Electric Quadrupole Transition Research Articles

Relativistic atomic structure calculations of Li-like ions used for plasma diagnostic studies

Abstract We have carried out atomic structure calculations using systematically enlarged multiconfiguration Dirac- Fock wavefunctions of Li-like ions of the most prominent plasma impurities (Ar, Ti, Fe, Ni, Kr and W) found in presently working tokamaks. Relativistic Breit interaction and quantum electrodynamic (QED) corrections such as vacuum polarization and self-energy corrections are also included in the calculations prior to the evaluation of low lying energy levels, transition probabilities, oscillator strengths and line strengths. Selective radiative data for electric dipole and magnetic quadrupole transitions are also reported. Special emphasis is given in the computations of fundamental quantities such as oscillator strengths as they are widely used in atomic data and analysis structure (ADAS) databases to evaluate quantities such as effective collision strengths. Present com- puted values are compared with existing available results on NIST database and few similar earlier computations and a good agreement has been found. We believe that the detailed atomic data with the relativistic and QED corrections will assist in spectroscopic studies such as accurate line identification and plasma modelling work in tokamak plasma, laser induced breakdown spectroscopy (LIBS), highly charged ions clocks and astrophysical observations.

Large-scale relativistic calculations of spectral data in Zr XXVIII, Nb XXIX and Tc XXXI of tokamak interest

Large-scale relativistic multiconfiguration Dirac–Fock calculations of energy levels and lifetimes of the 206 states arising from the 3s23p, 3p3, 3s3p3d, 3p3d2, 3s24p, 3s24f, 3s3p2, 3s23d, 3s3d2, 3s24d, 3s24s, 3s3p4s, 3s3p4d, 3p23d, 3d3, and 3s3p4p configurations of Zr XXVIII, Nb XXIX, and Tc XXXI of tokamak interest are carried out. The active space approximation is employed for the calculations. To obtain accurate and convergent results, the calculations take into account the valence and core-valence correlations within the n= 9 complex, as well as the Breit interaction, self-energy corrections, and vacuum polarization corrections. Detailed information regarding the decay properties of these ions is provided, including the transition wavelengths, line strengths, and radiative transition rates for various types (electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole transitions) of transitions among the levels of the aforementioned configurations. The uncertainties of each dipole transition are evaluated. The present data sets are compared to previous results and a good agreement is observed, which is valuable for emission line identification and fusion modeling, especially in situations where experimental data are scarce.

Study of Octupole Transitions in Xe, Ba, Ce and Nd Nuclei within Interacting Boson Model

For nuclei with 54≤Z≤60 and 86≤N≤94, the results regarding the excitation spectra at low energies, both in positive and negative parity, as well as the transition probabilities for electric dipole (B(E1)), quadrupole (B(E2)), and octupole transitions (B(E(3)), indicate the emergence of significant octupole behavior. These observations have been made using the Interacting Boson Model-1 (IBM-1). The study examines the onset of octupole deformation and its impact on the spectroscopic characteristics in even-even neutron-rich lanthanide isotopes, specifically in the Ba and Nd nuclei. The investigation compares the results obtained from the Interacting Boson Model-1 (IBM-1) with the existing experimental data. The focus is on understanding how the addition of neutrons influences the development of octupole deformation and its manifestation in the observed spectroscopic features. The onset of strong octupolarity for Z≈ 56 and N ≈ 88 nuclei is indicated by the results obtained for the electric dipole, quadrupole, and octupole transition probabilities, as well as the low-energy positive and negative-parity excitation spectra. Conversely, discrepancies between the spectroscopic data and the IBM results suggest that the mapping quality needs to be evaluated in order to determine if the mapped boson Hamiltonian or the fermionic calculations are the source of the issues.

Calculation of forbidden transitions in doubly ionized neodymium (Nd III) of interest for kilonova nebular phase analysis

In this paper, we present new radiative rate calculations for forbidden transitions, namely magnetic dipole (M1) and electric quadrupole (E2) transitions, involving all the experimentally known energy levels within the 4f4 ground configuration of doubly ionized neodymium (Nd III). To do this, and in order to estimate the accuracy of the results obtained, two independent computational approaches based on the pseudo-relativistic Hartree–Fock and the fully relativistic Dirac-Hartree–Fock methods were used. The transition probabilities calculated with these two approaches showed good overall agreement, in particular for the most intense forbidden lines for which the relative differences did not exceed 25%. From these new atomic data, some astrophysical implications were deduced such as the possibility (or not) of observing some [Nd III] lines on the infrared spectra recorded by the James Webb Space Telescope, more precisely for the analysis of nebular phase kilonova spectra following compact object mergers.

Measurement of infrared magic wavelength for an all-optical trapping of 40Ca+ ion clock

For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4s2S1/2→3d2D5/2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.

