High-lying Energy Research Articles

Complex WKB analysis of energy-level degeneracies of non-Hermitian Hamiltonians

The Hamiltonian H = p 2 +x 4 +iAx, where A is a real parameter, is investigated. The spectrum of H is discrete and entirely real and positive for |A| < 3.169. As |A| increases past this point, adjacent pairs of energy levels coalesce and then become complex, starting with the lowest-lying energy levels. For large energies, the values of A at which this merging occurs scale as the three-quarters power of the energy. That is, as |A |→∞ and E →∞ , at the points of coalescence the ratio a =| A|E −3/4 approaches a constant whose numerical value is acrit = 1.1838363072914 ··· . Conventional WKB theory determines the high-lying energy levels but cannot be used to calculate acrit. This critical value is predicted exactly by complex WKB theory.

Reevaluation of term isotope shifts of low even levels of 4f 86s 2 configuration and high odd-parity levels of neutral gadolinium atoms

Isotope shift Δ T( 156Gd– 160Gd) of the even-parity energy levels of 4f 86s 2 and 4f 76s 26p configurations of neutral gadolinium atoms (Gd I) have been reevaluated using the level isotope shift (Δ T) of two odd-parity levels reported recently. Earlier the isotope shifts of these even-parity energy levels were evaluated using empirical relation. Our extensive isotope shift data has been used for the reevaluation of Δ T values of these low even-parity energy levels which have been utilised for revision of the Δ T values of high-lying odd-parity energy levels of Gd I.

Investigations of new high-lying even-parity energy levels of the samarium atom below its first ionization limit

Systematic mapping of high-lying even-parity levels (low-lying configurations) of the samarium atom below the first ionization potential was carried out with a two-step photoexcitation and photoionization method. Five hundred seventy-one new energy levels were discovered in the region 34 850–45 300 cm-1, and an unambiguous assignment of angular momenta was given to most of the energy levels in accordance with the electric dipole selection rules.

High-lying Rydberg states and ionization energy of vinyl chloride studied by two-photon resonant ionization spectroscopy

High-lying Rydberg states of jet-cooled vinyl chloride at 9.3–10 eV are investigated using 2+1 resonance-enhanced multiphoton ionization spectroscopy. Four Rydberg series are observed and tentatively assigned as due to the transitions of π→ ns, npσ, npπ, and nf Rydberg orbitals associated with quantum defects of 0.94, 0.89, 0.48, and 0.02, respectively. All of the four series converge to the same ionization energy limit corresponding to the ground state of vinyl chloride cation. The adiabatic ionization energy of vinyl chloride is determined to be 80 720±6 cm −1, in excellent agreement with previously reported values.

Electron-impact excitation cross sections of neon

To determine the direct electron-impact excitation cross sections with the optical method, one must measure all transitions out of a level, as well as the cascade into the level of interest from higher-lying energy levels. Considered here are the ten levels of the ${2p}^{5}3p$ configuration of neon, whose emissions to lower levels fall within a range of 540--810 nm. This allows an investigation via a monochromator-photomultiplier tube system. Cascades into these levels from ${2p}^{5}4s$ and ${2p}^{5}3d,$ however, emit radiation in the 740--1720-nm range, part of which is outside the limit of photomultiplier detection. We employ a Fourier-transform spectrometer to examine the near-infrared lines. We report direct electron excitation cross sections for the ten ${2p}^{5}3p$ levels for electron energies up to 200 eV. In addition, we provide apparent excitation functions for the ${2p}^{5}4s$ and ${2p}^{5}3d$ levels. We have also observed a dependence of the optical emission cross sections on pressure, and describe this effect within the framework of the resonance radiation reabsorption model.

Spectroscopic investigations of the 4ƒ5d energy levels of Pr^3+ in fluoride crystals by excited-state absorption and two-step excitation measurements

Excited-state absorption spectra obtained by a pulsed pump–probe technique specially designed for the near-UV spectral domain were recorded in three Pr3+-doped fluoride crystals (KY3F10,LiYF4, and BaY2F8). These excited-state absorption spectra correspond to optical transitions from the 3P0 or the 1D2 metastable levels of the 4f2 configuration up to the first energy levels of the 4f5d electronic configuration. The position, the anisotropic behavior, and the line shape of the observed excited-state absorption bands are discussed and compared with ground-state absorption (from level 3H4) or direct excitation spectra available in the literature. Subsequently, two-step excitation into the 4f5d high-lying energy levels of Pr3 by means of 3P0 and 1D2 is shown to be an efficient way to produce broadband UV fluorescence by use of pump beams in the blue and the near UV.

