High Principal Quantum Number Research Articles

Theoretical study of opacity for a mixture of gold and gadolinium at a high temperature.

Using the detailed configuration accounting with the term structures treated by the unresolved transition array model, we have presented a method to calculate the spectral-resolved opacity for high temperature and density plasmas. Due to the fully relativistic treatment, incorporated with the quantum defect theory to handle the huge number of transition arrays from configurations with high principal quantum number, we can calculate the opacity of any medium- and high-Z plasmas conveniently. In the present work, the frequency-dependent opacity and the Rosseland mean opacity are calculated for a mixture of gold and gadolinium at a high temperature, 250 eV, and three densities, 0.1 g/cm(3), 1.0 g/cm(3), and 10.0 g/cm(3). Agreement between our theoretical results and experimental measurements and other theoretical simulations is obtained.

Collisional Plasma Models with APEC/APED: Emission-Line Diagnostics of Hydrogen-like and Helium-like Ions

New X-ray observatories (Chandra and XMM-Newton) are providing a wealth of high-resolution X-ray spectra in which hydrogen- and helium-like ions are usually strong features. We present results from a new collisional-radiative plasma code, the Astrophysical Plasma Emission Code (APEC), which uses atomic data in the companion Astrophysical Plasma Emission Database (APED) to calculate spectral models for hot plasmas. APED contains the requisite atomic data such as collisional and radiative rates, recombination cross sections, dielectronic recombination rates, and satellite line wavelengths. We compare the APEC results to other plasma codes for hydrogen- and helium-like diagnostics, and test the sensitivity of our results to the number of levels included in the models. We find that dielectronic recombination with hydrogen-like ions into high (n=6-10) principal quantum numbers affects some helium-like line ratios from low-lying (n=2) transitions.

Relativistic calculation of dielectronic recombination on theC4+ground state

The measurement of the dielectronic recombination (DR) cross section of ${\mathrm{C}}^{4+}$ with a high resolution [S. Mannervik et al., Phys. Rev. A 55, 1810 (1997)] provides a rigorous test case for various theoretical methods. In the earlier work, the relativistic multichannel theory was applied to the DR process on the ${\mathrm{He}}^{+}$ ion for both the $\ensuremath{\Delta}N=1$ and $\ensuremath{\Delta}N=2$ transitions with a principal quantum number of the outermost electron up to 5. In principle, that method can be applied to resonances with any high principal quantum numbers. Practically, however, the calculations become very time consuming. In the present work, the method is extended by incorporating the Bell-Seaton theory. The DR cross sections of ${\mathrm{C}}^{4+}$ for the resonances with $2<~n<~25$ are calculated. The results are in good agreement with those of the experiment except for the $n=6$ and $7$ resonances. According to the present calculation, the Rydberg cutoff due to field ionization could be about ${n}_{\mathrm{max}}=25$ instead of ${n}_{\mathrm{max}}=16$ to take into account the effect of the radiative decay during the time of flight. A sudden decrease is observed between the $n=7$ and $8$ resonances due to the opening of the $1s2s{}^{1}S\ensuremath{\epsilon}l$ continuum. From the agreement with experiment, it would appear that the present method is applicable to both the low-$n$ and high-$n$ resonances.