First detection and absolute transition frequencies in the (3-0) band of D2.

Three electric quadrupole transitions in the second overtone band of D2 are newly measured by comb-referenced cavity ring down spectroscopy around 1.18 µm. These extremely weak transitions (line intensities smaller than 10-29 cm/molecule) are the first to be detected in the (3-0) band of D2. The spectra of the O(3), O(2), and Q(2) lines near 8321, 8446, and 8607cm-1, respectively, are recorded at room temperature for pressure values ranging between 100 and 600 Torr. Accurate transition frequencies and line intensities of the three D2 transitions are determined from a line fitting procedure using beyond-Voigt profiles, including strong Dicke narrowing. Considering statistical fit errors and possible biases due to the interference with water lines (which are six orders of magnitude stronger than the studied D2 lines), total uncertainties on the frequencies extrapolated at zero pressure are estimated below 14MHz (∼4.7 × 10-4cm-1). The derived experimental frequencies and intensities are compared to abinitio values. An overall agreement is achieved, confirming the positional accuracy of the most advanced theoretical calculations.

Extended calculations of energy levels and transition rates for Yb LVII

Abstract Extended energy levels and transition data for the Yb LVII are calculated with the GRASP2018 package, which is based on the multiconfiguration Dirac–Hartree–Fock and relativistic configuration methods. Complete and consistent data sets of energy levels, transition rates and lifetimes for electric-dipole (E1), electric-quadrupole (E2), magnetic-dipole (M1), and magnetic-quadrupole (M2) transitions among all these levels are given in this calculation. Three methods of uncertainty estimators are used to evaluate the accuracy of transition data. The computed results are also compared with other theoretical computations. The present results are reported as benchmarks for future calculations and measurements.

The 5P3/2→6PJ(J=1/2,3/2) Electric Dipole Forbidden Transitions in Rubidium

This paper presents a general review of the results of the experimental and theoretical work carried out by our research group to study the 5P3/2→6PJ electric quadrupole transition in atomic rubidium. The experiments were carried out with room-temperature atoms in an absorption cell. A steady-state population of atoms in the 5P3/2 excited state is produced by a a narrow-bandwidth preparation laser locked to the D2 transition. A second CW laser is used to produce the forbidden transition with resolution of the 6PJ hyperfine states of both rubidium isotopes. The process is detected by recording the 420(422) nm fluorescence that occurs when the atoms in the 6PJ state decay directly into the 5S ground state. The fluorescence spectra show a strong dependence on the relative polarization directions of the preparation laser and the beam producing the forbidden transition. This dependence is directly related to a strong anisotropy in the populations of the 5P3/2 intermediate magnetic substates, and also to the electric quadrupole selection rules over magnetic quantum numbers. A calculation based on the rate equations that includes velocity and detuning dependent transition rates is adequate to reproduce these results. The forbidden transition is also shown to be an ideal probe to measure the Autler–Townes splitting generated in the preparation of the 5P3/2 state. Examples of spectra obtained with cold atoms in a magneto-optical trap (MOT) are also presented. These spectra show the expected Autler–Townes doublet structure with asymmetric line profiles that result as a consequence of the red-detuning of the trapping laser in the MOT.

Wavelengths and E1, E2, M1, and M2 line strengths in Nb XXX

The calculations are performed to calculate the excitation energies, wavelengths, line strengths, transition probabilities, and weighted oscillator strengths for the electric-dipole (E1), electric-quadrupole (E2), magnetic-dipole (M1), and magnetic-quadrupole (M2) transitions between the lowest 301 fine-structure levels of the 3snl (n = 3 − 6, l = 0 − 5), 3pnl (n = 3 − 5, l = 0 − 4), and 3dnl (n = 3 − 5, l = 0 − 4) configurations in Mg-like niobium, Nb XXX. In addition, the level designations in the LS- and jj-coupling schemes and lifetimes are presented. The calculations are carried out using the GRASP2018 atomic structure package which is based on the multiconfiguration Dirac-Hartree-Fock (MCDHF) method, with the contributions of the Breit interaction and quantum electrodynamics (QED) corrections included. The accuracy of the present energies, lifetimes, and transition data is calculated utilizing a comparison of the results from the present MCDHF largest layers from two different approaches, as well as the comparison with theoretical and experimental data that are currently accessible.

The vortex light induced electric dipole and electric quadru-pole transition in Ca atom

The Laguerre–Gaussian beam induced electric transition model is presented. The major mechanism of angular momentum exchange between the light and the atomic system is discussed. The influence of the topological charge on the transition probability and selection rules is obtained. Our results show that the Ca(4s2 1S0–4s3d 1D2) electric quadrupole transition selection rules are sensitive to the sign of l, and the center of mass transition selection rules are governed by the topological charge l of the light. The electric dipole transition is possible in a field with topological charge l > 0, and the quadrupole transition is no longer forbidden. The overall transition probability difference between dipole transition and quadrupole transition can be decreased by the joint action of the light angular momentum exchange with the external and the internal motion.

