Cross Sections For Transitions Research Articles

The He–CaH(2Σ+) interaction. II. Collisions at cold and ultracold temperatures

We present cross sections for rotational, vibrational, and fine-structure transitions in He–CaH(2Σ) collisions at cold and ultracold temperatures calculated using the ab initio potential energy surface reported in the preceding paper. Rotational quenching is fast, vibrational quenching is slow. The spin-rotational interaction, although small and having no influence at temperatures above 10 K, changes significantly the rate coefficients for rotational quenching at lower temperatures. The theoretical rotational, vibrational, and elastic cross sections are compared with the results of a buffer gas cooling experiment carried out at a temperature of about 0.4 K. The theoretical predictions for the vibrational and elastic cross sections are larger than the measured values. The sensitivity to the potential energy surface is explored. A modified surface diminishes but does not remove the differences between theory and experiment.

Photoionization of the H2molecule in the random phase approximation

A detailed study of photoionization of the H2molecule is presented in the random phase approximation. The total photoionizationcross section in the photon energy region from the ionization threshold up to 200eV is in good agreement with experimental data. Partial cross sections for allnon-negligible transitions are presented. The Cooper-like minimum in the1σg → pσuchannel at about 80 eV photon energy is predicted. Molecular framephotoelectron angular distributions are presented for different kinds of lightpolarization, and compared with recent experiment, where available.

Collisional quantum interference on rotational energy transfer in Na2 (A 1Σu+, v = 8 ∼ b 3Π0u, v = 14)–Na system

Collisional quantum interference on rotational energy transfer was observed by Sha et al. (J. Chem. Phys., 1995, 102, 2772) and the interference phase angle which determines the magnitudes of the transition cross sections was introduced there. Collisional quantum interference was also observed in Na2 (A 1Σu+, v = 8 ∼ b 3Π0u, v = 14) system in collision with Na (Chem. Phys. Lett., 2000, 318, 107), but the interference angle had not been measured out due to the lack of enough experimental data. In this paper, we have computed the interference angles for singlet–triplet mixed states of Na2 (A 1Σu+, v = 8 ∼ b3Π0u, v = 14) system in collision with Na by using the first order Born approximation of time dependent perturbation theory. Two different interaction potentials (long range attractive and Lennard-Jones interactions) have been employed to simulate the interference angles. The relationships of the interference angle versus temperature have been obtained. And the various factors that influence the interference angle have been discussed.

Energy dependence of the intramultiplet mixing cross section in Hg–N2 collisions: Conical intersection mechanism, indication at tunneling and interference

Experimental results on the energy dependence of the cross section for the intramultiplet transitions in Hg atom induced by collisions with the rotationally cold nitrogen molecules, 3P1,v=0→3P0,v=1, v being the vibrational quantum number of N2 (M. Okunishi, J. Hashimoto, H. Chiba, K. Ohmori, K. Ueda and Y. Sato, J. Phys. Chem. A, 1999, 103, 1742.) are interpreted within rotationally sudden versions of the Landau–Zener and generalized Landau–Zener–Teller models. The broad threshold region of the cross section is ascribed to noticeable dependence of the avoided crossing seam energy on the collision angle between two conical intersection points (linear and T-shaped configurations) and to the tunneling/interference effects in the transition probability. The experimental energy dependence of the cross section is consistent with the anticipated values of the crossing-point energy at the optimal configuration.

Dissociative Excitation of Even Doublet Levels of the Cobalt Atom in Electron Collisions with Cobalt Dichloride Molecules

The dissociative excitation of the even doublet levels of the cobalt atom upon the collisions of cobalt dichloride molecules with 100-eV monoenergetic electrons was experimentally studied. Dissociative excitation cross sections for transitions from these levels turned out to be greater than the corresponding cross sections of direct excitation in electron-atom collisions (except for the e2P1/2 level). The total excitation cross sections (including the contribution of cascade population) were determined for ten levels.

Study of IR absorption and photoconductivity spectra of thermal double donors in silicon

AbstractThe IR absorption and photoconductivity spectra of a double donor (TDD) family with ionization energies less than 70 meV in silicon were investigated using Fourier transform spectroscopy with a resolution down to 0.25 cm–1. The values of line frequencies, widths, splitting and absorption cross sections for transitions from the ground to p‐states (including high‐excited states) were obtained. Determination of absorption cross sections was made using Hall data and concerted changes of boron and TDDi concentrations caused by neutralization of impurities under band gap illumination.

