Centrifugal Barrier Effects Research Articles

Consistent kinetic-continuum dissociation model I. Kinetic formulation.

In this article, we propose a generalized non-equilibrium chemical kinetics model from ab initio simulation data obtained using accurate potential energy surfaces developed recently for the purpose of studying high-temperature air chemistry. First, we present a simple cross section model for dissociation that captures recent ab initio data accurately. The cross section model is analytically integrated over Boltzmann distributions and general non-Boltzmann distributions to derive a general non-equilibrium dissociation model. The general non-Boltzmann model systematically incorporates key physics such as dependence on translational energy, rotational energy, vibrational energy, internal energy, centrifugal barrier, and non-Boltzmann effects such as overpopulation and depletion of high energy states. The model is shown to reproduce the rates from quasi-classical trajectory calculations for Boltzmann distributions of internal energy states. The reduced rates in a non-equilibrium steady state due to depletion of high internal energy states are also predicted well by the model. Furthermore, the model predicts the enhanced rates as observed due to significant overpopulation of high vibrational states relative to Boltzmann distributions while the gas is in non-equilibrium in the transient phase. The model provides a computationally inexpensive way of incorporating non-equilibrium chemistry without incurring additional cost in the existing computational tools. Further comparisons of the model are carried out in Paper II, where simplifications to the model are proposed based on the results.

Centrifugal—Barrier Effects and Determination of Interaction Radius

The interaction radius of a resonance is an important physical quantity to describe the structure of a resonance. But, for a long time, physicists do not find a reliable way to measure the magnitude of the interaction radius of a resonance. In this paper, a method is proposed to measure the interaction radius in physics analysis. It is found that the centrifugal barrier effects have great influence to physical results obtained in the PWA fit, and the interaction radius of some resonances can be well measured in the fit.

Centrifugal barrier effects in metallic clusters

We report calculations of Rydberg states for spherical metallic clusters. These calculations demonstrate that centrifugal barrier effects operate, but that they act differently from the situation in atoms. Instead of orbital collapse, one sees a characteristic flattening of the effective potential: for and it occurs for the Rydberg electron, and for and , the Rydberg electron, which become very sensitive to core polarization effects. The effect of the centrifugal barrier on the quantum defects has been explored for various values of angular momentum.

Probing the spatial distribution of excited atomic states

We review several new optical techniques which reveal the spatial distribution of excited atomic states. These techniques have been developed in different laboratories, largely as a result of exploiting laser excitation, which provides additional flexibility in the choice of excitation paths. Several methods are in use, which possess different advantages, but all share one common property. They sample the wavefunction of the excited state at different radii using different excitation paths, and are thereby sensitive to size. Amongst the radial phenomena which control the size of an atomic orbital, the most important are the centrifugal barrier effects which determine orbital collapse.

Atomic spectra and instabilities of valence

The concept of valence is discussed in relation to recent studies of the subvalence spectra of free atoms. It is argued that valence can be profoundly modified by accidental degeneracies which occur as a result of centrifugal barrier effects. Examples of “atomic hybridisation” are given, and their effects on observed spectra are discussed. Another kind of valence change occurs when a radial wavefunction is poised on the verge of orbital collapse. An example is given where a change of valence can be triggered in an atomic cluster by varying the cluster size. The origin of the effect is traced to properties of the inner short-range well in the effective atomic potential when the centrifugal term is included. It is concluded that more account needs to be taken of the underlying atomic effects and especially radial properties when setting up theories of valence for transition elements.

An examination of centrifugal barrier effects in iodine pentafluoride by inner shell electron energy loss spectroscopy

Electron energy loss spectroscopy was used to study the core (I 4d, I 3d, and F Is) level electronic excitation spectra of IF5. The spectra were collected under experimental conditions such that dipole transitions were dominant (high electron impact energy (3 keV) and 0° scattering angle). The spectra were assigned using term value arguments, and by analogy with those of the isoelectronic molecules TeF6 and XeF4. In common with the spectra of TeF6 and XeF4, the spectra of IF5 show features that are consistent with a centrifugal potential-barrier model. In particular, transitions to virtual valence orbitals and to above-edge shape resonance channels are relatively intense, whereas transitions to Rydberg orbitals are, in comparison, very weak or absent. As in the case of TeF6, it was necessary to include atomic 4f orbitals in the molecular orbital basis to adequately account for the continuum resonance features observed in the IF5 spectra. The valence shell electron energy loss spectrum of IF5 from 5 to 35 eV was also obtained.

