Electric Multipole Transitions Research Articles

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.

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.

Energy levels, lifetimes and transition data for Cu-like Nd[formula omitted] to Br-like Nd[formula omitted] ions

We have performed calculations for Cu-like to Br-like neodymium (Nd) ions using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) approaches. An extensive set of fine structure energy levels, lifetimes, wavelengths, and radiative transitions for electric and magnetic multipole transitions is provided. We systematically include the electronic correlation effects between valence electrons and two subshells of core electrons. In the RCI procedure, both the Breit interaction and the leading quantum electrodynamic effects are taken into account. The reliability and accuracy are confirmed by comparing our results to accessible experimental and theoretical data.

Photonic Chern insulators from two-dimensional atomic lattices interacting with a single surface plasmon polariton

We study the polaritonic bandstructure of two-dimensional atomic lattices coupled to a single excitation of a surface plasmon polariton mode. We show the possibility of realizing topological gaps with different Chern numbers by having resonant atomic transitions to excited states with different angular momentum. We employ a computational method based on the recently proposed Dirichlet-to-Neumann (DtN) map technique which accurately models non-Markovian dynamics as well as interactions involving higher-order electric and magnetic multipole transitions. We design topologically robust edge states which are used to achieve unidirectional emission and non-reciprocal transmission of single photons. We also point out the challenges in realizing bands with higher Chern numbers in such systems.

Astrophysical S-factor of the ${d(\alpha ,\gamma )^{6}Li}$ process by Effective Field Theory

Radiative capture reaction $d(\alpha ,\gamma )^{6}Li $ is the only process in the Big-Bang model that produces ${}^{6}Li $. We develop the formalism based on pionless Effective Field Theory (EFT) for deuteron-alpha scattering to derive the cross-section of deuteron-alpha radiative capture. Based on this model, nucleons and alpha particle interact through separable two-body forces. The alpha particle is assumed point particle and the astrophysical S-factor for the $d(\alpha ,\gamma )^{6}Li $ reaction is calculated in the low-energies. The coulomb effects are also considered as a coulomb correction in the cross-section for two first electric multipole transitions, up to Next to Leading Order (NLO). The obtained results are shown a satisfactory agreement between theoretical and experimental results for the calculated observables.

Electric Multipole Transitions of Resonant X-ray Scattering for Studying Orbital Specific Magnetization in TmB4

Strongly intertwined interaction among spin, orbital and charge degrees of freedom is the essence to induce emergent materials properties, and the investigation to understand their interplay has been actively pursued. In particular, resonant X-ray scattering technique has demonstrated powerful applications in unveiling their long-range ordering behavior with its enhanced sensitivity to the aforementioned degree of freedom. Here, we further demonstrated the spectroscopic application of the technique by providing experimental evidence to reveal spin polarizations in 4f and 5d orbital of the magnetic Tm ions with the orbital-selectivity, which introduced a route to understand fundamental mechanism of spin polarization in the compound. The enhanced sensitivity of the resonant X-ray scattering to various electric multipole transitions expects to find strong applications in studying various spin and polar ordering in materials to include high-order moments.

Energy levels, oscillator strengths, radiative transition probabilities, level lifetimes and electron-impact excitation rate coefficients for Ne-like Mo XXXIII

