Measured Transition Energies Research Articles

High-precision Transition Energy Measurements of Neon-like Fe xvii Ions

We improve by a factor of 4–20 the energy accuracy of the strongest soft X-ray transitions of Fe xvii ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10–15 meV, or velocity equivalent ±∼5 km s−1 in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than 4 million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and the development of optical clocks with highly charged ions.

Improved ionization potential of calcium using frequency-comb-based Rydberg spectroscopy

We report new frequency-comb-based measurements of Ca Rydberg energy levels. Counter-propagating laser beams at 390 nm and 423 nm excite Ca atoms from the $4s^2~^1\mbox{S}_0$ ground state to $4sns~^1\mbox{S}_0$ Rydberg levels with $n$ ranging from 40 to 110. Near-resonant two-photon two-color excitation of atoms in a thermal beam makes it possible to eliminate the first-order Doppler shift. The resulting lineshapes are symmetric and Gaussian. We verify laser metrology and absolute accuracy by reproducing measurements of well-known transitions in Cs, close to the fundamental wavelengths of our frequency-doubled ti:sapphire lasers. From the measured transition energies we derive the ionization potential of Ca, $E_{\rm IP} = 1, 478, 154, 283.42 \pm 0.08 \mbox{(statistical)} \pm 0.07 \mbox{(systematic)}$ MHz, improving the previous best determination by a factor of 11.

Optical evidence of many-body effects in the zincblende AlGaN alloy system

We present a quantitative description of the change in optical properties of zincblende aluminium-gallium-nitride thin films dependent on the free-carrier concentration due to band filling and renormalization effects. Free-electron concentrations above 1020 cm−3 in GaN are achieved by introducing germanium as a donor. Spectroscopic ellipsometry in the infrared and ultraviolet spectral range yields the dielectric function (DF). The plasmon contribution for the infrared part of the DF allows to determine the free-electron concentration all-optically. Furthermore, by utilizing the Kane model for the band structure of semiconductors near the Γ-point of the Brillouin zone as well as taking into account Burstein-Moss-shift and band-gap renormalization, measured transition energies are efficiently described.

QED calculation of ionization energies of 1snd states in helium

Quantum electrodynamical (QED) calculations of ionization energies of the $1snd\,D$ states are performed for the helium atom. We reproduce the previously known relativistic and QED effects up to order $m\alpha^5$ and extend the theory by calculating the complete $m\alpha^6$ correction. The total contribution of the $m\alpha^6$ effects is shown to be much smaller than previously estimated, due to a large cancelation between the radiative and non-radiative parts of this correction. As a result of our calculations, we confirm the previously reported deviations between measured transition energies and theoretical predictions for the $nD$--$2S$ and $nD$--$2P$ transitions. Possible reasons for this discrepancy are analyzed.

Reference-free measurements of the1s2s2p2P1/2,3/2o→1s22s2S1/2and1s2s2p4P5/2→1s22s2S1/2transition energies and widths in lithiumlike sulfur and argon ions

We have measured the widths and energies of the 1s2s2p 2 P 1/2,3/2 → 1s 2 2s 2 S 1/2 transitions in lithiumlike sulfur and argon, as well as the energies of the forbidden 1s2s2p 4 P 5/2 → 1s 2 2s 2 S 1/2 M2 transition in both elements. All measurements were performed with a double-flat crystal spectrometer without the use of any reference line. The transition energy measurements have accuracies ranging from 2.3 ppm to 6.4 ppm depending on the element and line intensity. The widths and the intensity ratios of the 1s2s2p 2 P 1/2,3/2 → 1s 2 2s 2 S 1/2 lines have also been measured. These are the first reference-free measurements of transitions in core-excited lithiumlike ions, and have an accuracy comparable to the best relative measurements. We have also performed multi-configuration Dirac-Fock calculations of the widths, energies and intensity ratios. Extensive comparison between existing experimental results and theory is performed, and Bayesian techniques employed to extract the energy of the 1s 2p 2 4 P 1/2 → 1s 2 2p 2 P 1/2 transition in sulfur and identify contaminant transitions.

Transition energy measurements of the X-ray lines of neon-like europium

We report the measurements of the n = 3 → n = 2 L-shell X-ray transitions of neon-like Eu53+. These include all seven allowed electric dipole (E1) transitions, five electric quadrupole (E2) transitions, and one magnetic quadrupole (M2) transition. The measurements were carried out at the EBIT-I electron beam ion trap facility at Livermore using an X-ray calorimeter. The measured values agree with many-body perturbation theory calculations within the experimental uncertainties. This includes the transitions that involve a 2s electron and that are, therefore, strongly affected by quantum electrodynamical effects.