Electromagnetic properties of Λ hypernuclei with a beyond relativistic mean-field approach

We present a microscopic study of electromagnetic properties of the low-lying states of single-Λ hypernucleus Λ9Be using a quantum-number projected generator coordinate method (HyperGCM) based on covariant density functional theory. All the configurations are restricted to have axial symmetry, with the Λ hyperon in the lowest-energy state. The results are compared to the predictions of a simple particle-rotor model (PRM), for which analytic expressions are available. We show that the electromagnetic properties of Λ9Be from the HyperGCM calculation are close to those by the PRM. In particular, it is found that the magnetic moments and M1 transition strengths are less sensitive to the coupling strengths of the ΛN interaction than the electric quadrupole transition strengths. The latter may provide additional constraints on the ΛN interaction.

Absorption of hybrid fibre modes by Cs atoms in quadrupole transitions

We evaluate the rate of the absorption of an optical nanofibre mode by a Cs atom in an electric quadrupole transition. With the Cs atom localised near the outer surface of the optical nano-fibre, an interaction occurs between the atomic quadrupole tensor components and the gradients of the vector components of the electric field of a hybrid fibre mode. The absorption rate is evaluated as a function of the radial position of the atom from the fibre axis, assuming a specific value of the laser power and we use experimentally accessible parameters. We find that the absorption of the hybrid modes by the Cs atom decreases as the atom recedes away from the fibre axis and it formally vanishes at sufficiently large radial distances. Close to the fibre, however, the absorption rate for the input power chosen can be two orders of magnitude larger than the quadrupole de-excitation rate despite the moderate power used.

Quadrupole Effects in the Photoionisation of Sodium 3s in the Vicinity of the Dipole Cooper Minimum

A procedure to obtain relativistic expressions for photoionisation angular distribution parameters using the helicity formulation is discussed for open-shell atoms. Electric dipole and quadrupole transition matrix elements were considered in the present work, to study the photoionisation dynamics of the 3s electron of the sodium atom in the vicinity of the dipole Cooper minimum. We studied dipole–quadrupole interference effects on the photoelectron angular distribution in the region of the dipole Cooper minimum. Interference with quadrupole transitions was found to alter the photoelectron angular distribution, even at rather low photon energies. The initial ground and final ionised state discrete wavefunctions of the atom were obtained in the present work using GRASP, and we employed RATIP with discrete wavefunctions, to construct continuum wavefunctions and to calculate transition amplitudes, total cross-sections and angular distribution asymmetry parameters.

Study of the velocity-selection satellites present in the () electric quadrupole transitions in atomic rubidium

This article presents detailed experimental and theoretical studies of the satellite fluorescence lines observed when the , (, ) electric quadrupole transition (E2) is excited in a room temperature vapor of rubidium atoms. The initial state of this E2 transition is prepared by a narrow linewidth (9 MHz) laser locked to one of the dominant D2 hyperfine excitations for zero-velocity atoms. Effects due to the selection of different atomic velocity classes in this preparation step are responsible for the presence of several satellite lines that can be found in the fluorescence decay spectra of both 85Rb and 87Rb. Compared to the main lines, these satellites do not show a strong dependence on the relative linear polarization directions of the lasers used in the preparation and the electric quadrupole steps. The relative intensities of the satellites decrease as the intensity of the preparation laser increases. Results of a rate equation calculation that explicitly includes selection-of-velocity effects indicate that optical pumping plays a central role in determining the relative intensities and the polarization dependence of the satellite lines. When the preparation laser is locked to the low-F cyclic transition in 87Rb, six lines were found in addition to the lone electric quadrupole transition for zero velocity atoms. In this case, the calculated spectrum is necessary for the correct interpretation of the experimental results, clearly indicating that optical pumping and selection of velocities are responsible for these six additional electric quadrupole lines.

Nuclear Shape-Phase Transition From Spherical U(5) to Deformed gamma-Unstable O(6) Dynamical Symmetries of Interacting Boson Model Applied to Ru, Pd, and Xe Isotopic Chains

The shape transition from spherical vibrator U(5) to gamma-unstable deformed rotor O(6) in even-even Ru, Pd, and Xe isotopic chains are studied in framework of sd interacting boson model (IBM1) using the coherent state formalism to obtain the potential energy surfaces (PES’s). The location of critical points in the transition are identified by analysis the PES’s in terms of the deformation parameter beta and by using the catastrophe theory in terms of the two essential parameters (r_1, r_2). By using the most general IBM1 Hamiltonian in Casimir form with neglecting the U(5) and SU(3) quadratic Casimir operators and introducing only one control parameter the PES leads to the same energy surface as the Q-consistent IBM Hamiltonian at gamma =0. For the studied isotopic chains, the chi ^2-test is used to perform the fitting between the experimental and the corresponding calculated IBM for some selected energy levels and electric quadrupole transition probabilities B(E2) values using a simulated search program. A good agreement is produced for both energies and B(E2) transition rates. The present model calculations suggest that ^{100}Ru, ^{102}Pd and ^{130}Xe nuclei are good candidates for the E(5) critical point symmetry.