The energy levels, oscillator strengths, radiative decay rates, lifetimes, collision strengths, direct and resonance electron-impact excitation rate coefficients have been computed for the 257 fine-structure levels arising from 1s22s22p5nl and 1s22s2p6n′l′ configurations belonging to the Mo32+ ion with n≤7, l≤4 and n′≤5, l′≤4. The model-potential approach is used for the target ion structure calculations. Additionally, we employ the multiconfiguration Dirac–Hartree–Fock method to further assess the energy levels and transition probabilities. The collision strengths for the electron-impact direct excitation are computed within the relativistic distorted-wave approximation at 34, 135, 680, 1700, 5436, and 12,740 eV scattered electron energy values. We also perform collision calculations at 85, 175, and 450 keV electron energies using the plane-wave approximation and interpolate the reduced cross section within Fano plots, thus accounting for relativistic effects at asymptotic energies. This assures the convergence of Maxwellian integration for effective collision strengths calculation at electron temperatures up to 80 keV. The resonance contribution to the excitation rates is accounted for within the independent process isolated resonance approximation by including Na-like Mo31+ doubly excited autoionization states arising from the 1s227nln′l′ configurations with n≤7,l≤4,n′≤20,l′≤8. Contributions from high n′≥21 Rydberg states to the excitation rate coefficients are included by employing the n′−3 extrapolation law for radiative and autoionization decay rates. Radiative decay of resonances to lower autoionization states followed by autoionization cascade as well as radiative damping via core transitions are included in our model. The highest rate coefficients corresponding to ground state excitations are the 2p–3d allowed and 2p–3p electric monopole transitions, respectively. Intercombination and generally higher-order electric multipole transitions amount to lower excitation rate coefficients but are not to be neglected. Magnetic transitions are only relevant for low electron temperatures since both their direct and resonance contributions to excitation significantly decrease with increasing electron energy. Present results compare well with existing data from literature. The resonance contributions play an important role in the accuracy of rate coefficients, especially for weak forbidden transitions at low electron temperatures. These results may be useful in fusion related plasmas, astrophysics and fundamental physics.

Ambit: A programme for high-precision relativistic atomic structure calculations

We present the ambit software package for general atomic structure calculations. This software implements particle–hole configuration interaction with many-body perturbation theory (CI+MBPT) for fully relativistic calculations of atomic energy levels, electric- and magnetic-multipole transition matrix elements, g-factors and isotope shifts. New numerical methods and modern high-performance computing techniques employed by this software allow for the calculation of open-shell systems with many valence-electrons (N≥5) to a high degree of accuracy and in a highly computationally efficient manner. Program summaryProgram Title:ambitProgram Files doi:http://dx.doi.org/10.17632/7xfxhr9mg6.1Licensing provisions: GPLv3Programming language: C++11Nature of problem: Calculation of atomic/ionic spectra, including energy levels, electric and magnetic multipole transition matrix elements, and isotope shifts.Solution method: The programme calculates energy levels and wavefunctions using either configuration interaction (CI) only, or CI with many-body perturbation theory (CI+MBPT) in the Brillouin–Wigner MBPT formalism.Restrictions: The programme is not designed to treat highly-excited (Rydberg) states or continuum processes to a high degree of accuracy.Additional comments: Programme github repository

First-principles modeling of x-ray Raman scattering spectra

X-ray Raman scattering (XRS) spectroscopy is a rapidly developing synchrotron-based technique employed to probe the local electronic structure of condensed matter. The use of hard x-rays makes XRS particularly well-suited for studying low-energy edges of bulk materials, even under highly absorbing sample environments, opening up a wealth of possibilities for $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ experiments. Here, the authors propose an efficient method for calculating $K$-edge XRS spectra, developed within the framework of density functional theory and designed to fully account for the electric multipole transitions observed when a finite momentum is transferred to the photoelectron.

Analyzing supersymmetric transformed α-nucleus potentials with electric-multipole transitions

Alpha(4He or α)-cluster models have often been used to describe light nuclei. Towards the application to multi-cluster systems involving heavy clusters, we study the relative wave functions of the α+16O and α+40Ca systems generated from phase-shift-equivalent potentials. In general, a potential between clusters is deep accommodating several redundant bound states which should be removed in an appropriate way. To avoid such a complicated computation, we generate a shallow-singular potential by using supersymmetric transformations from the original deep potential. Changes in the relative wave functions by the transformations are quantified with electric-multipole transitions which give a different radial sensitivity to the wave function depending on their multipolarity. Despite the fact that the original and transformed potentials give exactly the same phase shift, some observables are unfavorably modified. A possible way to obtain a desired supersymmetric potential is proposed.

Selection rules for electric multipole transition of triatomic molecule in scattering experiments**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant No. U1732133), and the Science Fund from Chinese Academy of Sciences (Grant No. 11320101003).

