Electric-dipole Forbidden Transitions Research Articles

Including vibrational effects in magnetic circular dichroism spectrum calculations in the framework of excited state dynamics.

In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4- and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements.

Perturbation of the UV transitions of formaldehyde by TiO2photocatalysts and Aunnanoclusters

In the gas phase, formaldehyde has an electric-dipole forbidden transition that becomes allowed by vibronic coupling. In this paper we explore whether perturbation by surfaces could also enhance light absorption by CH2O. We investigate the electronic transitions of formaldehyde in the gas phase and interacting with rutile (110) TiO2, Aun nanoclusters, and Aun on (110)-TiO2. These surfaces are chosen as being representative of metals and metal-oxide minerals, and also because of specific interest in photocatalysts and noble metal nanocluster catalysts. The oscillator strength of the forbidden n → π* transition of formaldehyde in vacuum is investigated by modelling vibrational coupling to the electronic transition with equation-of-motion coupled cluster theory. The excitation energies and oscillator strengths of formaldehyde are calculated for different orientations and distances to the surfaces using the coupled cluster singles and doubles linear response method within the Quantum Mechanical and Molecular Mechanical (QM/MM) model using the aug-cc-pVTZ basis set and compared with the values calculated in vacuo. The electronic transitions of formaldehyde vary very little when placed near a pure TiO2-surface with only minor variations depending on the orientation of formaldehyde. Introducing a gold nanoparticle (by itself or supported by TiO2) induces dramatic changes in the absorption properties. This is due to vibronic interactions and the effect of the broken symmetry on the n → π* transition. We see a large redshift in the transition of 90 nm and oscillator strengths larger than 1.0 × 10-4 for CH2O interacting with Aun.

Electric-dipole forbidden transitions for probing atomic state preparation: the case of the Autler–Townes effect

This work demonstrates an scheme in which a weak electric quadrupole (E2) transition with a controlled frequency detuning in a ladder configuration is used as an extremely non-perturbing probe for precisely identifying subtle details of the effects driven by AC fields coupling atomic states and the preparation of quantum states. For this purpose, we provide a precise experimental and theoretical study of the Autler Townes (AT) effect derived from a strong electric dipole transition stimulated by a resonant laser beam and probed by the E2 interaction. The experiment was carried out for a 87Rb atomic gas at room temperature in a velocity-selective scheme. The AT effect was monitored via the splitting of the fluorescence spectra associated with the spontaneous decay to the ground state. The theoretical description incorporates the modification of standard few-level schemes introduced by forbidden electric-dipole transitions selection rules. We develop an analytic ladder three-level scheme to approximate the cyclic 5S1/2 F = 2 → 5P3/2 F = 3 → 6P3/2 F = 1, 2, 3 → 5S1/2 F = 2 path. Other levels that could have effects on the fluorescence are included via a fourth level with effective parameters. Doppler effects and finite bandwidths of the laser beams are included in the theoretical model to closely reproduce the experimental results.

Exact semi-classical light-matter interaction operator applied to two-photon processes with strong relativistic effects.

X-ray processes involve interactions with high-energy photons. For these short wavelengths, the perturbing field cannot be treated as constant, and there is a need to go beyond the electric-dipole approximation. The exact semi-classical light-matter interaction operator offers several advantages compared to the multipole expansion such as improved stability and ease of implementation. Here, the exact operator is used to model x-ray scattering in metal K pre-edges. This is a relativistic two-photon process where absorption is dominated by electric-dipole forbidden transitions. With the restricted active space state-interaction approach, spectra can be calculated even for the multiconfigurational wavefunctions including second-order perturbation. However, as the operator itself depends on the transition energy, the cost for evaluating integrals for hundreds of thousands unique transitions becomes a bottleneck. Here, this is solved by calculating the integrals in a molecular-orbital basis that only runs over the active space, combined with a grouping scheme where the operator is the same for close-lying transitions. This speeds up the calculations of single-photon processes and is critical for the modeling of two-photon scattering processes. The new scheme is used to model Kα resonant inelastic x-ray scattering of iron-porphyrin complexes with relevance to studies of heme enzymes, for which the total computational time is reduced by several orders of magnitude with an effect on transition intensities of 0.1% or less.

Analysis of an Optical Lattice Methodology for Detection of Atomic Parity Nonconservation

We present an extension and a deepened analysis of a suggested experimental scheme for detecting atomic parity violation, previously published in Phys. Rev. A 2019, 100, 050101. The experimental concept is described in more detail and we compute new ab initio data necessary for assessing the plausibility of the approach. Original theoretical data for transition matrix elements on the electric dipole forbidden transition in caesium 6 s 2 S 1 / 2 – 5 d 2 D 3 / 2 are reported, as are a range of electric dipole matrix elements connected to the ground state 6s. The latter is used for an analysis of the wavelength-dependent light shift in Cs. A range of experimental details is presented, combined with a survey of realistic lasers parameters. These are adopted to project the feasibility of the scheme to eventually be capable of delivering data beyond the standard model of particle physics.

