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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

High Mg activation in implanted GaN by high temperature and ultrahigh pressure annealing

Not provided.We demonstrate high p-type conductivity and hole concentrations >10 18 cm -3 in Mg-implanted GaN. The implantation was performed at room temperature and by post-implantation annealing at 1 GPa of N 2 and in a temperature range of 1200–1400 °C. The high pressure thermodynamically stabilized the GaN surface without the need of a capping layer. We introduce a “diffusion budget,” related to the diffusion length, as a convenient engineering parameter for comparing samples annealed at different temperatures and for different times. Although damage recovery, as measured by XRD, was achieved at relatively low diffusion budgets, these samples did not show p-type conductivity. Further analyses showed heavy compensation by the implantation-induced defects. Higher diffusion budgets resulted in a low Mg ionization energy (~115 meV) and almost complete Mg activation. For even higher diffusion budgets, we observed significant loss of Mg to the surface and a commensurate reduction in the hole conductivity. High compensation at low diffusion budgets and loss of Mg at high diffusion budgets present a unique challenge for shallow implants. A direct control of the formation of compensating defects arising from the implantation damage may be necessary to achieve both hole conductivity and low Mg diffusion.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Probing the Coherence of Metal Absorbers toward Background Quasar Pairs

Abstract We investigate the spatial coherence of metal absorption lines in the circumgalactic medium using 4115 quasar pairs from Sloan Digital Sky Survey DR16. We identify 184 Mg ii (15 with dual detections) and 50 C iv (11 with dual detections) absorber pairs. The fraction of pairs with fractional equivalent width difference δW r ≤ 0.5 declines with projected separation: for Mg ii , it drops from ∼52% at 0–25 kpc to ∼7% at 100–200 kpc, while for C iv , it decreases from ∼100% to ∼21% over 0–200 kpc. In every separation bin, C iv absorbers with δW r ≤ 0.5 maintain a higher fraction than Mg ii absorbers. Similar results are obtained when the nondetections are treated as 2 σ W r upper limits in a survival analysis. The transverse autocorrelation function shows strong Mg ii clustering within 0–25 kpc, whereas the C iv excess remains relatively flat out to ∼100 kpc. These findings suggest that high-ionization C iv gas retains coherence over larger transverse scales than low-ionization Mg ii gas, in agreement with previous lensed quasar and high-resolution studies.

Li, Jing [Guangxi University] (ORCID:0009000148751↗
DOE OSTI2024

Dielectronic satellite emission from a solid-density Mg plasma: Relationship to models of ionization potential depression

Here, we report on experiments where solid-density Mg plasmas are created by heating with the focused output of the Linac Coherent Light Source x-ray free-electron laser. We study the K-shell emission from the helium- and lithium-like ions using Bragg crystal spectroscopy. Observation of the dielectronic satellites in lithium-like ions confirms that the M-shell electrons appear bound for these high charge states. An analysis of the intensity of these satellites indicates that when modeled with an atomic-kinetics code, the ionization potential depression model employed needs to produce depressions for these ions which lie between those predicted by the well known Stewart-Pyatt and Ecker-Kroll models. These results are largely consistent with recent density functional theory calculations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Path integral Monte Carlo and density functional molecular dynamics simulations of warm dense MgSiO 3

In order to provide a comprehensive theoretical description of MgSiO 3 at extreme conditions, we combine results from path integral Monte Carlo and density functional molecular dynamics simulations and generate a consistent equation of state for this material. We consider a wide range of temperature and density conditions from 10 4 to 10 8 K and from 0.321 to 64.2 g/cm -3 (0.1- to 20-fold the ambient density). We study how the L and K shell electrons are ionized with increasing temperature and pressure. We derive the shock Hugoniot curve and compare with experimental results. Our Hugoniot curve is in good agreement with the experiments, and we predict a broad compression maximum that is dominated by the K shell ionization of all three nuclei while the peak compression ratio of 4.70 is obtained when the Si and Mg nuclei are ionized. To conclude, we analyze the heat capacity and structural properties of the liquid.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Radiation-Induced Long-Lived Transients and Metal Particle Formation in Solid KCl–MgCl 2 Mixtures