Influence of the free-electron concentration on the optical properties of zincblende GaN up to 1×1020cm−3

We analyze the optical properties of zincblende gallium-nitride in the infrared and ultraviolet spectral range ($\ensuremath{\approx}27\phantom{\rule{0.16em}{0ex}}\mathrm{meV}--6.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$) experimentally by spectroscopic ellipsometry and provide a quantitative description of these results by $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ perturbation theory. Free-electron concentrations above ${10}^{20}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ are achieved by introducing germanium as a donor. We determine the dielectric function as well as band filling effects like the Burstein-Moss shift and band gap renormalization. The Kane model for the band structure of semiconductors near the $\mathrm{\ensuremath{\Gamma}}$-point allows to calculate the effective electron mass and to determine the nonparabolicity of the conduction band. At the same time, these results can be used to derive the free-electron concentration all-optically. The combination of Kane's model, Burstein-Moss shift, and band-gap renormalization can be used to expertly describe the measured transition energies up to $\ensuremath{\approx}3.7\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ dependent on the carrier concentration, yielding an averaged hole mass of $\ensuremath{\approx}0.61\phantom{\rule{0.16em}{0ex}}{\mathrm{m}}_{\mathrm{e}}$ for the contributing valence bands.

Lifetime Measurement of Highly Charged Ions Relevant to Astrophysics

We have measured the \(\rm 1s2s2p ~^4P^0_{5/2}\)-\(\rm 1s^22s~^2S_{1/2}\) magnetic quadrupole X-ray transition energy in Li-like Fe along with the \(\rm 1s2s~^3S_1\)-\(\rm 1s^2~^1S_0\) transition energy in He-like Fe using multi channel doppler tuned spectrometer. These states have been produced through the interaction of 165 MeV Fe\(^{12+}\) ion beam with 100 \(\mu\)g/cm\(^2\) thin carbon foil. Further we have measured the lifetime of \(\rm 1s2s2p ~^4P^0_{5/2}\) level in Li-like Fe. The measured transition energy of \(\rm 1s2s~^3S_1\)-\(\rm 1s^2~^1S_0\) is in good agreement with the available theoretical predictions and experimental measurements, whereas the measurement of \(\rm 1s2s2p ~^4P^0_{5/2}\)-\(\rm 1s^22s~^2S_{1/2}\) energy is little lower than the theoretical estimations. However, the measured lifetime of \(\rm 1s2s2p ~^4P^0_{5/2}\) level compares well with the theoretical predictions.

Determination of type-I band offsets in GaBixAs1–x quantum wells using polarisation-resolved photovoltage spectroscopy and 12-band k.p calculations

Using photovoltage (PV) spectroscopy we analyse the electronic structure of a series of GaBixAs/(Al)GaAs dilute bismide quantum well (QW) laser structures. The use of polarisation-resolved PV measurements allows us to separately identify transitions involving bound light- and heavy-hole states in the QWs, as well as bound-to-continuum transitions from the QWs to the barriers. Analysis of these transitions enables us to probe the GaBixAs/(Al)GaAs conduction and valence band offsets, thereby quantifying the band offsets. Using a 12-band Hamiltonian, we extract the band offsets in the QWs explicitly by constraining the Bi-related parameters of the model against the experimentally measured transition energies. The PV measurements and calculations we present provide the first explicit confirmation of a type-I band offset at the GaBixAs/GaAs heterointerface near x = 2%. This result, combined with the theory we present for calculating the band offsets at GaBixAs/(Al)GaAs heterointerfaces, can be used to determine the band offsets at arbitrary Bi composition x.

Precision studies of deep-inner-shell photoabsorption by atomic ions

With emphasis on K-shell ionization and K-shell excitation mediated by the absorption of a single photon the present paper provides an overview of the status of experiments in which deep-inner-shell photoabsorption by atomic ions has been investigated. For inner-shell processes not involving the K-shell only photon energies beyond about 350 eV are considered. Mechanisms of photoabsorption and subsequent relaxation as well as relations between photoionization and photorecombination are discussed. New possibilities for precise measurements of transition energies have been provided by the high photon-energy resolution available at 3rd generation synchrotron light sources. This is particularly interesting for studies of K-shell excitation of few-electron systems. By using atomic ions as targets, either in form of a collimated beam or trapped in electromagnetic fields, it has been possible to reach a high level of precision in the spectroscopy of transitions involving the decay of K vacancies by photoemission or Auger processes. Examples for absolute cross section measurements and precision spectroscopy are presented.