A Laboratory Astrophysics Problem: The Lifetime of Very Long-Lived Levels in Low-Charge Ions

Emission lines of singly charged ions populate many astrophysical spectra. However, the interpretation of the line intensities (usually line ratios) often depends on the transition rates of the decays of very long-lived low-lying levels. For example, the line ratio of two electric-dipole forbidden transitions in the 3s 2 3p 3 ground configuration of singly ionized sulfur (ion S + , spectrum S II) has been interpreted in terms of a density diagnostic for planetary nebulae, i.e., for densities in the order of 10 4 cm − 3 . The predicted lifetimes of the 2 D 3 / 2 , 5 / 2 o levels are in the order of one hour. Modeling indicates that a 10% uncertainty of the lifetime determination in this case corresponds to a 50% uncertainty of the density diagnostic. The available theoretical lifetime predictions scatter by much more than 10%. Considerations about an experimental approach are presented with the goal of instigating a measurement of the actual level lifetimes.

Spectroscopic parameters and transition probabilities of several doublet and quartet states of sulfoxide cation

In this work, the potential energy curves of 11 doublet, 11 quartet, and 2 sextet states of a sulfoxide cation are reported and the transition dipole moments between them were calculated. The radiative lifetimes were on the order of 10–6 s for the A2Π, C2Π, b4Σ–, and 12Σ+ states, approximately 10–6 – 10–7 s for the 12Δ and B2Σ– states, and on the order of 10–7 s for the 22Σ+ state. The radiative lifetimes of these states were short, suggesting that the spontaneous emissions generated from them occurred readily. Many transitions are strong, including A2Π – X2Π, C2Π – X2Π, C2Π – A2Π, B2Σ– – X2Π, B2Σ– – A2Π, 12Δ – X2Π, 12Δ – A2Π, and b4Σ– – a4Π. In addition, the transitions from the the first well of the 12Σ+ state to the X2Π state, and from the first well of the 22Σ+ state to the X2Π, A2Π, and C2Π states, are also strong. These strong transitions were easy to measure through spectroscopy. The properties of the transitions between certain Ω states generating from the X2Π, A2Π, a4Π, and b4Σ– states were investigated, including several electric dipole–forbidden transitions. The A2Π1/2 – X2Π1/2, A2Π3/2 – X2Π1/2, b4Σ–3/2 – a4Π5/2, b4Σ–1/2 – a4Π1/2, and b4Σ–1/2 – a4Π3/2 transitions are strong. The radiative litimes of the A2Π1/2, A2Π3/2, a4Π–1/2, a4Π1/2, a4Π3/2, a4Π5/2, b4Σ–1/2, and b4Σ–3/2 states were calculated and the distributions of their radiative lifetime varying as rotational angular momentum quantum number J were studied. The radiative lifetimes of the a4Π1/2 and a4Π3/2 states are on the order of several ms; those of the a4Π5/2 state are approximately several–ten ms; while those of the a4Π–1/2 state are on the order of several s. The results calculated herein can provide some useful guidelines for further experimental and astronomical observations and theoretical studies.

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.

Observation of the5p3/2→6p3/2electric-dipole-forbidden transition in atomic rubidium using optical-optical double-resonance spectroscopy

Direct evidence of excitation of the 5p3/2 -> 6p3/2 electric dipole forbidden transition in atomic rubidium is presented. The experiments were performed in a room temperature rubidium cell with continuous wave extended cavity diode lasers. Optical-optical double resonance spectroscopy with counterpropagating beams allows the detection of the non-dipole transition free of Doppler broadening. The 5p3/2 state is prepared by excitation with a laser locked to the maximum F cyclic transition of the D2 line, and the forbidden transition is produced by excitation with a 911 nm laser. Production of the forbidden transition is monitored by detection of the 420 nm fluorescence that results from decay of the 6p3/2 state. Spectra with three narrow lines (~ 13 MHz FWHM) with the characteristic F - 1, F and F + 1 splitting of the 6p3/2 hyperfine structure in both rubidium isotopes were obtained. The results are in very good agreement with a direct calculation that takes into account the 5s -> 5p3/2 preparation dynamics, the 5p3/2 -> 6p3/2 non-dipole excitation geometry and the 6p3/2 -> 5s1/2 decay. The comparison also shows that the electric dipole forbidden transition is a very sensitive probe of the preparation dynamics.

