Multipole Transitions Research Articles

Interference between multipolar two-photon transitions in quantum emitters near plasmonic nanostructures

In the vicinity of plasmonic nanostructures that support highly confined light fields, spontaneous emission processes, such as two-photon spontaneous emission (TPSE), exhibit higher-order multipolar emission pathways beyond the dipolar one. These multipolar emission channels occur simultaneously and can interfere with each other. We develop a novel framework that computes these interference effects for TPSE of a quantum emitter close to an arbitrary nanostructure. The model is based on the computation of Purcell factors that can be calculated with conventional electromagnetic simulations, which avoids complex analytic calculations for the environment. For a transition of a hydrogen-like emitter close to a graphene nanotriangle, we demonstrate a breakdown of the dipolar selection rule in the TPSE process. This breakdown is due to a huge enhancement of the two-electric dipole (2ED) and of the two-electric quadrupole (2EQ) transitions. We observe an important interference between these multipolar transitions, as it increases the total rate by 67%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$67 \\, \\%$$\\end{document}. In the end, our framework is a complete tool to design emitters and nanostructures for TPSE, where the exploitation of previously ignored interference effects provides an additional degree of freedom, for example to boost desired transitions and to supress undesirable ones.

A comparative study of transition oscillator strengths and static polarizabilities of the hydrogen atom confined in Gaussian potential

Abstract The multipole (dipole, quadrupole, and octopole) photon-absorption transition oscillator strengths for the ground state of hydrogen atom confined in Gaussian potential are investigated for a great variety of potential depths and confining radii. It is interestingly found that at fixed potential depth the gradual increase of confining radius shows first destructive and then constructive effect on the multipole oscillator strengths. Such an effect can be understood from the overlap between the initial and final states. Multipole polarizabilities of the system are obtained through the sum-over-states formalism where the contributions from both the bound and continuum spectra of the system are included. Although the separate bound and continuum contributions can not be determined accurately, due to the long-range nature of the Coulomb potential introduced by the nucleus, their summations can be obtained to reasonably good accuracy, leading to fast convergence of numerical calculations of multipole polarizabilities. The present results are compared with previous calculations available in the literature. Although good agreement is observed for the dipole polarizability, significant differences exist in the quadrupole polarizability and orders-of-magnitude differences appear in the octopole polarizability. The possible reason for such large differences is analyzed by comparing the sum rule of corresponding oscillator strengths.

Excitation of Multipolar Transitions in Nuclei by Twisted Photons

Excitation of Multipolar Transitions in Nuclei by Twisted Photons

Electromagnetic properties of nuclei from first principles: a case for synergies between experiment and theory.

One of the overarching goals in nuclear science is to understand how the nuclear chart emerges from the underlying fundamental interactions. The description of the structure of nuclei from first principles, using ab initio methods for the solution of the many-nucleon problem with inputs from chiral effective field theory, has advanced dramatically over the past two decades. We present an overview over the available ab initio tools with a specific emphasis on electromagnetic observables, such as multipole moments and transition strengths. These observables still pose a challenge for ab initio theory and are one of the most exciting domains to exploit synergies with modern experiments. Precise experimental data are vital for the validation of the theory predictions and the refinement of ab initio methods. We discuss some of the past and future experimental efforts highlighting these synergies. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Relativistic calculations of energy levels, lifetimes, transition parameters, and electron impact excitation cross sections for Kr XIX