Analytical method for finding the general optical properties of semiconductor deep centers

The optical properties of deep centers and their dependence on general materials parameters are predicted from an analytical eight-band k⋅p model of deep-center states. A wide variety of deep centers in a wide variety of direct-gap semiconductors can be modeled this way. Scanning-tunneling-microscopy images and measured optical dipoles are in excellent agreement with our model. Our model of deep-center optical properties is the most detailed, multiband k⋅p model which remains fully analytical. Our model of deep centers goes beyond previous work in being able to simultaneously explain, within an analytical framework, both the size and spectral shape of the experimentally measured cross sections for optical transitions from deep levels to (i) the valence band, and (ii) the conduction band; as well as, (iii) observed optical selection rules, and (iv) scanning-tunneling-microscopy images of deep-level bound states. Very good agreement is observed between our model and experiment for deep levels in a variety of (large and small band-gap) semiconductors: the arsenic antisite in both GaAs and In0.53Ga0.47As; the chromium substitutional impurity in both GaAs and InP; and the indium vacancy in InSb. Good agreement is achieved between our model and experiment because both the size and spectral shape of the cross sections for direct optical transitions from the deep level (to the conduction or valence-band edge) is found to be determined by the small-wave-vector component of the deep-center wave function. It is precisely the small-wave-vector component of the deep-center wave function which is described well by our eight-band k⋅p model. Significantly, this agreement between our model and experiment is a vindication of the general materials parameters (Kane dipole, nonparabolic effective masses, band-gap energy, spin-orbit splitting) characterizing our eight-band model of deep centers, rather than a result of careful use of adjustable parameters. Our model shows that the spatial extent of the deep-center bound state is proportional to the Kane dipole, and is thus larger (more delocalized) in a smaller band-gap semiconductor. Moreover, our model shows that, in order to successfully predict optical properties, a linear combination of atomic orbitals describing deep centers must extend over many lattice sites: more than just the neighbors and next-nearest neighbors of the deep center.

Resonance contributions to collision strengths for transitions between magnetic sublevels in highly charged ions by impact with an electron beam

A fully relativistic approach is described for obtaining the resonance contribution to the cross sections for transitions between magnetic sublevels in highly charged ions due to impact with an electron beam. We derive the relativistic distorted-wave cross section for the ion in a lower N-electron magnetic sublevel to capture a directive electron and form a doubly excited $(N+1)$-electron magnetic sublevel. Also the autoionization rate from this magnetic sublevel to an N-electron magnetic sublevel is derived. The resonances are then treated as the two-step process of electron capture followed by autoionization to the final sublevel with the effects of autoionization to a different final level or radiative decay of the doubly excited sublevels included. These resonance contributions are added to the relativistic distorted-wave results for the ``direct'' contribution to give the complete cross section. Numerical results expressed in terms of the collision strengths are calculated and studied for He-like oxygen and iron and for Be-like oxygen. These are of interest for electron beam ion trap experiments and population alignment analysis.

Lu-Fano plot for interpretation of the photoassociation spectra

Recently, the method of Lu-Fano plots was extended to potentials with general R - n asymptotic behavior. The aim of this paper is to discuss the efficiency of this method for the interpretation of experimental vibrationalspectra of long-range diatomic molecules when two channels are coupled. A Lu-Fano analysis is implemented on experimental data for the Cs 2 0 + u (6S+6P 1 / 2 , 3 / 2 ) photoassociation spectra below the 6S+P 1 / 2 and 6S+P 3 / 2 dissociation limits. The parameters are fitted on level energies and predissociation widths, giving information about the asymptotic coefficients C 3 for both channels and about a coupling parameter which determines the variation of predissociation widths as a function of detuning. This parameter can be extrapolated above the 6S+P 3 / 2 threshold to yield the fine-structure transition cross section between the two channels. The probability for such a transition in a model where hyperfine structure effects are neglected is found to be 0.54.

Determination of the radiation cross sections of low-energy transitions of isomeric nuclei from observation of laser-induced γ fluorescence

Theoretical estimates are given along with the first experimental results on the observation of resonance fluorescence in nuclei of rubidium isomer under conditions of laser plasma X-ray pumping of the contiguous transition with an energy of 3.4 keV. The laser plasma is prepared by irradiating a silver target by a powerful radiation of a Nd laser with a pulse duration of 600 ps. It is demonstrated how one can use the recorded number of emitted γ quanta to determine the probability of low-energy nuclear transition excited by laser plasma X rays.

Calculations of photodissociation cross sections by the smooth exterior complex scaling method

We show that total photodissociation cross sections can be calculated directly by the smooth exterior complex scaling method. First, an application to a model problem, characterized by the resonance-dominated cross section is considered, in which the detailed comparisons with approaches employing the standard complex scaling and the complex absorbing potentials are made. Second, the photodissociation cross sections for transitions from the ground vibrational state of the X 2 Π electronic state of HCl + to the continua of the (2) 2 Π and (3) 2 Π states are calculated, by using a discrete set of realistic molecular data.