Near-threshold Behaviour of Generalised Oscillator Strengths for 2p Ionisation

Near the ionisation threshold, the behaviour of the generalised oscillator strength (GOS) is sensitive to the choice of the model atomic potential. In electron-impact ionisation, 'delayed maxima' of the GOS often occur near the ionisation threshold due to centrifugal barrier effects. In the present work, the sensitivity of this important effect of the centrifugal barrier to the model atomic potential has been studied using two local density atomic potentials, namely, the nonrelativistic Hartree-Slater potential and the relativistic RCB potential. Calculations have been done for electron-impact 2p ionisation of atomic oxygen, neon, aluminium, argon, iron and zinc. The GOS results for 2p ionisation of oxygen and aluminium are presented to illustrate the results.

Centrifugal barrier effects in the 3p spectrum of calcium

The authors report a new high-resolution study of the 3p spectrum of calcium at eight times the dispersion and resolution available to previous workers. The experiment was performed at the synchrotron radiation laboratory of the 500 MeV accelerator in Bonn. As a direct consequence of improved resolution, the analysis of the spectrum has been almost completely revised with the help of multichannel quantum defect theory. Centrifugal barrier effects are found to be responsible for a large difference in quantum defects between the singlet and triplet series. Some consequences are drawn concerning two-step autoionisation.

Multiconfiguration resonating-group theory of the seven-nucleon system with realistic cluster wave functions.

The properties of the seven-nucleon system are examined with a multiconfiguration and multi- channel resonating-group calculation. The cluster internal functions employed explain the charge-form-factor data over a wide range of ${q}^{2}$ and satisfy the variational stability condition quite well. The model space used is spanned by $^{3}$H+\ensuremath{\alpha}, n${+\mathrm{}}^{6}$Li, n${+\mathrm{}}^{6}$${\mathrm{Li}}^{\mathrm{*}}$, and d${+\mathrm{}}^{5}$He cluster configurations. The result shows that the specific distortion of the $^{3}$H+\ensuremath{\alpha} system is quite significant. With our multiconfiguration calculation, the ground-state energy is improved by more than 1 MeV. The calculated level spectrum agrees well with the level spectrum empirically determined. The energy positions of both natural-parity and unnatural-parity levels are reasonably explained. In addition, we find that, because of centrifugal-barrier effects, the aligned configuration generally makes the most sig- nificant contribution. The characteristics of nucleon-exchange terms are also briefly examined. Here it is found that, at sufficiently high energies where sharp resonance levels do not exist, the essential properties of these terms can already be learned by performing relatively simple single-configuration calculations.

Centrifugal barrier effects in the high Rydberg states and autoionising resonances of neon

The photoabsorption spectrum of neon in the range 500-700 AA has been investigated at high resolution using synchrotron radiation and a 3 m normal incidence vacuum spectrograph equipped with holographic gratings. All of the five Rydberg series 2p5(2P32/)ns(3/2)10, nd(1/2)10 and 2p5(1P12/)ns(1/2)10, nd(3/2)10 have been extended to high principal quantum numbers yielding accurate values for the ionisation potentials (2P32/=173 929.6+or-0.2 cm-1 and 2P12/=174 709.8+or-0.2 cm-1). In contrast with the corresponding features of heavier rare gases, the ns-nd interchannel interactions and autoionisation broadening are shown to be weak. The behaviour is discussed with reference to multichannel quantum defect and Hartree-Fock theory, and is shown to result from centrifugal barrier effects in the nd channels.