In this study, we present a detailed analysis of atomic properties for Kr XIX, specifically focusing on the lowest 128 fine-structure levels originating from the 3s23p6, 3s23p53d, 3s3p63d and 3s23p43d2 configurations. We report energy levels, lifetimes, wavelengths, weighted oscillator strengths, and transition probabilities for multipole transition types (E1, E2, M1, and M2). To achieve this, we employed the GRASP2018 code, which implements the fully relativistic multiconfigurational Dirac–Hartree–Fock method and accounts for Breit interaction and quantum electrodynamic effects. We performed another set of calculations using the many-body perturbation theory implemented in the flexible atomic code (FAC). By comparing the results obtained from GRASP2018 and FAC, we established the accuracy and consistency of our calculations. Furthermore, using the relativistic distorted wave theory, we studied electron impact excitation of all transitions to upper levels from the ground and metastable levels and reported excitation cross sections for incident electron energies up to 5 keV. To enhance the practical utility of our findings, we also provided analytical fittings of these cross sections and excitation rate coefficients for their applications in plasma modeling. This work contributes to the atomic properties and excitation cross sections of Kr XIX, addressing a marked gap in the available atomic data.

The LSU-Argonne conversion electron spectrometer: A new detector for the X-Array and SATURN decay station

A new conversion electron detector has been commissioned at the ATLAS/ CARIBU facility at Argonne National Laboratory. The LSU-Argonne Conversion Electron Spectrometer (LACES) is a LN2-cooled Si(Li) detector system designed to be incorporated into a decay station that comprises the dedicated HPGe clover array with a box geometry (X-Array) and the Scintillator and Tape Using Radioactive Nuclei (SATURN) device. This integration enables simultaneous measurements of conversion electrons and gamma-rays in decay experiments, yielding novel information on transition multipolarities, electric monopole transitions, and isomeric states that decay mostly via conversion electrons. A measurement of the energy resolution of LACES yielded 2.3-keV FWHM at 975 keV for electrons and 1.3-keV FWHM at 75 keV for X-rays. A detailed study of the absolute detection efficiency (at 5 mm from the source) was performed, where this quantity was determined experimentally in the range of electron transition energies between 25.5 keV and 1047.8 keV and subsequently simulated using the GEANT4 code. Measurement and simulations are found to be in excellent agreement. A precise characterization, for this type of detector system, of the absolute detection efficiency for such a wide energy range is reported for the first time.

Experimental and theoretical Ritz–Rydberg analysis of the electronic structure of highly charged ions of lead and bismuth by optical spectroscopy

Intra-configuration fine-structure transitions in highly charged ions (HCIs) result in most cases from changes in the coupling of equivalent electrons. They are multipole forbidden to varying degrees and often occur within the optical range. In HCI with semi-filled nd and nf subshells, electrons can in principle couple to states which are energetically close but with very different total angular momenta, e.g. 0⩽J⩽10 . This gives rise to metastable states with very long lifetimes that exhibit particularly interesting clock transitions or, as in the case of orbital level crossings, acquire a considerable sensitivity to a possible variation of the fine-structure constant α. We investigate both experimentally and theoretically connecting the ground state and adjacent states of Pb XXII to Pb XXXIV and Bi X to Bi XV, respectively, covering complex couplings of electrons in the 4f and 5d shells. These and others such as nd and nf , which also contain equivalent electrons, are of interest for frequency metrology using quantum logic spectroscopy, for atomic structure and QED theory tests, and for the search for Dark Matter candidates. We infer their level structure, benchmark calculations from two different electronic structure codes, and lay the groundwork for inferring the wavelengths of forbidden transitions of higher multipolarity in the optical and VUV region.

Induced Isotensor Interactions in Heavy-Ion Double-Charge-Exchange Reactions and the Role of Initial and Final State Interactions