X-ray Measurements of Highly Charged Europium

We present spectroscopic measurements of the M-shell emission of highly charged europium performed at the Livermore SuperEBIT electron beam ion trap facility using the EBIT Calorimeter Spectrometer (ECS). There is significant blending among the emission lines from the different charge states but despite the complexity of the observed spectra we have successfully identified the ten brightest n = 4 → 3 transitions from sodium-like Eu52+ utilizing the Flexible Atomic Code (FAC). We find that the difference between the calculated and measured transition energies for these ten Eu52+ lines does not exceed 3 eV. In fact, for four of the identified lines we find agreement within the measured uncertainties. Additional comparison with semi-empirical transition-energy predictions for sodium-like ions from laser-generated plasmas is included and shows that overall the semi-empirical predicted values for the transition energies are slightly higher than the measured values, while the FAC values that didnt agree with the measured transition energies are almost 1 eV lower than the measured values.

X-ray measurements in helium-like atoms increased discrepancy between experiment and theoretical QED

A recent 15 parts per million (ppm) experiment on muonic hydrogen () found a major discrepancy with quantum electrodynamics (QED) and independent nuclear size determinations. Here we find a significant discrepancy in a different type of exotic atom: a medium-Z nucleus with two electrons. Investigation of the data collected is able to discriminate between available QED formulations and reveals a pattern of discrepancy of almost six standard errors of experimental results from the most recent theoretical predictions, with a functional dependence proportional to Zn where . In both the muonic and highly charged systems, the sign of the discrepancy is the same, with the measured transition energy higher than predicted. Some consequences are possible or probable, and some are more speculative. This may give insight into effective nuclear radii, the Rydberg, the fine-structure constant, or unexpectedly large QED terms.

Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations

Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations

Helium-like titanium x-ray spectrum as a probe of QED computation

We discuss the first absolute energy measurements of the intercombination and forbidden transitions () in trapped Ti20+ ions to 15 parts per million accuracy. We present new measurements on helium-like titanium, in which the orbital radius is reduced and QED terms are magnified by the increased nuclear charge. The measured transition energies are higher than predicted.

Coherent cancellation of geometric phase for the OH molecule in external fields

The OH molecule in its ground state presents a versatile platform for precision measurement and quantum information processing. These applications vitally depend on the accurate measurement of transition energies between the OH levels. Significant sources of systematic errors in these measurements are shifts based on the geometric phase arising from the magnetic and electric fields used for manipulating OH. In this article, we present these geometric phases for fields that vary harmonically in time, as in the Ramsey technique. Our calculation of the phases is exact within the description provided by our recent analytic solution of an effective Stark-Zeeman Hamiltonian for the OH ground state. This Hamiltonian has been shown to model experimental data accurately. We find that the OH geometric phases exhibit rich structure as a function of the field rotation rate. Remarkably, we find rotation rates where the geometric phase accumulated by a specific state is zero, or where the relative geometric phase between two states vanishes. We expect these findings to be of importance to precision experiments on OH involving time-varying fields. More specifically, our analysis quantitatively characterizes an important item in the error budget for precision spectroscopy of ground-state OH.

REMPI and MATI spectroscopic study of selected cis and trans 3-chlorostyrene rotamers

The ab initio and DFT calculations predict two stable rotamers, cis and trans, for 3-chlorostyrene in each of the S0, S1 and D0 states. In the two-color resonant two-photon ionization (2C-R2PI) spectra, the band origins of S1←S0 electronic transition of cis and trans 3-chlorostyrene appears respectively at 33766±3 and 34061±3cm−1. The mass-analyzed threshold ionization (MATI) spectra give the adiabatic ionization energies of 69701±4cm−1 and 69571±4cm−1 for cis and trans rotamers. Within the experimental detection limit, the measured transition energies are the same for both the 35Cl and 37Cl isotopomers. The observed active modes of rotamers in the S1 and D0 states involve mainly the in-plane ring deformation and substituent-sensitive bending vibration. It is derived from the 2C-R2PI and MATI spectroscopic data that the cis rotamer is more stable than the trans rotamer by 218±30, 513±30 and 88±30cm−1 for the S0, S1 and D0 states, respectively.