Optical properties of YVO4 crystals singly doped with Er3+, Ho3+, Tm3+

In this work the spectroscopic properties of YVO4 singly doped with erbium, holmium and thulium are considered. Multiphonon relaxation rates have been estimated. Stimulated emission cross sections for laser transitions in the near IR region have been assessed.

Use of radiation trapping for measuring electron-impact excitation cross sections for higher resonance levels of rare-gas atoms

Radiation trapping causes the optical emission cross sections for transitions from an atomic resonance level to lower levels to be dependent on the atom number density. We have measured the optical emission cross sections for a number of heavy rare-gas resonance transitions over the pressure range of 0.04 to 30 mTorr. We compare the results with the theory of Heddle, using it to extrapolate our cross-section data to the high-pressure regime where the resonance radiation is completely reabsorbed. This allows us to obtain the apparent excitation cross section for seven resonance levels of Ne, Ar, and Kr without measuring the resonance radiation that would otherwise entail vacuum ultraviolet radiometry. In some cases, our analysis of the measured pressure dependence of the optical emission cross sections points out the need for improved transition probabilities values.

Characterization of spectroscopic and laser properties of Pr3+ in Sr5(PO4)3F crystal

Spectroscopic and laser properties have been characterized for Pr3+ incorporated into Sr5(PO4)3F crystal belonging to the apatite structure family. The standard Judd–Ofelt analysis has been applied to the measured optical absorption intensities to determine the radiative decay rates, branching ratios, and emission cross sections of principal intermanifold transitions of Pr3+ from the D21 and P03 states to the lower-lying manifolds in the visible region. The measured room temperature fluorescence lifetimes of the D21→3H4 (594 nm) and P03→3F2 (625 nm) transition are 325 and 105 μs, respectively, while the Judd–Ofelt analysis predicts the radiative lifetimes for the D21 and P03 states to be 822 and 116 μs, respectively. The room temperature emission cross sections of the D21→3H4 and P03→3F2 intermanifold transitions have been also determined to be 0.54×10−20 and 4.15×10−20 cm2, respectively.

Theoretical Study of the Effect of the Intermolecular Spin−Orbit Interaction in the Collision-Induced Intersystem Crossing of S1 State Glyoxal by Ar

The intersystem crossing from S1 to T1 in glyoxal induced by the collision of Ar has been studied theoretically. In particular, we have focused on the effects of the intermolecular spin−orbit interaction, which was not considered important in this process. The interaction potential of S1 in the glyoxal and Ar system was carried out by the CASSCF method. Further, the interaction potential of T1 and the spin−orbit interaction, which is represented by the Breit-Pauli Hamiltonian, between S1 and T1 were calculated by the full-CI method with the same active spaces and molecular orbitals as those of the CASSCF calculations for S1. Using these calculation results, the semiclassical dynamics calculations were employed to estimate the transition cross sections and rate constants. It is found that the intermolecular spin−orbit interaction largely amplifies the transition probabilities and the relaxation on the T1 state is indispensable to describing the dynamics in this intersystem crossing.

Three-Dimensional Analytic Model of Vibrational Energy Transfer in Molecule-Molecule Collisions

Athree-dimensionalsemiclassicalanalyticmodelofvibrationalenergytransferincollisionsbetweentworotating diatomic molecules has been extended for molecule ‐molecule collision. The model is based on analysis of classical trajectories of free-rotating (FR) molecules acted upon by a superposition of repulsive exponential atom-to-atom potentials. The energy transfer probabilities have been evaluated using the nonperturbative Forced Harmonic Oscillator (FHO) model. The model predicts the probabilities for vibrational energy transfer as functions of the total collision energy, orientation of molecules during a collision, their rotational energies, and impact parameter. The model predictions have been compared with the results of three-dimensional close-coupled semiclassical trajectorycalculationsusingthesamepotentialenergysurface.Thecomparisondemonstratesnotonlyremarkably good agreement between the analytic and numerical probabilities across a wide range of collision energies, but also shows that the analytic FHO-FR model correctly reproduces the probability dependence on other collision parameters such as rotation angles, angular momentum angles, rotational energies, and impact parameter. The model equally well predicts the cross sections of single-quantum and multiquantum transitions and is applicable up to very high collision energies and quantum numbers. Most importantly, the resultant analytic expressions for the probabilities do not contain any arbitrary adjustable parameters commonly referred to as steric factors . The present work essentially completes development of the analytic rate database for vibrational energy transfer among air species, increasing the range of applicability of the FHO-FR model.