Predissociation ofH3Rydberg states

A fast-beam spectrometer is used to investigate the photofragmentation and autoionization dynamics of laser-excited triatomic hydrogen molecules. The yield of neutral products from rapidly predissociated states of ${\mathrm{H}}_{3}$ is monitored in parallel with the field ionization signal. Using this spectrometer, we have measured the natural lifetime of low principal quantum number Rydberg states ${\mathrm{nsA}}_{1}^{\ensuremath{'}}$ and ${\mathrm{npE}}^{\ensuremath{'}}.$ For the ${3sA}_{1}^{\ensuremath{'}},$ ${4sA}_{1}^{\ensuremath{'}},$ and ${5sA}_{1}^{\ensuremath{'}}$ electronic states, we find lifetimes decreasing with increasing principal quantum number. This is unexpected for a Rydberg series and confirms the observations of a previous investigation. In addition, our experiments give direct evidence that even very high principal quantum number Rydberg states of ${\mathrm{H}}_{3}$ are selectively subject to strong predissociation. This process appreciably shortens their natural lifetimes. In the high principal quantum number $\mathrm{ns}$- and $\mathrm{nd}$ Rydberg series converging to the lowest ionization threshold of ${\mathrm{H}}_{3}$ we find a significant variation of the predissociation yield with principal quantum number and electronic angular momentum. Windows with enhanced predissociation in the Rydberg series are explained by nonadiabatic couplings of the laser-prepared initial states with the repulsive ground states surface mediated by vibrationally degenerate mode excited ${4pE}^{\ensuremath{'}}$ and ${5pE}^{\ensuremath{'}}$ states. The relevance of the ${\mathrm{H}}_{3}$ predissociation mechanisms for the dissociative recombination of ${\mathrm{H}}_{3}^{+}$ is discussed.

Two-state model for top-of-barrier processes

A two-state model applicable to top-of-barrier processes in ion-atom collisions at low velocity $v$ is investigated. An expression for the Massey parameter of the transition $\stackrel{\ensuremath{\rightarrow}}{n}n+1$ is derived and is used to compute ionization, capture, and excitation from states of high principal quantum number in ${\mathrm{H}}^{+}+\mathrm{H}$ collisions. The Wannier law is obtained at the ionization threshold. The dependence of ionization on the initial n is computed. Total capture cross sections are in good agreement with other calculations, but an unreasonably large fraction goes to resonant capture. It is concluded that multicrossing models, which do not incorporate interference between different paths to the resonant state, overestimate resonant capture.

A New Technique for Measuring Impact‐broadened Radio Recombination Lines in Hii Regions: Confrontation with Theory at High Principal Quantum Numbers

ABSTRACTNew, low‐noise receivers have allowed detection, in several giant H ii regions, of Rydberg‐Rydberg transitions of hydrogen that cover a large range of Δn‐values in a single observing window. This, in turn, allows lines covering a large range in principal quantum number n to be detected simultaneously with the same antenna beam. We have employed a new frequency‐switching technique which allows a very precise determination of the line widths. We have used this technique with the NRAO 140 foot telescope to observe lines in W51 and Orion A near 6 GHz, with Δn‐values that vary by a factor of ∼21 (Δn = 1–∼21) and corresponding n‐values that vary by a factor of 2.7 (n = 102–274). By generating Voigt line profiles using Griem’s theory of impact broadening by electrons, inserting them into a telescope data file, and processing them in a manner identical to that of the telescope data, we have been able to examine how the observing and reduction techniques affect both the line widths and line areas as n increases. For n≤180,Δn≤6, our restored line widths and areas give densities of Ne = 2500 and 4000 cm−3 in W51 and Orion A, respectively. These densities are higher than reported previously with a 5′ beamwidth. For higher n‐values we are unable to fit our data using Griem’s theory. For n>180,Δn>6, our telescope‐measured line widths fall rapidly below predicted values, while the line areas simultaneously increase above predicted values. This behavior of the line area as the line widths decrease is inconsistent with Griem’s theory or an instrumental effect. Observations of Orion A at 17.6 GHz, with a 1.′7 beamwidth, require a density in excess of Ne = 20,000 cm−3 to fit. Although the detected lines cover a range in n and Δn from 71 to 177 and 1 to 17, respectively, there is no evidence for a line width decrease at the high Δn‐values. We conclude from this that the line narrowing seen at 6 GHz is related to the principal quantum number.

