Small Internuclear Separations Research Articles

Energies and angular characteristics of the resonance important for Penning and associative ionization in He(23S)-H collisions

We report R-matrix calculations for energies and width of the lowest 2 Sigma resonance important for Penning and associative ionization in He-H collisions. The ab initio determination of the angular distribution of the He (23S)-H (12S) resonance is reported. This resonance is anisotropic with considerable d character at small internuclear separation, whereas previously it had been assumed to have an isotropic distribution.

State-selective electron capture by slow N4+ ions in collisions with helium

Translational energy spectroscopy in an apparatus previously developed in this laboratory has been used to study one-electron capture by 4-28 keV N4+ ions in collisions with helium. The main excited N3+ product channels have been clearly identified and the relative cross sections determined. The two main channels are found to involve core rearrangement. While the N3+ 2p2 1 S product channel is dominant, it is shown that other channels involving large energy defects contribute significantly at the higher energies thereby resulting in an essentially energy invariant total one-electron capture cross section: MCLZ calculations, which have also been carried out, satisfactorily predict the main 2p2 1 S product channel but fail to account for the other channels arising from curve crossings at small internuclear separations.

One- and two-electron atomic screening in fusion reactions.

Recent laboratory experiments have measured fusion cross sections at center-of-mass energies low enough that the effects of atomic electrons are important. To extract the cross section for bare nuclei from these data (as required for astrophysical applications), it is necessary to understand these screening effects. We present a model in which the evolution of the electron wave function is treated dynamically in the time-dependent Hartree-Fock scheme, while the motion of the nuclei is treated classically. We have calculated screening in the d+2H and d+3He reactions and give the effective screening energy Ue at small internuclear separations as a function of E. The resulting Ue values do not exceed the previously established adiabatic limits, and thus cannot explain the higher screening energies derived from experiment.

Supplementary d and f functions in molecular wave functions at large and small internuclear separations

AbstractThe CO, CO2, CS, CIF, and SO2 molecules were used to test the dependence of supplementary d and f function exponents to changes in bond lengths and bond angles in MO calculations utilizing Gaussian basis sets in Hartree–Fock and Moller–Plesset calculations. Using Dunning–Hay double zeta basis sets, optimizations were performed at internuclear separations from 100–200 pm and beyond. The energy cost of not reoptimizing d function exponents when bonds are stretched or compressed is much smaller for correlated calculations than for those at the Hartree–Fock level and is greatest at the lower end of the range of internuclear distances. The problem is much less serious at all levels when multiple sets of d functions are used. © 1993 John Wiley & Sons, Inc.

Observation of collision-induced-dipole absorption bands in strontium–rare-gas mixtures. I. The 5s–4d bands

Reduced absorption coefficients have been measured for the collision-induced-dipole (CID) absorption bands associated with the 5s–4d transition of atomic strontium perturbed by He, Ne, Ar, Kr, Xe, and Sr. The main CID absorption band, assigned to 5sΣ–4dΣ, extends from the position of the atomic 5s–4d transition towards the shorter-wavelength side for every perturber. For Xe and Kr, an additional small absorption band is seen at the foot of the atomic 5s–4d transition. The former 5sΣ–4dΣ band is interpreted to result from collisional mixing of the 5p state of atomic Sr into the molecular 4dΣ state for small internuclear separations, while the latter band is interpreted to result from the collisional quadrupole (strontium)–dipole (Xe or Kr) interaction.

Depolarisation in Na-Ar optical collisions

The depolarisation of the redistributed Na D1 and D2 line fluorescence caused by Na-Ar collisions after far-wing excitation was investigated. In the limit of zero Ar density the J=1/2 orientation and J=3/2 alignment reflect the distribution among Zeeman sublevels of Na 32PJ produced after absorption of a photon into one or several excited Na-Ar molecular states at small internuclear separation, followed by a mixing between these states during dissociation. Measurements of these quantities as functions of the detuning up to Delta omega J=50 cm-1 in the red wings are compared with quantum-mechanical coupled-channel (CC) calculations using realistic molecular potentials and thermal averaging, and with predictions from the factorisation approximation (FA) of the theory of redistribution. Fair agreement with CC calculations and FA predictions was obtained within the impact region, proving the validity of the factorisation assumption there. Outside this region the overall depolarisation is primarily due to reorientation of the Na 3P electronic angular momentum and is reproduced qualitatively by the CC calculations but not by the FA theory. Additional depolarisation connected with the fine-structure coupling was observed.