The role of initial state (ISI) and final state (FSI) ion–ion interactions in heavy-ion double-charge-exchange (DCE) reactions A(Z,N)→A(Z±2,N∓2) are studied for double single-charge-exchange (DSCE) reactions given by sequential actions of the isovector nucleon–nucleon (NN) T-matrix. In momentum representation, the second-order DSCE reaction amplitude is shown to be given in factorized form by projectile and target nuclear matrix elements and a reaction kernel containing ISI and FSI. Expanding the intermediate propagator in a Taylor series with respect to auxiliary energy allows us to perform the summation in the leading-order term over intermediate nuclear states in closure approximation. The nuclear matrix element attains a form given by the products of two-body interactions directly exciting the n2p−2 and p2n−2 DCE transitions in the projectile and the target nucleus, respectively. A surprising result is that the intermediate propagation induces correlations between the transition vertices, showing that DSCE reactions are a two-nucleon process that resembles a system of interacting spin–isospin dipoles. Transformation of the DSCE NN T-matrix interactions from the reaction theoretical t-channel form to the s-channel operator structure required for spectroscopic purposes is elaborated in detail, showing that, in general, a rich spectrum of spin scalar, spin vector and higher-rank spin tensor multipole transitions will contribute to a DSCE reaction. Similarities (and differences) to two-neutrino double-beta decay (DBD) are discussed. ISI/FSI distortion and absorption effects are illustrated in black sphere approximation and in an illustrative application to data.

Self-similarity of the dipole–multipole transition in rapidly rotating dynamos

The dipole–multipole transition in rapidly rotating dynamos is investigated through the analysis of forced magnetohydrodynamic waves in an unstably stratified fluid. The focus of this study is on the inertia-free limit applicable to planetary cores, where the Rossby number is small not only on the core depth but also on the length scale of columnar convection. By progressively increasing the buoyant forcing in a linear magnetoconvection model, the slow magnetic–Archimedean–Coriolis (MAC) waves are significantly attenuated so that their kinetic helicity decreases to zero; the fast MAC wave helicity, on the other hand, is practically unaffected. In turn, polarity reversals in low-inertia spherical dynamos are shown to occur when the slow MAC waves disappear under strong forcing. Two dynamically similar regimes are identified – the suppression of slow waves in a strongly forced dynamo and the excitation of slow waves in a moderately forced dynamo starting from a small seed field. While the former regime results in polarity reversals, the latter regime produces the axial dipole from a chaotic multipolar state. For either polarity transition, a local Rayleigh number based on the mean wavenumber of the energy-containing scales bears the same linear relationship with the square of the peak magnetic field measured at the transition. The self-similarity of the dipole–multipole transition can place a constraint on the Rayleigh number for polarity reversals in the Earth.

Fast and accurate excited states predictions: machine learning and diabatization.

The efficiency of machine learning algorithms for electronically excited states is far behind ground-state applications. One of the underlying problems is the insufficient smoothness of the fitted potential energy surfaces and other properties in the vicinity of state crossings and conical intersections, which is a prerequisite for an efficient regression. Smooth surfaces can be obtained by switching to the diabatic basis. However, diabatization itself is still an outstanding problem. We overcome these limitations by solving both problems at once. We use a machine learning approach combining clustering and regression techniques to correct for the deficiencies of property-based diabatization which, in return, provides us with smooth surfaces that can be easily fitted. Our approach extends the applicability of property-based diabatization to multidimensional systems. We utilize the proposed diabatization scheme to achieve higher prediction accuracy for adiabatic states and we show its performance by reconstructing global potential energy surfaces of excited states of nitrosyl fluoride and formaldehyde. While the proposed methodology is independent of the specific property-based diabatization and regression algorithm, we show its performance for kernel ridge regression and a very simple diabatization based on transition multipoles. Compared to most other algorithms based on machine learning, our approach needs only a small amount of training data.

Second quantization of many-body dispersion interactions for chemical and biological systems

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a second-quantized MBD formalism (SQ-MBD) that recasts a system of atomic quantum Drude oscillators in a Fock-space representation. SQ-MBD provides: (i) tools for projecting observables (interaction energy, transition multipoles, polarizability tensors) on coarse-grained representations of the atomistic system ranging from single atoms to large structural motifs, (ii) a quantum-information framework to analyze correlations and (non)separability among fragments in a given molecular complex, and (iii) a path toward the applicability of the MBD framework to molecular complexes with even larger number of atoms. The SQ-MBD approach offers conceptual insights into quantum fluctuations in molecular systems and enables direct coupling of collective plasmon-like MBD degrees of freedom with arbitrary environments, providing a tractable computational framework to treat dispersion interactions and polarization response in intricate systems.