Spectral resolved X-ray transmission in hot dense plasmas

Using the detailed configuration accounting with the term structures treated by the unresolved transition array model, we present a method to calculate the transmission spectra for high-power laser-produced plasmas. Due to our fully relativistic treatment, incorporated with the quantum defect theory to handle the huge number of transition arrays from many configurations with high principal quantum number, we can calculate the opacities for any middle- and high-Z plasmas with little computational effort. We can also conveniently identify the dominant configurations and the detailed features of transition arrays, which are very helpful for the diagnostics of plasma conditions. The accuracy of our theoretical method is tested by comparing the calculated transmission spectra of Nb and Fe plasmas with benchmark experimental data.

Theoretical Simulation of the Transmission Spectra of Fe and Ge Plasmas

Using the detailed configuration accounting with the term structures treated by the unresolved transition array model, we present a method to calculate the transmission spectra of hot dense plasmas. Due to the fully relativistic treatment, incorporated with the quantum defect theory to calculate the atomic parameters of the huge number of configurations with high principal quantum number, we can study the opacities for any middle- and high-Z plasmas with much less computational efforts. We can also conveniently identify the dominant configurations and the detailed features of transition arrays, which are very helpful for the diagnostic of the plasma conditions. The accuracy of our theoretical model is tested by comparing the calculated transmission spectra of Fe and Ge plasmas with the bench mark experimental data.

Atomic orbital basis sets for use with effective core potentials

Basis sets developed for use with effective core potentials describe pseudo-orbitals rather than orbitals. The primitive Gaussian functions and the contraction coefficients in the basis set must therefore both describe the valence region effectively and allow the pseudo-orbital to be small in the core region. The latter is particularly difficult using 1s primitive functions, which have their maxima at the nucleus. Several methods of choosing contraction coefficients are tried, and it is found that natural orbitals give the best results. The number and optimization of primitive functions are done following Dunning's correlation-consistent procedure. Optimization of orbital exponents for larger atoms frequently results in coalescence of adjacent exponents; use of orbitals with higher principal quantum number is one alternative. Actinide atoms or ions provide the most difficult cases in that basis sets must be optimized for valence shells of different radial size simultaneously considering correlation energy and spin-orbit energy. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 516–520, 2000

Electronic broadening model for high-nBalmer line profiles

A method for line profile computations of Stark broadened high principal quantum number (PQN) Balmer series transitions is presented. Since quasistatic electron effects must be included in these cases, the traditional low density/low quantum number impact approximation for the electron broadening operator cannot describe the entire profile. For the high plasma densities and/or high principal quantum numbers $(\mathrm{PQN}>12)$ considered, an improved electron broadening contribution is proposed. Using a frequency dependent electron broadening operator, the line profile of the H Balmer $n=13$ transition is calculated using this electron operator and compared with profiles obtained using very accurate numerical simulations. The good agreement suggests that the procedure is sufficiently accurate to provide a predictive capability.

Electron-impact ionization cross section of rubidium

A theoretical model for electron-impact ionization cross section has been applied to Rb and the theoretical cross section (from the threshold to 1 keV in incident energy) is in good agreement with the recent experimental data obtained using Rb atoms trapped in a magneto-optical trap. The theoretical model, called the binary-encounter--dipole (BED) model, combines a modified Mott cross section with the high-energy behavior of Born cross sections. To obtain the continuum dipole oscillator strength $df/dE$ of the $5s$ electron required in the BED model, we used Dirac-Fock continuum wave functions with a core polarization potential that reproduced the known position of the Cooper minimum in the photoionization cross section. For inner-shell ionization, we used a simpler version of $df/dE$, which retained the hydrogenic shape. The contributions of the $4\stackrel{\ensuremath{\rightarrow}}{p}4d$, $5s$, and $5p$ autoionizing excitations were estimated using the plane-wave Born approximation. As a by-product, we also present the dipole oscillator strengths for the $5\stackrel{\ensuremath{\rightarrow}}{s}{\mathrm{np}}_{1/2}$ and $5\stackrel{\ensuremath{\rightarrow}}{s}{\mathrm{np}}_{3/2}$ transitions for high principal quantum numbers $n$ near the ionization threshold obtained from the Dirac-Fock wave functions with the same core polarization potential as that used for the continuum wave functions.