Theoretical Herman-Wallis coefficients for C70 and D70 and the dipole-moment function of HCl

Theoretical expressions for the Herman-Wallis coefficients C 7 0 and D 7 0 and a correction term of order 2 B e /ω e times the leading term for C 6 0 have been derived in terms of the Dunham potential-energy parameters and series dipole-moment expansion coefficients by the method of computer algebra. After reviewing previous work on the extraction of the dipole-moment function for HCl from experimental data, the present results are applied to a determination of the series representation up to seventh order in the reduced displacement from the equilibrium internuclear separation. Coefficients for an alternate representation in terms of a Padé approximant are also obtained; this model dipole-moment function should enable one to estimate more accurately the higher overtone and highly excited hot-band intensities since it circumvents the divergence difficulties of the series expansion and has the correct asymptotic behavior at both small and large internuclear separations.

Analysis of the polarization-dependent rate of associative ionization of radiatively excited Na(3p) atoms.

Kircz, Morgenstern, and Nienhuis [Phys. Rev. Lett. 48, 610 (1982)] have measured the cross section for the associative ionization of partially oriented pairs of excited [(3p) $^{2}P_{3/2}$] sodium atoms. Here, we extract information from these data about the identities of the participating adiabatic Born-Oppenheimer states of ${\mathrm{Na}}_{2}$. It is definitely established that more than one of these states is involved. The greatest contributor is the X $^{1}\ensuremath{\Sigma}_{g}^{+}$ state with the dominant molecular-orbital configuration ${\ensuremath{\sigma}}_{g}^{2}$ (at small internuclear separations). It is highly probable that only one other state (either the $^{1}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{+}$ or $^{3}\mathrm{\ensuremath{\Sigma}}_{\mathrm{g}}^{\mathrm{\ensuremath{-}}}$ state with the dominant molecular-orbital configuration ${\ensuremath{\pi}}_{u}^{2}$) is involved, but a small contribution from one state ${(}^{1}$${\ensuremath{\Pi}}_{u}$ or $^{3}\mathrm{\ensuremath{\Pi}}_{\mathrm{u}}$) with the configuration ${\ensuremath{\sigma}}_{g}$${\ensuremath{\pi}}_{u}$ cannot be unequivocally dismissed.

The vibrations and rotations of the pseudogaussian oscillator

Abstract In this paper we discuss the energy levels and wavefunctions of a rotating diatomic molecule using a three-parameter model potential called the pseudogaussian potential which is reasonably behaved for both small and large internuclear separations. The solutions to this model problem provide a reasonable description of the rotating diatomic molecule and also will be useful in discussing large amplitude vibrations in triatomic and larger molecules. A comparison is made with the Morse oscillator.

Adiabatic translation factors in slow ion-atom collisions

The authors discuss the general properties of translation factors in slow atomic collisions. It is emphasised that an acceptable form of translation factors must be conceptually consistent with the basic underlying assumption of the molecular model; i.e. translation factors must relax adiabatically at intermediate and small internuclear separations. They apply a simple physical argument to derive a general parameter-free expression for the translation factor pertinent to an electron in a two-centre Coulomb field. Within the present approach the adiabatic translation factor is considered to be a property of the two-centre field independently of the molecular state under consideration. The generalisation to many-electron systems is therefore readily made. Their discussion is illustrated by a simple example.

Molecular effects in beam-foil collision-induced alignment of He I

We have measured the alignment of beam-foil collision-excited states of He I produced by bombarding carbon foils of various (1.3-110 \ensuremath{\mu}g/${\mathrm{cm}}^{2}$) areal densities with beams of ${\mathrm{He}}^{+}$ and He${\mathrm{H}}^{+}$. In addition, we have measured the total light yield of several transitions in He I, He II, and H as a function of foil thickness using beams of He${\mathrm{H}}^{+}$ ions. Experiments were done with He-foil exit energies of 125, 500, 550, and 650 keV. He I alignment decreases in all cases for the thinnest foils when molecular projectiles are used. Total light intensities generally increase with thin foils (small proton-He emergent internuclear separation), but a few decrease or are independent of foil thickness. We are able to explain several features of the alignment and intensity data in terms of the formation of quasimolecular He${\mathrm{H}}^{+}$ states at or near the foil surface. Alignment reduction results from incoherent Stark mixing of the He I excited states in the field of the close proton. A calculation of the rms emergent H-He internuclear separation as a function of foil thickness and beam energy is presented.