Manipulation of Giant Multipole Resonances via Vortex γ Photons.

Traditional photonuclear reactions primarily excite giant dipole resonances, making the measurement of isovector giant resonances with higher multipolarities a great challenge. In this Letter, the manipulation of collective excitations of different multipole transitions in even-even nuclei via vortex γ photons is investigated. We develop the calculation method for photonuclear cross sections induced by the vortex γ photon beam using the fully self-consistent random-phase approximation plus particle-vibration coupling (RPA+PVC) model based on Skyrme density functional. We find that the electromagnetic transitions with multipolarity J<|m_{γ}| are forbidden for vortex γ photons due to the angular momentum conservation, with m_{γ} being the projection of total angular momentum of γ photon on its propagation direction. For instance, this allows for probing the isovector giant quadrupole resonance without interference from dipole transitions using vortex γ photons with m_{γ}=2. Furthermore, the electromagnetic transition with J=|m_{γ}|+1 vanishes at a specific polar angle. Therefore, the giant resonances with specific multipolarity can be extracted via vortex γ photons. Moreover, the vortex properties of γ photons can be meticulously diagnosed by measuring the nuclear photon-absorption cross section. Our method opens new avenues for photonuclear excitations, generation of coherent γ photon laser and precise detection of vortex particles, and consequently, has significant impact on nuclear physics, nuclear astrophysics and strong laser physics.

Level structure and transition multipolarities of 54Mn

Excited states up to 3 MeV in the odd-odd 54Mn have been populated in the 54Cr(p,n)54Mn reaction at Ep = 4.5 MeV. Conversion coefficients (αK and απ ) were deduced using the NPG method for the first time in 54Mn. Multipolarities were unambiguously assigned in 16 transitions for the first time using the obtained conversion coefficient values. Spin and parity has been restricted for three transitions.

Calculations of multipole transitions in Sn II for kilonova analysis

We use the method that combines linearized coupled-cluster and configuration interaction approaches for calculating energy levels and multipole transition probabilities in singly ionized tin ions. We show that our calculated energies agree very well with the experimental data. We present probabilities of magnetic dipole and electric quadrupole transitions and use them for the analysis of the AT2017gfo kilonova emission spectra. This study demonstrates the importance and utility of accurate atomic data for forbidden transitions in the examination of future kilonova events.Graphical abstract

Multipole theory of optical spatial dispersion in crystals

Natural optical activity is the paradigmatic example of an effect originating in the weak spatial inhomogeneity of the electromagnetic field on the atomic scale. In molecules, such effects are well described by the multipole theory of electromagnetism, where the coupling to light is treated semiclassically beyond the electric-dipole approximation. That theory has two shortcomings: it is limited to bounded systems, and its building blocks -the multipole transition moments- are origin dependent. In this work, we recast the multipole theory in a translationally-invariant form that remains valid for crystals. Working in the independent-particle approximation, we introduce "intrinsic" multipole transition moments that are origin independent and transform covariantly under gauge transformations of the Bloch eigenstates. Electric-dipole transitions are given by the interband Berry connection, while magnetic-dipole and electric-quadrupole transitions are described by matrix generalizations of the intrinsic magnetic moment and quantum metric. In addition to multipole-like terms, the response of crystals at first order in the wavevector of light contains band-dispersion terms that have no counterpart in molecular theories. The full response is broken down into magnetoelectric and quadrupolar parts, which can be isolated in the static limit where electric and magnetic fields become decoupled. The rotatory-strength sum rule for crystals is found to be equivalent to the topological constraint for a vanishing chiral magnetic effect in equilibrium, and the formalism is validated by numerical tight-binding calculations.