Transition energies and direct-indirect band gap crossing in zinc-blende AlxGa1−xN

The electronic and optical properties of zinc-blende (zb) Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N over the whole alloy composition range are presented in a joint theoretical and experimental study. Because zb-GaN is a direct (${\ensuremath{\Gamma}}_{v}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{c}$) semiconductor and zb-AlN shows an indirect (${\ensuremath{\Gamma}}_{v}\ensuremath{\rightarrow}{X}_{c}$) fundamental band gap, the ternary alloy exhibits a concentration-dependent direct-indirect band gap crossing point the position of which is highly controversial. The dielectric functions of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N alloys are measured employing synchrotron-based ellipsometry in an energy range between 1 and 20 eV. The experimentally determined fundamental energy transitions originating from the $\ensuremath{\Gamma}$, $X$, and $L$ points are identified by comparison to theoretical band-to-band transition energies. In order to determine the direct-indirect band gap crossing point, the measured transition energies at the $X$ point have to be aligned by the calculated position of the highest valence state. Thereby density-functional theory (DFT) based approaches to the electronic structure, ranging from the standard (semi)local generalized gradient approximation (GGA), self-energy corrected local density approximation (LDA-1/2), and meta-GGA DFT (TB-mBJLDA) to hybrid functional DFT and many-body perturbation theory in the $GW$ approximation, are applied to random and special quasirandom structure models of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N. This study provides interesting insights into the accuracy of the various numerical approaches and contains reliable ab initio data on the electronic structure and fundamental alloy band gaps of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N. Nonlocal Heyd-Scuseria-Ernzerhof-type hybrid-functional DFT calculations or, alternatively, $GW$ quasiparticle calculations are required to reproduce prominent features of the electronic structure. The direct-indirect band gap crossing point of zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N is found in the Al rich composition range at an Al content between $x=0.64$ and $0.69$ in hybrid functional DFT, which is in good agreement with $x=0.71$ determined from the aligned experimental transition energies. Thus our study solves the long-standing debate on the nature of the fundamental zb-Al${}_{x}$Ga${}_{1\ensuremath{-}x}$N alloy band gap.

High-resolution photocurrent spectroscopy of the positive trion state in a single quantum dot

We demonstrate high-resolution photocurrent spectroscopy of the positive trion state (X+) in a single InAs/GaAs self-assembled quantum dot (QD). Exploiting a Coulomb-mediated renormalization of the X+ transition energy, our approach allows for a sub-mu eV resolution, which is more than four orders of magnitude higher than that in previous approaches. Furthermore, such high-resolution spectroscopy of X+ permits us to obtain precise values for the X+ permanent dipole moment and polarizability, by fitting a theoretical model to the measured transition energy as a function of electric field. Since optical initialization, manipulation, and readout of a QD spin rely on the trion state as an intermediary state, such high-resolution measurements of the X+ spectrum and its dipole moment are essential for performing high-fidelity quantum computing operations on QD spin qubits.

Cubic III‐nitride coupled quantum wells towards unipolar optically pumped lasers

AbstractOptical and structural properties of asymmetric coupled cubic‐GaN/‐AlN quantum wells (QW) are studied. The samples are grown by molecular beam epitaxy on a 50 nm c‐GaN buffer on 3C‐SiC substrate. The active region contains 100 periods of a 2.3 nm AlN barrier, a 1.9–2.1 nm silicon doped GaN QW and a 1.0–1.2 nm undoped GaN QW coupled by a 0.9–1.1 nm AlN tunnelling barrier. Phase purity and partial relaxation of the superlattice is observed in reciprocal space maps measured by high resolution X‐ray diffraction. Optical properties of coupled QWs are investigated using cathodoluminescence spectroscopy. A clear shift in the emission energy associated with the thickness of the QWs can be observed. Furthermore clear TM‐polarized infrared absorption in the 0.55–0.87 eV range is observed at room temperature using Fourier transform infrared spectroscopy. The asymmetric shape of the infrared absorptions reveals the existence of a three level system in the QWs and is explained by contributions of the e1–e3 and e2–e3 intersubband transitions. Measured transition energies are compared to model calculations using a Schrödinger–Poisson solver based on an effective mass model (nextnano3).

Nature of yrast excitations nearN=40: Level structure of67Ni

Excited states in ${}^{67}$Ni were populated in deep-inelastic reactions of a ${}^{64}$Ni beam at 430 MeV on a thick ${}^{238}$U target. A level scheme built on the previously known 13-$\ensuremath{\mu}$s isomer has been delineated up to an excitation energy of 5.3 MeV and a tentative spin and parity of (21/2${}^{\ensuremath{-}}$). Shell model calculations have been carried out using two effective interactions in the ${f}_{5/2}p{g}_{9/2}$ model space with a ${}^{56}$Ni core. Satisfactory agreement between experiment and theory is achieved for the measured transition energies and branching ratios. The calculations indicate that the yrast states are associated with rather complex configurations, herewith demonstrating the relative weakness of the $N=40$ subshell gap and the importance of multi-particle-hole excitations involving the ${g}_{9/2}$ neutron orbital.