Foil Dissociation of Fast Molecular Ions into Atomic Excited States

We have measured the intensity and polarizations of light emitted from atomic excited states of dissociated molecular ions. The dissociations are induced when fast molecular ions (50-500 keV/amu) are transmitted through thin carbon foils. A calculation of multiple scattering and the Coulomb explosion gives the average internuclear separation of the projectile at the foil surface. Experimentally, we vary the foil thickness to give varying internuclear separations at the foil surface and observe the consequent variation in light yield and optical polarization. Using HeH+ projectiles, we have observed factors of 1-5 enhancements of the light yields from n=3, P,D states of He I and some He II and H I emissions. The results can be explained in terms of molecular level crossings which provide mixings of the various final states during dissociation of the molecular ions at the exit surface. They suggest a short range surface interaction of the electron pick-up followed by a slow molecular dissociation. Alignment measuremerts confirm the essential features of the model. Observations of Lyman ? emission after dissociation of H2+ and H3+ show rapid variations in light yield for small internuclear separations at the foil surface.

Quasi-molecular binding corrections to the two-state atomic expansion method for electron capture at low energies

The two-centre, two-state atomic expansion method previously developed for calculating electron capture cross sections for ion-atom collisions at intermediate energies is generalised to the lower energy region. By replacing the asymptotic energy defect term between initial and final states of the atomic expansion theory by the difference of the corresponding quasi-molecular energies, the effect of transient molecule formation during the collision is partially accounted for. The increased quasi-molecular binding at small internuclear separation has the effect of reducing electron capture cross sections at lower incident energies; the cross sections thus calculated show improved agreement with experimental data.

Self-consistent-field potential energies for the ground negative-ion and neutral states of HeH, ArH, and ArCl

Self-consistent-field (SCF) calculations have been used to determine the ground negative-ion and ground neutral potential-energy curves for HeH, ArH, and ArCl. In the systems studied, the $X^{1}\ensuremath{\Sigma}$ potential of the negative-ion state is more repulsive at intermediate internuclear separations than the $X^{2}\ensuremath{\Sigma}$ potential of the neutral partners, leading to a curve crossing of the negative-ion state into the continuum. However, at small internuclear separations the negative-ion potential becomes less repulsive than the neutral potential, leading to a second curve crossing out of the continuum. The calculated potential-energy curves are used to provide estimates of the energy thresholds and cross sections for electron detachment in the collisions ${\mathrm{H}}^{\ensuremath{-}}$ + He, ${\mathrm{H}}^{\ensuremath{-}}$ + Ar, and ${\mathrm{Cl}}^{\ensuremath{-}}$ --Ar. The angular thresholds for electron detachment in differential-scattering measurements are also given and compared to experimental data.

SCF potential curves for AlH and AlH+ in the attractive and repulsive regions

Self-consistent-field calculations have been carried out for the systems AlH and AlH+ in their ground and excited states. Distances considered range from separated atoms and ions to 0.1 bohr, or ΔE ?2700 eV. Additional calculations were performed to determine the effect of core and valence electrons at small internuclear separations. A comparison was made of the ab initio potential curve obtained for the 1Σ+ state with results obtained from the Thomas–Fermi statistical model.

Relativistic and nonrelativistic effective core potentials for xenon. Applications to XeF, Xe2, and Xe2+

Valence electron calculations on the low-lying electronic states of XeF, Xe2, and Xe2+ are reported using recently developed nonrelativistic and relativistic effective core potentials. The results indicate that apart from spin–orbit coupling relativistic effects are negligible for xenon. Comparison with previous all-electron calculations reveals that the valence electron dissociation and transition energies agree to 0.1 eV or better with all-electron results. The errors in the calculated values for Re are slightly greater (0.05 Å for XeF and 0.1 Å for Xe+2). The valence electron calculations generally appear to underestimate repulsive two-center interactions leading to significant errors at small internuclear separations in the repulsive wall of the potential curves. Comparison with the valence electron results of Lee, Ermler, Pitzer, and Winter shows excellent agreement, indicating that the simple, approximate approach used here for including relativistic effects in the effective core potential is valid.