The High-Lying Vibrational Levels and Dissociation Energy of the a3Σ+u State of 7Li2

Perturbation-facilitated optical–optical double resonance (PFOODR) has been used to access the 23Πg state of 7Li2 via the excitation scheme using two single-mode tunable lasers. The selected () mixed level provides a gateway through which the triplet manifold can be accessed. Fluorescence from single rovibrational levels of 23Πg to the state was detected at high resolution using a Fourier transform spectrometer. Transitions to v = 0–9 in the state were observed, covering the potential well almost to the dissociation limit. The data were analyzed using a near dissociation expansion (NDE) technique and the resulting vibrational and rotational parameters were used to calculate a new RKR potential curve which reproduced the observed energy levels to within a rms error of 0.02 cm−1. The following parameters were obtained for the state: D0 = 301.829 ± 0.015 cm−1, De = 333.69 ± 0.10 cm−1, Te = 8183.12 ± 0.12 cm−1.

Dynamics of refractive-index changes in a Nd:YAG laser crystal under excitation of Nd^3+ ions

The mechanism for refractive-index changes that accompany changes in population during pumping and amplification of an optical beam is studied in a Nd:YAG laser crystal by both resonant four-wave mixing and interferometric techniques. It is found that these refractive-index changes (connected with the difference in polarizability of excited and unexcited Nd3+ ions) have two components: a small noninertial component that accompanies an amplified optical pulse and the major changes that are intensified with a delay time of ∼3 µs. The latter effect is explained by population (or depopulation) of a higher-lying energy level 2(F2)5/2 of the 4f electron shell of Nd3+ ions, which has large polarizability in near-IR and visible light. The real part of the nonlinear optical resonant susceptibility of the inverted Nd:YAG caused by the refractive-index changes is also discussed.

Dissociative excitation of the fluoromethanes by electron impact

Emission spectra following electron impact on molecules of the homologous series of fluoromethanes CHxF4-x with x=0-4 have been investigated from the near infrared at 700 nm to the ultraviolet VUV-spectral region at 100 nm. Earlier experimental data for the visible and ultraviolet spectral region were revised and evaluated again on the basis of reliable new data for the dynamic viscosity of the molecules. The measurement of absolute and relative cross-sections were systematically extended into the VUV region from 100 nm to 200 nm. The examination of atomic lines as well as molecular band systems in the VUV gives further insight into the dissociation mechanism and shows that many excited levels even of atomic and molecular species cannot be populated directly, but only by transitions from higher-lying energy levels. Simple steric effects can be distinguished from more complex transition phenomena.

Quantization of a generic chaotic 3D billiard with smooth boundary. I. Energy level statistics

Numerical calculation and analysis of extremely high-lying energy spectra, containing thousands of levels with sequential quantum number up to 62000 per symmetry class, of a generic chaotic 3D quantum billiard is reported. The shape of the billiard is given by a simple and smooth deformation of a unit sphere, which gives rise to nearly fully chaotic classical dynamics. We present an analysis of (i) the quantum length spectrum whose smooth part agrees with the 3D Weyl formula and whose oscillatory part is peaked around the periods of classical periodic orbits, (ii) the nearest neighbor level spacing distribution and (iii) the number variance. Although the chaotic classical dynamics quickly and uniformly explores almost the entire energy shell, while the measure of the regular part of phase space is insignificantly small, we find small but significant deviations from GOE statistics which are explained in terms of localization of eigenfunctions onto lower dimensional classically invariant manifolds.

Berry’s conjecture and information theory

It is shown that, by applying a principle of information theory, one obtains Berry’s conjecture regarding the high-lying quantal energy eigenstates of classically chaotic systems.

New odd-parity high-lying energy levels of the europium atom by resonance ionization spectroscopy

Odd-parity energy levels of the neutral europium atom (Eu I) have been investigated by employing both single-colour and two-colour stepwise laser excitation using the technique of resonance ionization spectroscopy in a heat-pipe thermionic diode system. Fifty-two new odd-parity energy levels of Eu I have been found in the energy region 40 575 - 43 410 . The J values for most of these new energy levels have been assigned unambiguously. In addition to this, 19 odd levels which were reported earlier, in the region of our present study, have also been investigated; the assignments of J values to nine of these levels have been confirmed and four levels, which had no unique J assignments, have been assigned definite J values.

Up-converted luminescence by two- and three-photon excitation in LaF3:Nd3+ crystals.

Three- and two-photon excitation of high-lying energy levels of ${\mathrm{Nd}}^{3+}$ was realized in La${\mathrm{F}}_{3}$: ${\mathrm{Nd}}^{3+}$ crystals using fundamental radiation of a tunable ${\mathrm{Ti}}^{3+}$ -sapphire laser. Strong UV and green-red luminescence lines were obtained by the three- and two-photon excitation process, respectively. The UV luminescence due to the three-photon excitation was observed to be delayed by about 25 ns from the visible luminescence due to the two-photon excitation. A mechanism of the excitation and luminescence process is proposed.