Here, the electron paramagnetic resonance and diffuse reflectance-optical absorption spectra of room-temperature γ-irradiated KCl–MgCl 2 binary solid salt mixtures (98:2 mol % and 2:98 mol %) and the eutectic (68:32 mol %) are reported. Additionally, powder X-ray diffraction of the pristine salts and thermal annealing studies of the irradiated salts were performed to evaluate the radiolysis product stability, annihilation, and association in metallic particles. The main long-lived transient species detected in 98:2 mol % KCl–MgCl 2 salts were perturbed F-centers, that is, trapped electrons (e t – ) in the vicinity of Mg ions (λ max at 561 nm), and the radiolytic reduction of Mg 2+ to Mg + and Mg 0 . Thermal annealing promoted the diffusion of defects to yield polycations (Mg n + ). On the other hand, irradiation of 2:98 mol % KCl/MgCl 2 salts showed the formation of cationic and neutral Mg dimers (Mg 2 + and Mg 2 ) and trimers as well as centers with a rhombic powder pattern apparently consisting of an electron shared between three Mg 2+ nuclei associated with an anion vacancy (ν a + –Mg 3 5+ ). Trapped electrons (e t – ) (F-centers) were not observed in the irradiated eutectic mixture; instead, Mg 2 , Mg 0 , and Cl 3 – were observed. It was observed that the higher temperature for thermal ionization of radiation-reduced Mg species decreased the extent of electron recombination reactions and the disproportionation of Cl 3 – compared to the pure KCl but enhanced the aggregation of Mg into larger metallic microstructures (metallic particles).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Many-body effects for the Mg 2s XPS of MgO

The energy separation of the higher lying cation XPS binding energies, BEs, for MgO is examined. It is shown that the Hartree–Fock BEs overestimate the separation of the Mg BE(2s) and BE(2p), because an important many-body effect is neglected in the determination of the Hartree–Fock BEs. Once the many-body effect is taken into account, there is good agreement between theory and the XPS measurement. The character of this atomic many-body effect is established in terms of a nearly degenerate configuration that is needed to describe the wavefunction when an Mg 2s electron is ionized. Further, the results provide additional evidence of the ionic character of the MgO crystal. Given the atomic character of the many-body effect, it is likely to apply also to the BE separations of other closed shell oxides.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comparison of Mg-based liquid metal ion sources for scalable focused-ion-implantation doping of GaN

We compare the suitability of various magnesium-based liquid metal alloy ion sources (LMAISs) for scalable focused-ion-beam (FIB) implantation doping of GaN. We consider GaMg, MgSO 4 $\bullet$7H 2 O, MgZn, AlMg, and AuMgSi alloys. Although issues of oxidation (GaMg), decomposition (MgSO 4 $\bullet$7H 2 O), and excessive vapor pressure (MgZn and AlMg) were encountered, the AuMgSi alloy LMAIS operating in a Wien-filtered FIB column emits all Mg isotopes in singly and doubly charged ionization states. We discuss the operating conditions to achieve <20 nm spot size Mg FIB implantation and present Mg depth profile data from time-of-flight secondary ion mass spectrometry. We also provide insight into implantation damage and recovery based on cathodoluminescence spectroscopy before and after rapid thermal processing. Prospects for incorporating the Mg LMAIS into high-power electronic device fabrication are also discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Study of the 22 Mg Waiting Point Relevant for X-Ray Burst Nucleosynthesis via the 22 Mg(α,p) 25 Al Reaction

The 22 Mg(α, p) 25 Al reaction rate has been identified as a major source of uncertainty for understanding the nucleosynthesis flow in Type-I x-ray bursts. Here, we report a direct measurement of the energy-and angle-integrated cross sections of this reaction in a 3.3-6.9 MeV center-of-mass energy range using the MUlti-Sampling Ionization Chamber (MUSIC). The new 22 Mg(α, p) 25 Al reaction rate is a factor of ~4 higher than the previous direct measurement of this reaction within temperatures relevant for x-ray bursts, resulting in the 22 Mg waiting point of x-ray burst nucleosynthesis flow to be significantly bypassed via the (α, p) reaction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Connecting Low- and High-redshift Weak Emission-line Quasars via Hubble Space Telescope Spectroscopy of Lyα Emission