Cross section for production of the metastableH(2S)state in proton collisions with atomic hydrogen

Cross sections for production of the metastable $\mathrm{H}(2S)$ state in collisions of 6-25-keV protons with atomic hydrogen have been measured in a modulated crossed-beam experiment. The metastable states excited through the process ${\mathrm{H}}^{+}+\mathrm{H}\ensuremath{\rightarrow}{\mathrm{H}}^{+}+\mathrm{H}(2\mathrm{S})$ (direct excitation) and ${\mathrm{H}}^{+}+\mathrm{H}\ensuremath{\rightarrow}\mathrm{H}(2S)+{\mathrm{H}}^{+}$ (charge transfer) were quenched in a weak electric field applied at the collision region. The emitted Lyman-$\ensuremath{\alpha}$ radiation was detected in a direction perpendicular to the plane of the crossed beams. The processes were separable since the direct excitation signals saturated well before the charge transfer signals did as the quench field was increased. The present values were normalized to the absolute total cross section for $\mathrm{H}(2P)$ production measured by Kondow et al. The charge-transfer cross sections are in satisfactory agreement with the measurements of Morgan et al. and Bayfield except at 6 keV, where their values also begin to differ. The direct-excitation cross section differs in shape from the only other measurement of Morgan et al., but agrees in absolute magnitude when normalization uncertainties are included. The coupled-state calculations of Cheshire et al. using a pseudostate expansion show good agreement with the present results, indicating the importance of the inclusion of molecular features at small internuclear separations.

On the convergence properties of the Rayleigh–Schrödinger and the Hirschfelder–Silbey perturbation expansions for molecular interaction energies

AbstractThe Rayleigh–Schrödinger polarization and the Hirschfelder–Silbey (HS) perturbation theories are applied, through the 38th order, to the interaction of a ground‐state hydrogen atom with a proton. The calculations were made with high precision using a large basis set of orbitals expressed in the confocal elliptic coordinates. The results obtained show that for small internuclear separations R the polarization series converges slowly in an oscillatory way to the energy of the ground 1sσg state of the H molecule. At large R, however, the polarization expansion reproduces only the Coulomb part of the interaction energy effectively. When the value of the Coulomb energy is reached, the rate of convergence deteriorates drastically so that the exchange energy is not reproduced practically. The HS method converges fast when applied to both the 1sσg and the 2pσu states, the rate of convergence being roughly independent of the internuclear distance. If the finite basis set employed to solve the perturbation equations is stable under the symmetry operations, the HS expansion is shown to converge to the energy obtained by minimizing the Rayleigh–Ritz functional within the space spanned by the functions used in the perturbation theory calculations.

Classical trajectory studies of alkali atom-alkali dimer exchange reactions : Na+Li2and Li+Na2

The endoergic and exoergic alkali atom-alkali dimer exchange reactions, Na+Li2→NaLi+Li and Li+Na2→LiNa+Na, have been studied using classical trajectory methods on LEPS surfaces exhibiting shallow potential wells at small internuclear separations. For both systems the total reaction cross section, collision lifetime, differential reaction cross section and product energy disposal were calculated for a range of initial collisional energies. Comparison with the results from statistical theories for the energy disposal and angular scattering show good agreement at the lower collisional energies. At these energies the reactions are found to proceed via the formation of a long-lived complex which is non-rigid and non-linear; as the energy is increased the reaction dynamics become direct. For the exoergic reaction about 60–70 per cent of the total available energy goes into internal motion of the product molecule; for the endoergic system, the fraction is 50–60 per cent. The effect of vibrational excitation of t...

Morse Franck-Condon Factors and R-Centroids for Some Lyman Bands of H2, HD and D2

Abstract Using new rotational and vibrational constants, Morse Franck-Condon factors and r-centroids are computed for 108 Lyman bands of astrophysical importance H2, HD and D2 molecules. Experimental oscillator strengths conjoint with Morse Franck-Condon Factors for six Lyman bands of molecular hydrogen yield radiative lifetimes for v = 0–5 levels of the B 1σu + state that are inconsistent with the experimental lifetime measurements. The limitation of analytic Morse function in the region of small internuclear separation for the B 1σu + state of H2 is discussed. The r-centroids (rv′v″) are found to increase with frequencies of the Lyman bands of H2, HD and D2. For a sequence, Δr = rv′+1,v″+1 - rv′v″ is constant. A comparison of rv′v″ values of the Lyman bands shows that rv′vv″ of the band (v′v″) increases in going from H2 to D2.