which a signal is produced at a different wavelength from the excitation wavelength. In particular, four-wave mixing (FWM) is a third order nonlinear optical process that allows, for instance, the generation of visible frequencies by tuning near-infrared laser pumps. Here, in order to augment the very weak FWM conversion efficiency, we design silicon Mie resonators that exhibit two resonances of the internal electric field intensity around the frequency range of the laser pumps. The linear extinction spectrum of the individual Si resonator is first measured by bright field spectroscopy and compared with numerical simulations to confirm the existence of the two resonances corresponding to electric and magnetic dipole excitations. The FWM signal is then measured for a single Si nanoresonator when the first pump is set to the electric resonance while tuning the frequency of the second pump across the magnetic dipolar resonance. We show that the FWM signal generated in the visible spectrum is maximum when the frequency of the tunable pump corresponds to the maximum of the internal electric field intensity. At this position, the FWM signal is enhanced by more than 2 orders of magnitude compared with the FWM signal generated by the unpatterned silicon film.

Enhanced absorption in all-dielectric metasurfaces due to magnetic dipole excitation

All-dielectric nanophotonics lies at a forefront of nanoscience and technology as it allows to control light at the nanoscale using its electric and magnetic components. Bulk silicon does not experience any magnetic response, nevertheless, we demonstrate that the metasurface made of silicon parallelepipeds allows to excite the magnetic dipole moment leading to the broadening and enhancement of the absorption. Our investigations are underpinned by the numerical predictions and the experimental verifications. Also surprisingly we found that the resonant electric quadrupole moment leads to the enhancement of reflection. Our results can be applied for a development of absorption based devices from miniature dielectric absorbers, filters to solar cells and energy harvesting devices.

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS)

Objective. A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. Approach. We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. Main results. In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. Significance. This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

Tailoring toroidal and magnetic dipole excitations with the same dielectric structure.

The toroidal dipole (TD) and magnetic dipole (MD) are usually overlooked due to their relatively weak coupling to the electromagnetic fields. However, recent investigations have shown that they can play an important role in the optical response from some designed nanostructures. Different nanostructures have been designed for tailoring TD and MD excitations. Here we demonstrate that a single structure can be designed to tailor both TD and MD excitations. Near-perfect TD and MD excitations from the same structures have been realized by using various electric dipoles, which is very beneficial for designing optical functional devices such as nanoantennas and sensors.

Matrix models of strength distributions

In this work, we use matrix models to study the problem of strength distributions. This is motivated by noticing near exponential falloffs of strengths in calculated magnetic dipole excitations. We emphasize that the quality of the exponential falloffs depends on the parameters in our matrices, especially the relative size of the couplings to the unperturbed level separations. We also find a dark matrix for which all transitions vanish.

Structural correlations and dependent scattering mechanism on the radiative properties of random media

The dependent scattering mechanism is known to have a significant impact on the radiative properties of random media containing discrete scatterers. Here we theoretically demonstrate the role of dependent scattering on the radiative properties of disordered media composed of nonabsorbing, dipolar particles. Based on our theoretical formulas for the radiative properties for such media, we investigate the dependent scattering effects, including the effect of modification of the electric and magnetic dipole excitations and the far-field interference effect, both induced and influenced by the structural correlations. We study in detail how the structural correlations play a role in the dependent scattering mechanism by using two types of particle system, i.e., the hard-sphere system and the sticky-hard-sphere system. We show that the inverse stickiness parameter, which controls the interparticle adhesive force and thus the particle correlations, can tune the radiative properties significantly. Particularly, increasing the surface stickiness can result in a higher scattering coefficient and a larger asymmetry factor. The results also imply that in the present system, the far-field interference effect plays a dominant role in the radiative properties while the effect of modification of the electric and magnetic dipole excitations is subtler. Our study is promising in understanding and manipulating the radiative properties of dipolar random media.

Analysis of dependent scattering mechanism in hard-sphere Yukawa random media

The structural correlations in the microscopic structures of random media can induce the dependent scattering mechanism and thus influence the optical scattering properties. Based on our recent theory on the dependent scattering mechanism in random media composed of discrete dipolar scatterers [B. X. Wang and C. Y. Zhao, Phys. Rev. A 97, 023836 (2018)], in this paper, we study the hard-sphere Yukawa random media, in order to further elucidate the role of structural correlations in the dependent scattering mechanism and hence optical scattering properties. Here, we consider charged colloidal suspensions, whose effective pair interaction between colloids is described by a screened Coulomb (Yukawa) potential. By means of adding salt ions, the pair interaction between the charged particles can be flexibly tailored and therefore the structural correlations are modified. It is shown that this strategy can affect the optical properties significantly. For colloidal TiO2 suspensions, the modification of electric and magnetic dipole excitations induced by the structural correlations can substantially influence the optical scattering properties, in addition to the far-field interference effect described by the structure factor. However, this modification is only slightly altered by different salt concentrations and is mainly because of the packing-density-dependent screening effect. On the other hand, for low refractive index colloidal polystyrene suspensions, the dependent scattering mechanism mainly involves the far-field interference effect, and the effective exciting field amplitude for the electric dipole almost remains unchanged under different structural correlations. The present study has profound implications for understanding the role of structural correlations in the dependent scattering mechanism.