We present ultraviolet spectroscopy covering the Lyα + N v complex of six candidate low-redshift (0.9 < z < 1.5) weak emission-line quasars (WLQs) based on observations with the Hubble Space Telescope. The original systematic searches for these puzzling Type 1 quasars with intrinsically weak broad emission lines revealed an N ≈ 100 WLQ population from optical spectroscopy of high-redshift (z > 3) quasars, defined by a Lyα + N v rest-frame equivalent width (EW) threshold <15.4 Å. Identification of lower-redshift (z < 3) WLQ candidates, however, has relied primarily on optical spectroscopy of weak broad emission lines at longer rest-frame wavelengths. With these new observations expanding existing optical coverage into the ultraviolet, we explore unifying the low- and high-z WLQ populations via EW[Lyα+N v]. Two objects in the sample unify with high-z WLQs, three others appear consistent with the intermediate portion of the population connecting WLQs and normal quasars, and the final object is consistent with typical quasars. The expanded wavelength coverage improves the number of available line diagnostics for our individual targets, allowing a better understanding of the shapes of their ionizing continua. The ratio of EW[Lyα+N v] to EW[Mg ii] in our sample is generally small but varied, favoring a soft ionizing continuum scenario for WLQs, and we find a lack of correlation between EW[Lyα+N v] and the X-ray properties of our targets, consistent with a "slim-disk" shielding gas model. We also find indications that weak absorption may be a more significant contaminant in low-z WLQ populations than previously thought.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Temporal characterization of fundamental plasma parameters in pulsed liquid electrode plasma (LEP) optical emission spectrometry

The fundamental characteristics of liquid electrode plasma (LEP), a pulsed plasma source for optical emission spectrometry, were investigated. Two distinct phases were observed during the process of pulsed plasma generation, namely bubble generation and active plasma discharge. Additionally the ionization efficiency of the LEP, with Mg as a representative analyte, was gauged from the ratio of Mg II 279.553 nm to Mg I 285.213 nm emission and was found to increase from about 5% to 20% in a close-to-linear fashion with the discharge voltage from 800 V to 1200 V. The Mg II/Mg I ratio of the LEP was 2.5 to 3 orders of magnitude less than that typically offered by an inductively coupled plasma (ICP) but was comparable to other solution-based glow discharges. It was found that an off-time interval of more than 150 ms between successive discharge pulses was required to obtain a stable pulse-to-pulse discharge current. Temporally resolved emissions of Mg II 279.6 nm, Mg I 285.2 nm, Fe I 373.5 nm, OH band head at 306 nm, and Hα line at 656.3 nm showed that the background species (OH band and Hα line) reached their maximum emission intensities at around 0.5 ms to 0.7 ms with respect to the onset of the discharge pulse whereas the maximum emissions were observed between 0.7 ms to 0.9 ms for analyte species (Mg and Fe lines). The electron density observed in the present work was in the range from 5.7 × 10 15 cm -3 to 8.2 × 10 15 cm -3 , which was similar to those found in an analytical ICP. The temporal averaged OH rotational temperature was 3300 K, which was comparable to the values of an analytical ICP and solution-based glow discharges. By contrast, the temporally averaged Fe I excitation temperature was around 8900 K, which was even higher than that of an analytical ICP and roughly triple the values obtained by techniques based on glow discharge of liquid samples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Equation of state of hot, dense magnesium derived with first-principles computer simulations