(Invited) Rare Earth Luminescence in Nanostructured Amorphous Silicon Alloys

Amorphous silicon and its alloys are widely used in semiconductor industry. Due to short range order, doping can be achieved by substituting phosphorus or boron for silicon. Moreover, the optical bandgap can be increased by alloying with C, N or O or decreased by alloying with Ge. Due to its amorphous nature the network can accommodate a variety of elements up to relatively high concentrations at the expense of an increased density of defects in the bandgap. Rare earth elements (RE) have been introduced in the form of trivalent ions in amorphous silicon or its wider bandgap alloys. They present characteristic intra-4f luminescence if their chemical neighborhood is non-centrosymetric and the electric dipole forbidden transitions become partially allowed. In the amorphous alloys excitation through the network can be efficiently achieved when a RE transition corresponds to roughly half the bandgap. The RE act as nucleation centers to induce formation of Si nanocrystals under high temperature annealing. Samples were prepared by reactive RF sputtering from a Si target partially covered with metallic RE platelets using appropriate reactive atmospheres. Annealing was used either to optimize the photoluminescence or to induce the formation of Si nanocrystals.We will present characterization by photoluminescence and EXAFS of Er, Nd, Eu and Tb in a-Si:H, a-SiOx:H and a-SiNx:H. The RE ions tend to occupy low coordination low symmetry sites in the network in the amorphous samples. This favors relatively strong wide photoluminescence lines. The RE present two luminescence lifetimes, the fast component determined by the host and the slow associated to the local symmetry of the RE ions.Models for the excitation of luminescence and recombination processes and their relation with the local nanostructure around the RE ions will be presented.

Cross-sections of bound-free and bound–bound transitions at a fundamental harmonic of the Nd:YAG laser

Bound-free electric dipole allowed and bound–bound electric dipole allowed and electric dipole forbidden transitions at a fundamental harmonic of the Nd:YAG laser, , have been studied. Excitation spectra of the I2 (B, vB, JB → X, vX = 1, JX) luminescence from the B, vB = 18, 20, 21, JB rovibronic states have been measured with switched on and switched off generation. Temporal behaviors of the luminescence intensities from these states with switched on and switched off generation have also been measured. These data allow us to determine or estimate cross-sections of the electric dipole allowed and electric dipole forbidden transitions under study. Dipole moment of the transition has also been determined.

M1 and E2 decay-dependent lifetime of the lowest 1S0 level in C-like ions up to Ne4+ measured at a heavy-ion storage ring

Electric-dipole forbidden transitions within the ground configuration of many ion species play an important role in the diagnostics of terrestrial and astrophysical plasmas, and knowing their rates is essential for collisional-radiative models and spectral simulation. The dominant decay channel of the 2s22p2 1S0 level in the ground configuration of C-like ions changes from electric quadrupole to magnetic dipole within the first few ions of the isoelectronic sequence. Using an electron cyclotron resonance ion source at the TSR heavy-ion storage ring, we realize a lifetime measurement on the system Ne4+ where the magnetic dipole decay channel becomes dominant. These data complement our earlier storage ring lifetime measurements on N+, O2+ and F3+, which we discuss together with the present new result and the available theoretical calculations in their isoelectronic context.

Coherent control of AC Stark allowed transition in Λ system

We show that quantum-interference-related phenomena, such as electromagnetically induced transparency, gain without inversion and enhanced refractive index may occur on electric-dipole forbidden transitions. Gain/dispersion characteristics of such transitions strongly depend upon the relative phase between the driving and probe fields. Unlike allowed transitions, gain/absorption behavior of forbidden transitions exhibit antisymmetric feature on the Rabi sidebands. Absorption/gain spectra possess extremely narrow sub-natural resonances.

Atomic lifetime measurements with electron beam ion traps

Electron beam ion traps have been employed to measure very short (femtosecond) and long (microsecond to many millisecond) level lifetimes in highly charged ions. The lifetime measurement techniques reflect interesting properties of the apparatus. The measurement of very short lifetimes exploits the fact that the Doppler broadening in electron beam ion traps can be reduced to below the natural line width. For the measurement of long lifetimes (measured on electric-dipole forbidden transitions), the electron beam ion trap is switched periodically between electronic and magnetic trapping modes. It is then also necessary to learn about the charge exchange processes that limit long term ion storage. Investigations of the sources of systematic error as well as cross checks with heavy-ion storage ring techniques have confirmed that electron beam ion trapping techniques are capable of delivering accurate lifetime data. The best atomic lifetime data achieved with electron beam ion traps have reached uncertainties of less than one percent.