Electric Field Induced Dissociation of Molecules in Rydberg-like Highly Vibrationally Excited Ion-Pair States

The energetic thresholds for ion-pair photodissociation of diatomic oxygen $[{\mathrm{O}}_{2}+h\ensuremath{\nu}\ensuremath{\rightarrow}{\mathrm{O}}^{+}+{\mathrm{O}}^{\ensuremath{-}}(^{2}P_{3/2},^{2}P_{1/2})]$ were measured using a novel technique. The technique depends on the production and selective detection of highly vibrationally excited ion-pair states which last for at least $5\ensuremath{\mu}\mathrm{s}$ following single photon excitation from the ground electronic state of ${O}_{2}$. These ion-pair states are analogous to Rydberg states, and they may be dissociated by an electric field in a similar manner to the field ionization of high principal quantum number Rydberg states, allowing for their selective detection.

Two-photon dissociative photoionization and photodissociation of single rotational states

We report on an experimental study of dissociative photoionization and neutral dissociation of by two-photon excitation from single rotational states (photon energy ). The B-state rovibrational levels are excited in the same light pulse by three-photon absorption from . Angle resolved photoelectron and ion kinetic energy distributions allow us to discriminate between the different decay channels. Neutral decay is detected by one-photon ionization of excited atomic hydrogen product states. The kinetic energy distribution of photoelectrons from dissociative photoionization shows an oscillatory structure which depends on the initial B-state rotational quantum number J. An indication of a corresponding structure in the ion kinetic energy distributions is only found for J = 0. Similar to results reported by Verschuur et al we find neutral decay preferentially into high principal quantum number atomic states. The results indicate that the doubly excited states play a crucial role in the decay processes.

Spectroscopy of high n Rydberg states of the triatomic deuterium molecule D3

We report first investigations of high principal quantum number Rydberg states of the neutral triatomic deuterium molecule. The experiments were performed using a fast neutral beam photoionization spectrometer recently developed at Freiburg. A fast beam of metastable D3 molecules was created by charge transfer of a D3+ beam in cesium. Rydberg states of D3 were analyzed by pulsed-laser excitation using two-photon resonance-enhanced ionization, electric field ionization and autoionization. Our data identify the 2p 2A2″(N=K=0) state of D3 to be metastable with a lifetime of about 1 μs. The spectral lines following excitation in the ultraviolet spectral range were assigned to s-type and d-type Rydberg-series converging to vibrational ground state, symmetric stretch excited and degenerate mode excited D3+ ion states. By a combination of vibrationally diagonal and non-diagonal transitions, we determined the ionization potential, the symmetric stretch and degenerate mode vibrational frequencies of the 2p 2A2″ state in D3. The data give insight into the influence of the coupling between the Rydberg electron and the ion core on the potential energy surface.

Hydrogen-Assisted Laser-Induced Resonant Transitions between Metastable States of Antiprotonic Helium Atoms

Laser resonance transitions between normally metastable states of antiprotonic helium atoms were observed making use of state dependent quenching effects caused by small admixtures of ${\mathrm{H}}_{2}$ molecules. By selectively shortening the lifetimes of states with higher principal quantum number $n$ as compared to those of lower $n$, this method for the first time provides access to all initially populated metastable states of $\overline{p}{\mathrm{He}}^{+}$ atoms. This was demonstrated by observing the transitions $(n,l)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(38,l)\ensuremath{\rightarrow}(39,l+1)$, $l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}35,36,37$ and $(n,l)\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}(37,l)\ensuremath{\rightarrow}(38,l+1)$, $l\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}34,35,36$.