In the electron or x-ray scattering experiment, the measured spectra at larger momentum transfer are dominated by the electric dipole-forbidden transitions, while the corresponding selection rules for triatomic molecules have not been clearly elucidated. In this work, based on the molecular point group, the selection rules for the electric multipolarities of the electronic transitions of triatomic molecules are derived and summarized into several tables with the variation of molecular geometry in the transition process being considered. Based on the summarized selection rules, the electron energy loss spectra of H2O, CO2, and N2O are identified, and the momentum transfer dependence behaviors of their valence-shell excitations are explained.

Molecular-frame EELS experiment on inner-valence ionization of N2

SynopsisWe report molecular-frame electron scattering cross sections of N2, obtained using an electron-ion coincidence technique. The vector correlation between the scattered electron and the fragment ion has been measured at incident electron energy of 1.4 keV for inner-valence ionization of N2. The angular distributions of the electron scattering cross sections thus obtained exhibit clear momentum transfer dependence, indicating the significant change of the ionization dynamics due to contributions from electric multipole transitions.

Excitation enhancement in electric multipole transitions near a nanoedge.

We investigate enhancement of electric multipole excitations of atoms in the vicinity of an object with a nanoscale edge resulted from a large electromagnetic field gradient. We calculate the excitation efficiencies of a Rb atom around a nanoedge and find the excitations are enhanced by several orders of magnitude. The efficiencies with the change in the magnetic quantum number resolved are also examined. Each resolved efficiency shows rotationally symmetric spatial distribution, with continuous modification in shape from the far field to the near field. Furthermore, we estimate photon emission rates accompanied with multipole excitations in alkali (Rb and Cs) atoms and discuss the possibility to observe the enhancement in the multi-pole excitation in cold atoms.

Novel triaxial structure in low-lying states of neutron-rich nuclei aroundA≈100

Background: In recent years, the study of triaxiality in the low-lying states of atomic nuclei with transition character or shape coexistence has been of great interest. Previous studies indicate that the neutron-rich nuclei in the $A\ensuremath{\sim}100$ mass region with $Z\ensuremath{\sim}40,N\ensuremath{\sim}60$ serve as good grounds for examining the role of triaxiality in nuclear low-lying states.Purpose: The aim of this work is to provide a microscopic study of low-lying states for nuclei in the $A\ensuremath{\sim}100$ mass regions and to examine in detail the role of triaxiality in the shape-coexistence phenomena and the variation of shape with the isospin and spin values at the beyond mean-field level.Method: The starting point of our method is a set of relativistic mean-field plus BCS wave functions generated with a constraint on triaxial deformations $(\ensuremath{\beta},\ensuremath{\gamma})$. The excitation energies and electric multipole transition strengths of low-lying states are calculated by solving a five-dimensional collective Hamiltonian (5DCH) with parameters determined by the mean-field wave functions.Results: The low-lying states of Mo isotopes and of $N=60$ isotones in the $A\ensuremath{\sim}100$ mass region are calculated. The results indicate that triaxiality is essential to reproduce the data of excitation energies and electric quadrupole transition strengths in low-lying states and plays an important role in the shape evolution as a function of nucleon number. However, the decrease of nuclear collectivity with the increase of angular momentum in neutron-rich Mo isotopes has not been reproduced.Conclusions: The evolution of nuclear collectivity in the low-lying states of neutron-rich nuclei in the $A\ensuremath{\sim}100$ mass region as a function of nucleon number is governed by the novel triaxial structure. However, the mechanism that governs the variation of nuclear shape with spin in Mo isotopes remains unclear and deserves further investigation by taking into account the effects other than the collective motions.

Anatomy of molecular structures in 20Ne

We present a beyond mean-field study of clusters and molecular structures in low-spin states of 20Ne with a multireference relativistic energy density functional, where the dynamical correlation effects of symmetry restoration and quadrupole–octupole shapes fluctuation are taken into account with projections on parity, particle number and angular momentum in the framework of the generator coordinate method. Both the energy spectrum and the electric multipole transition strengths for low-lying parity-doublet bands are better reproduced after taking into account the dynamical octupole vibration effect. Consistent with the finding in previous studies, a rotation-induced dissolution of the α+O16 molecular structure in 20Ne is predicted.