Molecular and electronic structure of chromium(v) nitrido complexes with azide and isothiocyanate ligands

The first use of [Cr(N)Cl4]2- as a starting material in chromium(v) nitrido chemistry is demonstrated in simple, high yield, metathesis reactions with the pseudohalogens SCN- and N3- yielding five-coordinate, labile complexes: [Cr(N)(NCS)4]2- and [Cr(N)(N3)4]2-, which have been crystallized and characterized by single-crystal X-ray diffraction. Reaction of [Cr(N)(NCS)4]2- with 1,10-phenanthroline furnishes six-coordinate [Cr(N)(NCS)3(phen)]- wherein phenanthroline coordinates to the position trans to the nitrido ligand. The trans influence of the nitrido ligand leads to a bond length difference of 0.223 A between the axial and equatorial ligators from the phenanthroline ligand. The absorption band with lowest energy in these pseudo-linear complexes is assigned as the electric dipole forbidden transition d(xy) --> d(x-y) based on intensities and its variation with the nature of the equatorial ligators. This absorption provides the spectrochemical series for the equatorial ligands, which is found to be numerically almost identical to that determined for chromium(III). DFT calculations reproduce the observed structures and corroborate the ligand field picture of the electronic structure of these complexes.

M1/E2 decay rates in Co XI, Ni XII and Cu XIII measured at a heavy-ion storage ring

Rates of the electric-dipole forbidden transition in the ground configuration of Cl-like ions of Co, Ni and Cu have been measured optically at a heavy-ion storage ring. Besides testing theory and providing benchmark data for these ions, the data by isoelectronic extrapolation pertain to the Fe X spectrum of high solar interest, for which so far theory and experiment have disagreed.

Precise atomic lifetime measurements with stored ion beams and ion traps

For many years, atomic lifetime measurements on multiply-charged ions have been done almost exclusively by beam-foil spectroscopy. For low ion charges, however, spin-changing "intercombination" transitions have a rate that renders them too slow for traditional fast-beam techniques. Here ion traps and fast-ion beams have been combined in the concept of heavy-ion storage rings. These devices have permitted not only an extension of intercombination lifetime measurements down to singly charged ions, but they also facilitated similar measurements on electric-dipole forbidden transitions. The electron-beam ion trap (EBIT) complements the storage-ring work for work on highly charged ions. Achievements, technical issues, and prospects are outlined. PACS Nos.: 32.70Cs, 32.30Jc, 34.50Fa

Electric-dipole forbidden transitions in C 60: oscillator strengths induced by the spin–orbit coupling

The electric-dipole forbidden transitions of the C 60 molecule are studied. The oscillator strengths induced by the spin–orbit (SO) coupling have been estimated, using wavefunctions of the singlet and triplet excited states and their excited energies previously obtained by the Tamm–Dancoff approximation including all the 14,400 particle-hole pairs in the CNDO/S approximation. Effects of the SO coupling are treated in terms of the first-order perturbation theory. Singlet–triplet (ST) transitions from the ground state 1 1A g are allowed only to the 3A u , 3T 1 u and 3H u states. The 1 1A g →1 3A u transition gives the largest oscillator strength among them, and its transition process via virtual intermediate states is analyzed. It is shown that the large oscillator strength is due to a small energy difference between the final 1 3A u and the intermediate 3 1T 1 u states. Compared with the oscillator strengths of transitions induced by the vibronic coupling, the magnitudes of the oscillator strengths of the ST transitions are very small.

Intercombination and forbidden transition rates in C- and N-like ions(O2+,F3+,andS9+)measured at a heavy-ion storage ring

Rates of an intercombination transition and several electric-dipole forbidden transitions between the levels of the ground complex in C-like ions of O and F and in N-like ions of S have been measured optically at a heavy-ion storage ring. The lifetime results, 1.250(13) ms for the ${2s2p}^{3}$ ${}^{5}{S}_{2}^{o}$ level in ${\mathrm{O}}^{2+},$ 530(25) and 304(5) ms for the ${2s}^{2}$ ${2p}^{2}$ ${}^{1}{S}_{o}$ level in ${\mathrm{O}}^{2+}$ and ${\mathrm{F}}^{3+},$ respectively, and 5.20(15) and 2.10(6) ms for the ${2s}^{2}{2p}^{3}$ ${}^{2}{P}_{1/2,3/2}^{o}$ levels of ${S}^{9+},$ agree with only some of the theoretical predictions, while they have a lower estimated uncertainty than all of them.

Atomic Lifetime Measurements with Ion Traps of Many Sizes

Atomic lifetime measurements yield information on atomic wavefunctions that supplements the data from atomic energy levels, but is more sensitive to details of the radial wavefunctions. Transition rates of intercombination (spin-changing) and electric-dipole forbidden transitions are of interest also for applications in plasma diagnostics and astrophysics. Earlier lifetime measurements of low-charge state ions in radiofrequency, electrostatic and Penning ion traps have recently been supplemented and in some cases superseded by experiments on electron-beam ion traps (EBIT) and heavy-ion storage rings. Several of these measurements of lifetimes in the range from 10 µs to 500 ms have reached uncertainties of better than 0.5% and challenge theory. Typical features of ion trap experiments, performance problems and technical developments are reviewed, and likely routes of further progress are outlined.