Convergent series representation for the generalized oscillator strength of electron-impact ionization and an improved binary-encounter-dipole model

The use of the Bethe cross section in the binary-encounter-dipole (BED) model for electron-impact ionization is studied. While the dipole contribution in the Born approximation accounts for the longest-range interaction in electron-neutral atom/molecule inelastic collisions at any incident energy, the Bethe formula is applicable only at high energies. To derive a suitable representation of the Born cross section for dipole-allowed transitions, a convergent series representation for the generalized oscillator strength (GOS) of electron- impact ionization is studied. It is shown that by transforming to a new variable determined by the location of the singularities of the GOS on the complex plane of momentum transfer K, a series representation for the GOS is obtained that is convergent at all physically attainable values of K. An approximate representation of the GOS that truncates the series representation to the first three terms is also given. The approximate GOS describes the interaction of the electron with a shielded dipole potential and satisfies both Lassettre's limit theorem at $K=0$ and the asymptotic behavior at large K derived by Rau and Fano [A. R. P. Rau and U. Fano, Phys. Rev. 162, 68 (1967)]. The dipole-Born cross section so obtained is applicable at all incident energies and goes to the Bethe cross section at the high-energy limit. It provides a more suitable representation of the dipole contribution in the BED model than the Bethe cross section and is valid over the entire energy range. A similar analysis of the optical-oscillator strength (OOS) as a function of the complex momentum for the ejected electron ${k}_{p},$ plus the requirement that the OOS satisfies both the low- and $\mathrm{high}{\ensuremath{-}k}_{p}$ limits produces an analogous series representation for the OOS. An approximate one-term representation of the OOS is also developed that can be used in modeling calculations. Numerical examples of total ionization cross sections of ${\mathrm{N}}_{2},$ ${\mathrm{H}}_{2}\mathrm{O},$ ${\mathrm{CO}}_{2},$ ${\mathrm{CH}}_{4},$ and ${\mathrm{CF}}_{4}$ using the new analytical representation are presented to illustrate the applicability of the improved BED model.

Relativistic calculations for incoherent photoproduction of η mesons

We develop a relativistic model for incoherent η-photoproduction on nuclei. The elementary process is described using an effective Lagrangian containing photons, nucleons, the S 11(1535) and D 13(1520) nucleon resonances, and ρ, ω and η mesons. The nucleon and η wave functions are obtained from relativistic wave equations. Final-state interactions of the outgoing particles are included via optical potentials. The effects of these interactions are found to be large and lead to reduced cross sections.The incoherent cross sections for isovector transitions are much larger than those for isoscalar ones. The dominant contributions are those from the S 11 and D 13 resonances. We find important interference effects between the contributions of these two resonances. We give some detailed calculations for the cross sections for incoherent η-photoproduction on 12C. We find that the incoherent cross section for a subset of states in the excitation energy region below 17 MeV are significantly larger than those of the coherent process. These cross sections may thus be accessible experimentally.

Scaling of plane-wave Born cross sections for electron-impact excitation of neutral atoms

Two methods to scale plane-wave Born cross sections for electron-impact excitations of neutral atoms are shown to produce excitation cross sections comparable in accuracy to those obtained by more sophisticated collision theories such as the convergent close-coupling method. These scaling methods are applicable to integrated cross sections for electric dipole-allowed transitions. Scaled cross sections are in excellent agreement with available theoretical and experimental data for excitations in H, He, Li, Be, Na, Mg, K, Ca, Rb, Sr, Cs, Ba, Hg, and Tl, indicating the possibility of rapid and reliable calculations of excitation cross sections for many other neutral atoms.

Electron-impact excitation of lithium

The results of R-matrix with pseudostates (RMPS) and time-dependent close-coupling (TDCC) calculations of electron-impact excitation in Li are presented. We included 55 terms in the RMPS close-coupling expansion, of which nine are spectroscopic and 46 are pseudostates. The two-electron radial wave functions generated from earlier TDCC calculations for ionization from the ground state of Li by Colgan et al. [Phys. Rev. A 63, 062709 (2001)] are employed to determine the TDCC excitation cross sections. The RMPS and TDCC cross sections for transitions from ${1s}^{2}2s$ to ${1s}^{2}2p,$ ${1s}^{2}3l,$ and ${1s}^{2}4l$ are compared to each other and to cross sections determined from our R-matrix calculation without pseudostates, the convergent close-coupling calculations presented by Schweinzer et al. [At. Data Nucl. Data Tables 72, 239 (1999)], the coupled-channel optical calculations of Bray et al. [Phys. Rev. A 47, 1101 (1993)], and experimental measurements. These results indicate that coupling to the target continuum has a significant effect on electron-impact excitation in this atom; this increases with the principal quantum number of the excited term, and is large for transitions to ${1s}^{2}4l.$