Using two first-principles computer simulation techniques, path integral Monte Carlo and density functional theory molecular dynamics, we derive the equation of state of magnesium in the regime of warm dense matter, with densities ranging from 0.43 to 86.11 g cm –3 and temperatures from 20,000 K to 5×10 8 K. These conditions are relevant for the interiors of giant planets and stars as well as for shock compression measurements and inertial confinement fusion experiments. Here, we study ionization mechanisms and the electronic structure of magnesium as a function of density and temperature. We show that the L shell electrons, 2s and 2p energy bands, merge at high densities. This results in gradual ionization of the L-shell with increasing density and temperature. In this regard, Mg differs from MgO, which is also reflected in the shape of its principal shock Hugoniot curve. For Mg, we predict a single broad pressure-temperature region, where the shock compression ratio is approximately 4.9. Mg thus differs from Si and Al plasmas that exhibit two well-separated compression maxima on the Hugoniot curve for L and K shell ionizations. Finally, we study multiple shocks and effects of preheat and precompression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Emission of electromagnetic waves as a stopping mechanism for nonlinear collisionless ionization waves in a high-β regime

A high energy density plasma embedded in a neutral gas is able to launch an outward-propagating nonlinear electrostatic ionization wave that traps energetic electrons. The trapping maintains a strong sheath electric field, enabling rapid and long-lasting wave propagation aided by field ionization. Here, using 1D3V kinetic simulations, we examine the propagation of the ionization wave in the presence of a transverse MG-level magnetic field with the objective to identify qualitative changes in a regime where the initial thermal pressure of the plasma exceeds the pressure of the magnetic field (Beta > 1). Our key finding is that the magnetic field stops the propagation by causing the energetic electrons sustaining the wave to lose their energy by emitting an electromagnetic wave. The emission is accompanied by the magnetic field expulsion from the plasma and an increased electron loss from the trapping wave structure. The described effect provides a mechanism mitigating rapid plasma expansion for those applications that involve an embedded plasma, such as high-flux neutron production from laser-irradiated deuterium gas jets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

The Cosmic Ultraviolet Baryon Survey (CUBS) – III. Physical properties and elemental abundances of Lyman-limit systems at z < 1

ABSTRACT We present a systematic investigation of physical conditions and elemental abundances in four optically thick Lyman-limit systems (LLSs) at z = 0.36–0.6 discovered within the Cosmic Ultraviolet Baryon Survey (CUBS). Because intervening LLSs at z < 1 suppress far-UV (ultraviolet) light from background QSOs, an unbiased search of these absorbers requires a near-UV-selected QSO sample, as achieved by CUBS. CUBS LLSs exhibit multicomponent kinematic structure and a complex mix of multiphase gas, with associated metal transitions from multiple ionization states such as C ii, C iii, N iii, Mg ii, Si ii, Si iii, O ii, O iii, O vi, and Fe ii absorption that span several hundred km s−1 in line-of-sight velocity. Specifically, higher column density components (log N(H i)/cm−2≳ 16) in all four absorbers comprise dynamically cool gas with $\langle T \rangle =(2\pm 1) \times 10^4\,$K and modest non-thermal broadening of $\langle b_\mathrm{nt} \rangle =5\pm 3\,$km s−1. The high quality of the QSO absorption spectra allows us to infer the physical conditions of the gas, using a detailed ionization modelling that takes into account the resolved component structures of H i and metal transitions. The range of inferred gas densities indicates that these absorbers consist of spatially compact clouds with a median line-of-sight thickness of $160^{+140}_{-50}$ pc. While obtaining robust metallicity constraints for the low density, highly ionized phase remains challenging due to the uncertain $N\mathrm{(H\, {\small I})}$, we demonstrate that the cool-phase gas in LLSs has a median metallicity of $\mathrm{[\alpha /H]_{1/2}}=-0.7^{+0.1}_{-0.2}$, with a 16–84 percentile range of [α/H] = (−1.3, −0.1). Furthermore, the wide range of inferred elemental abundance ratios ([C/α], [N/α], and [Fe/α]) indicate a diversity of chemical enrichment histories. Combining the absorption data with deep galaxy survey data characterizing the galaxy environment of these absorbers, we discuss the physical connection between star-forming regions in galaxies and diffuse gas associated with optically thick absorption systems in the z < 1 circumgalactic medium.