Variance and shift of transition arrays for electric and magnetic multipole transitions

Generalized analytical expressions for the two-electron relativistic Unresolved-Transition-Array (UTA) energy variance and shift for electric and magnetic transitions of general multipole order are presented. The revised expressions are shown to agree with the exact moments calculated directly from the energy levels of two-electron configurations. We show that for electric transitions of even multipole order and for magnetic transitions, the available expressions in the literature, which are implemented in widely used atomic codes, are incorrect. We suggest an alternative method for the calculation of the UTA energy variance and shift by using the analytical expressions for the two-electron energy levels and line-strengths. The method is much more efficient and simple than the use of the traditional lengthy analytic expressions. Finally, the effect of UTA widths on Super-Transition-Array (STA) spectral opacity is shown for several examples.

Selection rules for electric multipole transition of diatomic molecule in scattering experiments**Project supported by the National Natural Science Foundation of China (Grant Nos. U1332204, 11274291, and 11320101003).

The knowledge of the energy level structures of atoms and molecules is mainly obtained by spectroscopic experiments. Both photoabsorption and photoemission spectra are subject to the electric dipole selection rules (also known as optical selection rules). However, the selection rules for atoms and molecules in the scattering experiments are not identical to those in the optical experiments. In this paper, based on the theory of the molecular point group, the selection rules are derived and summarized for the electric monopole, electric dipole, electric quadrupole, and electric octupole transitions of diatomic molecules under the first Born approximation in scattering experiments. Then based on the derived selection rules, the electron scattering spectra and x-ray scattering spectra of H2, N2, and CO at different momentum transfers are explained, and the discrepancies between the previous experimental results measured by different groups are elucidated.

Resonant X-ray scattering study of spinel Co2MnO4

X-ray resonant enhancement of the (200) crystallographically forbidden reflection in the inverse cubic spinel Co2MnO4 single crystal is presented. Anisotropic X-ray scattering results near the K absorption edges of both Co and Mn ions observed in the azimuthal angle dependence are interpreted with the anisotropic tensorial character of the X-ray susceptibility. Spectra calculations including the various electric multipole transition channels, such as dipole-dipole (E1-E1), dipole-quadrupole (E1-E2), and quadrupole-quadrupole (E2-E2), in two different polarization states of σ − σ and σ − π are discussed and compared with the experimental data to determine the channel of major contribution in the resonant scattering intensity.

Microscopic benchmark study of triaxiality in low-lying states of76Kr

We report on a seven-dimensional generator coordinate calculation in the two deformation parameters $\beta$ and $\gamma$ together with projection on three-dimensional angular momentum and two particle numbers for the low-lying states in $^{76}$Kr. These calculations are based on covariant density functional theory. Excellent agreement is found with the data for the spectrum and the electric multipole transition strengths. This answers the important question of dynamic correlations and triaxiality in a fully microscopic way. We find that triaxial configurations dominate both the ground state and the quasi $\gamma$-band. This yields a different picture from the simple interpretation in terms of "coexistence of a prolate ground state with an oblate low-lying excited state", which is based on the measured sign of spectroscopic quadrupole moments. This study also provides for the first time a benchmark for the collective Hamiltonian in five dimensions. Moreover, we point out that the staggering phase of the $\gamma$-band is not a safe signature for rigid triaxiality of the low-energy structure.

Does a proton “bubble” structure exist in the low-lying states of 34Si?

The possible existence of a “bubble” structure in the proton density of 34Si has recently attracted a lot of research interest. To examine the existence of the “bubble” structure in low-lying states, we establish a relativistic version of configuration mixing of both particle-number and angular-momentum projected quadrupole deformed mean-field states and apply this state-of-the-art beyond relativistic mean-field method to study the density distribution of the low-lying states in 34Si. An excellent agreement with the data of low-spin spectrum and electric multipole transition strengths is achieved without introducing any parameters. We find that the central depression in the proton density is quenched by dynamic quadrupole shape fluctuation, but not as significantly as what has been found in a beyond non-relativistic mean-field study. Our results suggest that the existence of proton “bubble” structure in the low-lying excited 02+ and 21+ states is very unlikely.