Benchmarking calculations of excitation energies and transition properties with spectroscopic accuracy of highly charged ions used for the fusion plasma and astrophysical plasma

Atomic radiative data such as excitation energies, transition wavelengths, radiative rates, and level lifetimes with high precision are the essential parameters for the abundance analysis, simulation, and diagnostics in fusion and astrophysical plasmas. In this work, we mainly focus on reviewing our two projects performed in the past decade. One is about the ions with Z ≲ 30 that are generally of astrophysical interest, and the other one is about the highly charged krypton (Z = 36) and tungsten (Z = 74) ions that are relevant in research of magnetic confinement fusion. Two different and independent methods, namely, multiconfiguration Dirac–Hartree–Fock (MCDHF) and the relativistic many-body perturbation theory (RMBPT) are usually used in our studies. As a complement/extension to our previous works for highly charged tungsten ions with open M-shell and open N-shell, we also mainly focus on presenting and discussing our complete RMBPT and MCDHF calculations for the excitation energies, wavelengths, electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2), and magnetic quadrupole (M2) transition properties, and level lifetimes for the lowest 148 levels belonging to the 3l 3 configurations in Al-like W61+. We also summarize the uncertainties of our systematical theoretical calculations, by cross-checking/validating our datasets from our RMBPT and MCDHF calculations, and by detailed comparisons with available accurate observations and other theoretical calculations. The data are openly available in Science Data Bank at https://doi.org/10.57760/sciencedb.10569.

A new mixed formalism based on SU(1,1) transition Hamiltonian in the investigation of deformed states and transition rates of 124Te

The existence of deformed states in nuclei such as 124Te leads to a change of the theoretical attitude to optimize the description of energy levels and electric quadrupole transition by using additional symmetries. The purpose of this contribution is to provide a detailed description of the energy gaps that appear in this nucleus using different mixing formalisms. To achieve this and also compare the accuracy of different formalisms, the transitional Hamiltonian in the affine SU(1,1) algebra was extended by adding the O(6)-Casimir operator. Also, the interacting boson model-2 is used to get theoretical predictions for the energy spectra and quadrupole transition rates of both regular and deformed states. Predictions of U(5) symmetry for the considered energy levels in 124Te nucleus show good agreement with experimental counterparts, except at 31+, 61+, and 62+ states where we tried to describe these levels by moving towards O(6) algebra. In this condition and using of both symmetries in the framework of mixing formalism, theoretical predictions for these deformed levels improved obviously, and transition probabilities were described in detail with high accuracy, too. Also, the IBM-2 suggests exact results for all regular states and intruder ones, and there are some suggestions about the advantages of each formalism in the description of energy levels and quadrupole transition rates of such nuclei.

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

Study of Nuclear Structure of 42-43 Ti isotopes by using F7MBZ & F742 interactions

In this work, The energy levels and lowered electric quadruple transition probability B(E2)  were calculated with the use of the OXBASH code in the F7shell and the F7MBZ& F742 effective interaction for the 42-43Ti isotopes. All nucleon combinations in the)  0 7/2, 1 3/2, 0 5/2, and 1 1/2 ( orbits are included in the model space. Additionally, the shell model does a good in describing the invading states' energies. Computations have been done using effective interactions F7MBZ and F742 in full f7 space, As well as the shell model, Lowlying states, and binding energies computed, and it was found that the calculated rates of electric quadrupole transitions between the isotopes 42-43Ti were consistent with the existing experimental published data.  

Hyperfine structure measurements on a forbidden transition of Bi I using fourier transform spectroscopy

Hyperfine structure (hfs) investigations have been performed on a forbidden transition of the Bi I emission spectral line in the visible region at 15,437.49 cm−1, between the levels 6p3 4S3/2 and 6p3 2D5/2, by means of a Fourier Transform spectrometer. Electrodeless discharge lamps (EDL) containing BiI3 were utilized to generate the bismuth plasma. In these observations, all the 6 components of electric quadrupole (ΔF = ±2) transitions have been detected for the first time, in addition to the 12 components of magnetic dipole (ΔF = 0, ±1) transitions. Magnetic dipole constant (A) and electric quadrupole constant (B) have been derived for the combining levels.