Zahedy, Fakhri S. (ORCID:0000000178692551)↗
DOE OSTI2023

Atmospheric Pressure Plasma Treatment of Magnesium Alloy for Enhanced Coating Adhesion and Corrosion Resistance

Atmospheric pressure plasma (AP) treatment, using an open-air jet of ionized CO 2 , N 2 , or air, was applied to AZ91D Mg alloy surfaces to investigate its effects on primer coating adhesion and corrosion resistance. The CO 2 and air AP treatments formed an O- and C-rich surface layer (Mg-O-C) consisting of agglomerated nanoparticles and pits with a depth of a few microns and increasing the surface roughness by 6–8 times compared with the reference 600 grit-finished surface. Then, three commercial primers, zinc phosphate (ZnP), chromate-containing epoxy, and MIL23377, were applied on the treated surfaces to evaluate the corrosion resistance associated with the coating adhesion. Microscopic analysis demonstrated stronger interlocking between the primer layer and the nano-/microrough Mg-O-C surface compared to the untreated (600 grit-finished) surfaces, indicating improved coating adhesion and corrosion resistance. Crosscut tests of the MIL23377 primer on the CO 2 and air AP-treated surfaces showed the highest level of adhesion, ASTM class 5B. Salt spray corrosion tests showed that after 8 days of exposure, the primer coatings on air AP-treated surfaces had corrosion areas that were more than four times smaller than that of the 600 grit-finished surface. The N 2 AP treatment showed similar adhesion enhancement. The preliminary operation expenses for AP treatment using CO 2 , N 2 , and air were estimated at USD 30.62, USD 35.45, and USD 29.75 (from an air cylinder)/USD 0.66 (from an air compressor) per m 2 , respectively.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Lyman alpha and Lyman continuum emission of Mg Ⅱ -selected star-forming galaxies

We present observations with the Cosmic Origins Spectrograph onboard the Hubble Space Telescope of seven compact low-mass star-forming galaxies at redshifts, z, in the range 0.3161–0.4276, with various O 3 Mg 2 = [O iii] λ5007/Mg ii λ2796+2803 and Mg 2 = Mg ii λ2796/Mg ii λ2803 emission-line ratios. We aim to study the dependence of leaking Lyman continuum (LyC) emission on the characteristics of Mg ii emission together with the dependencies on other indirect indicators of escaping ionizing radiation. LyC emission with escape fractions f esc (LyC) = 3.1–4.6 percent is detected in four galaxies, whereas only 1σ upper limits of f esc (LyC) in the remaining three galaxies were derived. A strong narrow Lyα emission line with two peaks separated by V sep ~ 298–592 km s -1 was observed in four galaxies with detected LyC emission and very weak Lyα emission is observed in galaxies with LyC non-detections. Our new data confirm the tight anticorrelation between f esc (LyC) and V sep found for previous low-redshift galaxy samples. V sep remains the best indirect indicator of LyC leakage among all considered indicators. It is found that escaping LyC emission is detected predominantly in galaxies with Mg 2 ≳ 1.3. A tendency of an increase of f esc (LyC) with increasing of both the O 3 Mg 2 and Mg 2 is possibly present. However, there is substantial scatter in these relations not allowing their use for reliable prediction of f esc (LyC).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Shake loss intensities in x-ray photoelectron spectroscopy: Theory, experiment, and atomic composition accuracy for MgO and related compounds