Limitations on CP-violating effects in strange particle decays

The difference in the partial weak decays between strange particles and antiparticles is suppressed by the ΔI= 1 2 rule or centrifugal barrier effects. However, for the case of heavier quarks, this difference can be of the order of 10 −3.

Predictive possibilities of unimolecular rate theory

This paper describes the calculation of rate constants for thermal unimolecular reactions and recombinations at the low pressure limit, at the high pressure limit, and in the intermediate falloff range, as well as the calculation of specific rate constants for unimolecular rearrangements. The most uncertain factors of the theory are identified by comparison with the NO/sub 2/, ClNO, H/sub 2/O, and O/sub 3/ systems. Weak collision and centrifugal barrier effects are discussed for low pressure rate constants. Simplified adiabatic channel calculations are proposed for specific rate constants and high pressure rate constants. Reduced falloff curves are presented in factorized form with weak collision and strong collision broadening factors. Simple falloff expressions are derived. 5 figures, 44 references, 3 tables.

Partial-wave analysis of theK¯Nsystem from 360 to 1320 MeV/c

In this paper we use new data from several recent $\overline{K}N$ experiments in conjunction with older data to make an energy-dependent partial-wave analysis of the $\overline{K}N$ system. The important new additions never used before in a partial-wave analysis are our precision measurements of the charge-exchange total cross sections, our measurements of the charge-exchange angular distributions, and the first measurements of the ${K}^{\ensuremath{-}}p$ polarization at these low momenta. A new feature introduced in the analysis is the $S$-wave cusp treatment at the $\ensuremath{\Lambda}\ensuremath{\eta}$ and ${\ensuremath{\Sigma}}^{0}\ensuremath{\eta}$ thresholds, which we find necessary to describe the observed behavior in the charge-exchange total cross sections near these thresholds. Other features include a single-channel unitary formulation for resonances and backgrounds and a parametrization of these amplitudes incorporating centrifugal-barrier effects. New values for masses, widths, and elasticities for resonances in this region are reported and better evidence is found for several of the less well established resonances. None of the new resonances suggested by recent $I=0$ and $I=1$ total-cross-section measurements are required. Fits are displayed for all the data used and predictions of this partial-wave analysis are compared with those of two other recent analyses for certain quantities yet to be measured. A table of the amplitudes, in steps of 20 MeV/c, is provided.

Molecular damping of centrifugal barrier effects in the 3d absorption spectrum of selenium vapour

In the light of recent work on shape resonances in diatomic systems, the question of a possible persistence of atomic centrifugal barrier effects in molecules arises, particularly as regards resonant penetration of f-waves. Experiments on selenium vapour suggest that two cases may be expected depending on whether localized f states are present or not in the atom. The evidence in Se is that f waves mainly external to the atom are scattered into several channels by the anisotropic molecular field and that damping of the f-maximum results. A reason is suggested for which inner shell absorption spectra of solids may not faithfully reproduce the density of states of the conduction band, even for elemental materials.

Molecular effects on inner-shell photoabsorption. K-shell spectrum of N2

K-shell photoabsorption spectra of the first-row diatomic molecules N2, CO, and NO are known to depart drastically from the behavior characteristic of K-shell excitation in atoms. Below the K-shell thresholds these spectra are dominated by a single, very intense peak rather than normal Rydberg structure, and the first 10–20 eV of the continuum exhibit a broad band of enhanced absorption, rather than a monotonic decrease. We use the multiple-scattering model to compute the discrete part and the first 100 Ry of the photoionization continuum for K-shell photoionization of N2. This calculation accounts for both novel features described above and shows that they arise from centrifugal barrier effects manifested as shape resonances in high-l components of the final state wavefunctions. These effects are molecular in origin, resulting from the interaction between the photoelectron and the anisotropic molecular field. We also discuss the energy dependence of the photoelectron angular distributions, Kronig structure in the high-energy continuum, bearing of the present results on valence-shell spectra, and the likelihood of widespread observation of shape resonances in ionization processes in other molecules.