Quantum surface-of-section method: Demonstration of semiclassical Berry-Robnik energy level-spacing distribution in a generic two-dimensional Hamiltonian system

The recently developed quantum surface of section method is applied to a search for extremely high-lying energy levels in a simple but generic Hamiltonian system between integrability and chaos, namely the semiseparable 2-dim oscillator. Using the stretch of 13,445 consecutive levels with the sequential number around $1.8\cdot 10^7$ (eighteen million) we have clearly demonstrated the validity of the semiclassical Berry-Robnik level spacing distribution while at 1000 times smaller sequential quantum numbers we find the very persistent quasi universal phenomenon of power-law level repulsion which is globally very well described by the Brody distribution.

A BOXCARS investigation of the V–V energy transfer from highly excited SF6 to CS2 and the sensitized photodissociation of CS2

The BOXCARS technique was used to investigate the vibrational energy transfer between highly excited SF6 and CS2, and for the sensitized photodissociation of CS2. The analysis of data, as reported in our previous studies, to extract vibrational temperature from the CARS signal has been revised in the present work to adjust for the fact that the ground-state population may not be constant. The current investigation suggests that IR laser excitation of SF6 and the energy exchange between excited SF6 and CS2 create a high-lying vibrational energy reservoir in the CS2 vibrational manifold. The rate of energy transfer depends on the partial pressures of SF6 and CS2, and the excitation intensity. The transfer rate shows greater dependence on the partial pressure of SF6 than on the partial pressure of CS2. At higher excitation energies, the energy reservoir leads to photofragmentation products.

Application of energy upconversion spectroscopy to novel laser and phosphor design

Energy-transfer and sequential-absorption upconversion processes, normally considered detrimental to conventional laser operation, are rapidly emerging as the key to an exciting new class of optical device. Energy-upconversion processes may be designed to take advantage of strong rare earth ion emission transitions in the visible region and of valuable co-incidences with diode-laser outputs in the near-infrared to produce compact visible lasers. This paper reviews the use of sequential-absorption and energy-transfer spectroscopy to derive information that is essential to the optimization of novel device designs as well as ‘conventional’ laser or phosphor designs. Transfer-rate extraction using upconverted temporal transients, determination of high-lying energy levels using sequential-absorption laser spectroscopy, ion dimer identification by line-narrowing experiments and direct identification of energy storage states using dual-laser techniques are presented. The use of dimer-dominated host crystals, such as CsCdBr 3, that can be used to isolate individual energy-transfer rates relevant to the optimization of many different laser types, is emphasized.

Identification of new high-lying odd energy levels of uranium by resonance ionization mass spectrometry

Two-colour resonance ionization spectroscopy was used for identification of 240 new levels of 238U in the energy range of 38 500 to 41 200 cm-1. A precision of +or-0.03 cm-1 (1 SD) for the energies was obtained by using laser-induced fluorescence signals of I2 for spectral calibration. The angular momentum quantum number, J, was uniquely assigned for 134 of these levels by using angular momentum selection rules.

Highly excited rovibrational states of small molecules

The use of first principles variational calculations for the calculation of high-lying energy levels, wavefunctions and transition intensities for triatomic molecules is considered. Theoretical developments are considered, including the use of generalized internal coordinates, the use of a two-step procedure for rotationally excited systems and a finite element method known as the discrete variable representation. Illustrative calculations are presented including ones for H 2, LiCN and the Ar-N2 Van der Waals molecule. A first principles ‘rotational’ spectrum of H 2D+ is computed using states up to J = 30. The transition intensities in this spectrum are reproduced accurately in a frozen dipole approximation but are poorly represented by models that involve approximating the wavefunction.

Absorptive Bistability of Carbon Monoxide Initiated by Resonance Radiation

Abstract The kinetics of the absorption of resonance radiation in carbon monoxide is analysed. It is found that when the radiation acts on high-lying vibrational energy levels of the CO molecule, absorptive bistability may arise. If the radiation flux is lower than a certain critical value, the gas is essentially transparent to radiation and the degree of vibrational non-equilibrium of the system is small. When the radiation flux exceeds a different critical value, we have another type of stable state. This state is characterized by a strong vibrational non-equilibrium, the radiation being effectively absorbed by the gas. Within the interval between these two critical values there are both lower and higher stable states of the system which are separated by an unstable state. A jump-like transition from one stable state to another, so called ‘absorptive instability’ is possible at certain values of the radiation flux and vibrational energy stored in the system. The development of absorptive instability is ...

The high-lying rotational energy levels of the OH radical in the ν = 0 level of the X 2Π state

Lambda-doubling and rotational transition frequencies for the OH radical in the ν = 0 level of its X 2Π state have been fitted close to the limit imposed by experimental error for a very wide range of J values. High power centrifugal distortion correction terms (up to N 12) were required in the effective Hamiltonian to achieve this. The traditional power series expansion of the rotational Hamiltonian is only very slowly convergent for the highest N values included (up to N = 47). Nevertheless, reliable interpolation of rotational transition frequencies for intermediate N values is possible from the results, giving values which are superior to those measured directly in the solar spectrum. A refined and extended table of rotational term values for OH in its ground state has been computed from the molecular parameters.