The relative intensities of XPS core levels, scaled by their photoionization cross sections, are regularly used to determine sample atomic composition. Cross sections, however, give the intensity to all possible final states for the core ionizations, not just to the main peak. This includes all intrinsic satellite structure (shake states and, for open shell systems, the different ionic multiplets). In practice, for solids, this is usually experimentally impossible to determine accurately because such a satellite structure sits on the inelastically scattered electron background and cannot be easily separated. Therefore, usually, only the intensity of the main peak is used. This limits the ultimate possible accuracy of XPS composition determination. The purpose of the present paper is to examine the contributions that a theoretical analysis of losses of intensity can make to improve quantitation. For an MgO single crystal, we show that the correct stoichiometry of 1:1 can be recovered using the theoretical analysis of the experimental MgO peak ratio intensities. For materials with a sufficient bandgap for the XPS main peaks to be separated from the scattered background, the intensity of main peaks can often be accurately determined. Thus, if one uses theory to calculate that fraction of the total intensity lost from a main peak into all its satellite structure, the intensity of just main peaks could then be used to more accurately determine relative atom % composition. This work tests this approach using a single crystal MgO (50% Mg, 50% O) standard. Ab initio electronic structure theory of representative MgO clusters is used to determine Hartree–Fock wave functions for the ground state and final ionized states corresponding to the main Mg 2p and O1s XPS peaks of the oxide. The sudden approximation, SA, is used to determine the fractional losses from these main peaks to shake satellites, which is found to be greater for O1s than Mg2p. This results in predicted “apparent composition” for stoichiometric MgO of 55.2% Mg, 44.8% O instead of the true 50% Mg, 50% O. Equivalent theory for CaO results in a predicted apparent Ca value of 53.4%. Experimentally, using Mg2s or 2p intensity ratio to O1s, we find values between 52.2% and 56.0% Mg using two crystals and four different instrument electron pass energies. The average value of the measurements is 54.5% Mg when corrected for the presence of an adventitious carbon overlayer and slight surface hydroxide. Though this agreement with theory may be somewhat fortuitous, given the potential experimental errors, which are fully discussed, it is similar to that in our earlier study on LiF. We also present preliminary experimental data on Mg(OH) 2 and MgSO 4 , which show a similar trend of apparently higher than 50% Mg, but we have no theory values. We are not yet able to experimentally test for validation of the difference between apparent composition for MgO (55.2% Mg) and CaO (53.4% Ca), owing to significant carbonate formation at the surface of the single crystal CaO. Here, an important conclusion is that the theoretical determination of shake losses, obtained with ab initio wavefunctions and the SA, is likely to be a useful way to calibrate the accuracy and reliability of compositions obtained from XPS intensities and merits further study.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

The Back Door to the Surface Hydrated Electron

We use a Mg + metal to extend the size regime of water clusters to extrapolate to the bulk limit of the Vertical Detachment Energy (VDE) of the solvated electron to >3,200, a value between one to over two orders of magnitude for clusters previously measured experimentally or computed theoretically. We relate the VDE to the energy difference between the Mg + (H 2 O) $n$ and Mg 2+ (H 2 O) $n$ systems and the metal’s second ionization potential. The extrapolated bulk VDEs of the localized surface electron, which moves away from the metal as n increases, are 1.89 ± 0.01 eV for semiempirical ($n$ ~ 3,200; PM6-D 3 H 4 ) and 1.73 ± 0.03 eV ($n$ ~ 150; HF), 1.83 ± 0.02 eV ($n$ ~ 150; MP2) for ab-initio, in excellent agreement with the 1.6 – 1.8 eV range of experimental results. In conclusion, the VDEs converge from above (larger values) to the bulk limit, in a manner qualitatively different than previous studies and experiments, a fact justifying the “back door” approach to the solvated electron.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Two-photon double photoionization of atomic Mg by ultrashort pulses: Variation of angular distributions with pulse length

We investigate the two-photon double ionization of atomic magnesium induced by ultrashort pulses. Though the initial and final state symmetries are comparable to the same process in helium, in stark contrast the range of photon energies for which nonsequential ionization is the only open pathway is narrow (less than 1 eV) in magnesium. Thus several sequential ionization pathways feature heavily in these processes. Nonetheless, it is found that for pulse durations between 0.25 and 2.0 fentoseconds, the joint angular dependence of the ejected electrons can depend sensitively on pulse length, varying between the strictly back-to-back ejection characteristic of nonsequential ionization to other distributions. The significance of excited-state correlating configurations in representing the initial state of magnesium is discussed in the light of their consequences for the resulting angular distributions at photon energies where sequential ionization can access intermediate states that lie nearby in energy, particularly for longer pulses.

74 ATOMIC AND MOLECULAR PHYSICS↗