Energy Dependence of Resonance Widths

The low-energy behavior of resonance widths can be explained by centrifugal-barrier effects, but this parametrization fails above the resonant energy. A recently proposed model for an inelastic resonance shows that resonance parameters are strongly influenced by an energy-dependent background amplitude. We present calculations for the ${P}_{33}$ partial wave in $\ensuremath{\pi}N$ scattering which show that the width of the $\ensuremath{\Delta}(1236)$ flattens out above 1450 MeV due to these background effects. We obtain a fit to the background amplitude up to 1800 MeV and find no evidence for a resonance at 1690 MeV.

Centrifugal-Barrier Effects in Resonance Partial Decay Widths, Shapes, and Production Amplitudes

(1) We review the experimental status of identifiable centrifugal-barrier effects in: (i) shapes of resonances, (ii) accounting for deviations in SU(2) and SU(3) predictions for ratios between partial decay widths, and (iii) accounting for the dependence on spin of the elastic widths of resonances lying on the same Regge trajectory. (2) We present a contour plot from which the "kinematic partial width" (centrifugal-barrier penetration factor times two-body phase space) of any resonance into any decay channel may be obtained immediately, given the orbital angular momentum, semiclassical impact parameter, and an assumed strong-interaction radius. Using this technique we display, as an example, the kinematically preferred decays of the high-spin mesons on the leading meson trajectory (assumed linear). (3) We obtain an approximate lower bound on the strong-interaction radius on the basis of general considerations. (4) We show that, for high-spin resonances, it can be expected that the mass enhancements in different decay channels associated with these resonances may be shifted by a half-width or so with respect to each other, because of different centrifugal-barrier effects in the different channels. (5) We also show that production cross sections of high-spin particles on leading linear trajectories by either formation or peripheral processes will be substantially suppressed by centrifugal-barrier effects. (6) Finally, we observe that the production cross sections and decay widths of mesons on the leading trajectory of the Veneziano model can be understood almost entirely on the basis of kinematical considerations if the radius of the region in which the decay particles interact strongly grows linearly with the mass of the decaying resonance.

NEW ALPHA-DECAY BARRIER PENETRABILITIES WITH IGO POTENTIAL: EVEN-MASS NUCLEI

The lgo potential is used for the calculation of barrier penetrabilities for ground-state and excited-state transitions of even–even nuclei and for transitions of odd–odd nuclei, measured after 1959. The barrier penetration factors were calculated by numerical integration in the WKB approximation, taking into consideration centrifugal barrier effects for even–even nuclei, but ignoring non-central interactions. Using the calculated penetration factors and the experimental alpha half-lives, the reduced level widths were calculated in each case. The barrier penetration factors and the reduced level widths are given for total decay energy (alpha-particle energy plus electron-screening correction plus recoil energy).

New alpha-decay barrier penetrabilities with Igo potential: Even- and odd-mass nuclei

TheIgo potential is used for the calculation of barrier penetrabilities for ground and excited state transitions of even mass nuclei and for transitions of odd-mass nuclei, measured after 1959. The barrier penetration factors were calculated by numerical integration in the WKB approximation, taking into account centrifugal barrier effects for even-even nuclei, but ignoring noncentral interactions. Using the calculated penetration factors and the experimental alpha half-lives, the reduced level widths were calculated in each case. Hindrance factors for odd-mass alpha-particle emitters are also given.

Alpha-Decay Barrier Penetrabilities with an Exponential Nuclear Potential: Even-Even Nuclei

The real potential derived by optical-model analysis of data on elastic scattering of alpha particles is used for calculation of barrier penetrabilities for all known alpha decay groups of even-even nuclei. The barrier penetration factors were calculated by numerical integration in the WKB approximation taking into account centrifugal barrier effects, but ignoring noncentral interactions. Using these penetration factors and the experimental alpha half-lives, the reduced level widths ${\ensuremath{\delta}}^{2}$ are calculated. Ratios of ${\ensuremath{\delta}}^{2}$ values for ground and excited-state alpha groups are tabulated as a set of reduced hindrance factors.