The interplay of single-particle and collective motions in the low-lying states of $$_\Lambda ^{21}$$ with quadrupole-octupole correlations

The beyond mean-field approach for low-lying hypernuclear states is extended by mixing the configurations associated with both single-particle and quadrupole-octupole collective excitations within the generator coordinate method based on a covariant density functional theory. The method is demonstrated in the application to the low-lying states of $$_\Lambda ^{21}$$ , where the configurations with the Λ hyperon occupying the first (Λs) and second (Λp) lowest-energy states are considered. The results indicate that the positive-parity states are dominated by the α + 12C + α + Λs structure. In contrast, the low-lying negative-parity states are dominated by a strong admixture of α +16O + Λs structure and α + 12C + α + Λp structure due to the inclusion of octupole correlations. As a result, the low-lying negative-parity states become much lower than what is expected from the previous studies without the mixing, and the electric multipole transition strengths are significantly quenched.

Spherical vector waves: their generation using a 4π optical array

Spherical vector waves (SVW) are the natural basis that correlates internal multipole transitions of atomic systems to specific configurations of the electromagnetic field. We theoretically identify the SVW fields that could be approximately generated from incident cylindrical beams using a 4π optical array. A comparison is made between the near electromagnetic field of ideal SVW to that of the spherical spots generated by cylindrical incident laser beams with the selected angular spectra and a finite lens aperture of the 4π system. The fidelity is taken as figure of merit. Some challenges on the implementation of the SVW are briefly discussed.

Photon angular distribution of radiative electron capture into high-Z projectiles: A brief review

With the revolutionary development in the design of heavy-ion cooler storage rings and detectors, increasing interest is being focused on ion-atom collisions, in which the projectiles with a velocity comparable to the speed of light and the electronic transitions in inner shells of high-[Formula: see text] ions are involved. For this purpose, a fundamental interaction mechanism between a photon and an atomic electron in the presence of a strong Coulomb field is reviewed from the perspective of radiative electron capture into highly-charged ions. This is followed by the discussions of photon-electron interactions beyond the dipole approximation, which can be unambiguously visible in the photon angular distributions. In addition, the interference between the leading electric dipole transition [Formula: see text] and the magnetic multipole transition [Formula: see text] for the case of Lyman-[Formula: see text] radiation in hydrogen-like projectiles is also discussed.

Atlas of nuclear isomers—Second edition

We present an updated version of the 2015-Atlas of Nuclear Isomers (Jain et al., 2015), compiling and evaluating experimental data for the isomers with half-life ≥ 10 ns, together with their spectroscopic properties such as excitation-energies, half-lives, decay modes, spins and parities, energies and multipolarities of isomeric transitions, along with the relevant original references in literature. The current version of Atlas presents many re-evaluated half-lives as compared to the 2015 edition, where values were referred to Nuclear Data Sheets publications, when no new data existed. The ENSDF database (Burrows, 1990), together with the XUNDL (XUNDL database, http://www.nndc.bnl.gov/ensdf/ensdf/xundl.jsp) and the NUBASE2020 (Kondev et al., 2021) databases have been consulted for completeness, yet, data from original papers from journals were considered in the present evaluation, and the NSR bibliographic database (Pritychenko et al., 2011) has been searched to ensure that this work is as complete and current as possible. Several useful systematic features of nuclear isomers covered in this Atlas have been discussed. Literature cutoff date for the extraction of data is October 31, 2022.

Toroidal optical transitions in hydrogen-like atoms.

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions involving electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also involve toroidal multipoles-toroidal absorption lines have been observed in electromagnetic metamaterials. Here, we show that a previously unexplored type of spectroscopy of the hitherto largely neglected toroidal dipolar interaction becomes feasible if, apart from the classical r × r × p toroidal dipole density term responsible for the toroidal transitions in metamaterials, the spin-dependent r × σ term (which only occurs in relativistic quantum mechanics) is taken into account. Toroidal dipole operators are odd under parity and time-reversal symmetries; toroidal dipole transitions can therefore be distinguished from electric multipole and magnetic dipole transitions.