Lifetimes of Rydberg states in ZEKE experiments. III. Calculations of the dc electric field dependence of predissociation lifetimes of NO

Results are presented of calculations on the experimentally observed lifetime enhancement of high principal quantum number nf(N+=2) and np(N+=0) Rydberg states of the NO molecule in small dc electric fields. A Hund’s case (d) molecular Hamiltonian is introduced, which describes intramolecular interactions between low angular momentum Rydberg states as a result of core penetration and l mixing caused by the electric field. Eigenstates of the molecule in the electric field are obtained by diagonalization of the Hamiltonian and an effective decay time is determined which describes the multiexponential decay of the superposition of (Stark) states which is excited experimentally. The calculations reproduce the striking onset of the lifetime enhancement of the np(N+=0) series, which was observed experimentally. Both for the nf(N+=2) and np(N+=0) Rydberg series, core penetration by low-l states leads to extensive interseries coupling for several values of the principal quantum number.

Basic matrix elements for level shifts and widths of hydrogenic levels in ion-surface interactions.

We present extensive studies of basic one-electron matrix elements involved in ion-metal surface scattering theory. Our method allows for the convenient generation of matrix elements for high principal quantum numbers of hydrogenic projectile states and thus provides basic building blocks for the ab initio description of the interaction of highly charged ions with surfaces. The matrix elements related to the energy shifts can be evaluated for an arbitrary one-dimensional potential therefore allowing for flexibility in the choice of model-perturbation potentials. The transfer matrix elements between hydrogenic levels and conduction-band states have been formerly evaluated for the special case of eigenfunctions to the step-function potential. We extend these calculations to wave functions generated from an arbitrary one-dimensional surface potential and show applications to various surface potentials and hydrogenic levels. \textcopyright{} 1996 The American Physical Society.

L X-ray emission from slow multiply charged Ar ions bombarding Be and Al targets

Projectile L X-rays are observed for 18–260 keV Ar q+ ions ( q =7 − 14) bombarding Be and Al targets. X-ray yields are found to increase with the L-shell hole number for q ≥ 9. The X-rays are shown to be emitted stepwise, which allows to disintegrate the spectra into the individual steps. It is found that 3s-2p transition is dominant in each step. Transitions from higher angular momentum states like 3d-2p and those from higher principal quantum numbers are relatively weak.

Lifetimes of Rydberg states in zero-electron-kinetic-energy experiments. I. Electric field induced and collisional enhancement of NO predissociation lifetimes

Lifetime measurements are reported for high principal quantum number (n=40–125) Rydberg states of the NO molecule, prepared using state-selective double resonance excitation with a narrow bandwidth laser. The influence of (i) the application of a dc electric field, and (ii) interactions of the Rydberg states with surrounding ions, were investigated. It is demonstrated that the presence of dc electric fields can lead to enhancements in the lifetimes due to l-mixing, and the conclusion is reached that under the conditions existing in a typical zero-electron-kinetic-energy (ZEKE) photoelectron spectroscopy experiment, the Rydberg states involved are excited in a regime where l-mixing is expected to be significant. It is observed that l- and m-mixing collisional interactions provide a further mechanism to stabilize the optically prepared Rydberg states, beyond the limits which can be achieved by l-mixing alone.

Zero-kinetic-energy electron spectroscopy of the predissociating A2 Sigma + state of HBr+

The rotationally resolved zero-kinetic-energy electron spectra for the ${\mathit{v}}^{+}$=1, 2, and 3 vibrational levels of the predissociating ${\mathit{A}}^{2}$${\mathrm{\ensuremath{\Sigma}}}^{+}$ state of ${\mathrm{HBr}}^{+}$ are reported. The results for the rapidly predissociating ${\mathit{v}}^{+}$=2 and 3 levels show that the high principal quantum number Rydberg states involved in the zero-kinetic-energy spectroscopy are unperturbed by ion core fragmentation. These data demonstrate the general applicability of this technique for rotationally resolved photoelectron spectroscopy.