Calculations are made of the double-differential cross section for incoherent neutron scattering from a hydrogen atom involved in a chemical bond. Processes are investigated which correspond to the excitation of successive vibrational states of the bound hydrogen atom leading eventually to a dissociation of the bond. Two examples are considered: a hydrogen atom involved in an O—H bond and in an O—H...O hydrogen bond such as in water. Experimental evidence for the latter case is also shown.

The fact that the Dirac Hamiltonian is not bounded from below has caused a long-standing difficulty in extending to relativistic ground-state energy estimates the powerful Rayleigh-Ritz variational technique extensively used for ground-state energy estimates of nonrelativistic systems. Here we show how the chief source of the difficulty, namely, the likely appearance of numerical instabilities (or ‘‘variational collapse’’), in the calculational procedure can be removed, at least for two relatively simple systems: a single Dirac particle in an external potential—which could be one or more fixed nuclei—and two Dirac particles bound by their mutual attraction. (The ultimate objective, discussed briefly but not achieved in the present exploratory paper, would be to remove variational collapse in bound-state energy calculations of arbitrary relativistic systems.) The method is based on a formal separation, done with the aid of the Casimir projection operators ${\Lambda }_{\mathrm{-}}$ and ${\Lambda }_{+}$ of the negative-energy and positive-energy continuum branches of the spectrum. A maximum principle is introduced to evaluate that component of an effective potential which accounts for virtual transitions into the negative-energy continuum. This effective potential appears in an eigenvalue equation confined to the subspace spanned by ${\Lambda }_{+}$, and here a Rayleigh-Ritz minimum principle can be used to obtain a variational approximation to (but unfortunately not a variational bound on) the ground-state energy; the extension of the method to excited states is straightforward.

Nonrelativistic variational calculations with the relativistic correction to order ${\alpha }^2$ have been carried out to obtain the energy levels for the n ${}_{}{}^1{}_{}{}^{}$,3S, n ${}_{}{}^1{}_{}{}^{}$,3P, and $n^1$,3D series in He up to n=8. The calculated term values have converged generally to within an uncertainty of ∼${10}^{\mathrm{-}4}$ ${\mathrm{cm}}^{\mathrm{-}1}$, a value matching the accuracy of recent high-precision wavelength measurements. The results are combined with theoretical Lamb shifts and systematically compared with currently available high-precision experimental data. The consistency between theory and experiment is good, although for some low-lying (n=3–6) S and P states there exist small discrepancies, presumably caused by the estimated Lamb shifts. The calculated term values for high-lying excited states have better accuracies than existing experimental data. Addition of the theoretical term values to the corresponding experimental excitation energies suggests a value of 198 310.7725(5) ${\mathrm{cm}}^{\mathrm{-}1}$ for the ground-state ionization energy on the energy scale fixed by the $2^1$P value of 171 135.0000 ${\mathrm{cm}}^{\mathrm{-}1}$.

Two information-theoretic relationships have been derived for assessing the convergence behavior of arbitrary Rayleigh-Schrödinger (RS) perturbation expansions; these provide sensitive global information indices for quantitatively estimating the rapidity and regularity of convergence. The procedure has been applied to nine different high-order RS eigenvalue series for the ground states of ${\mathrm{H}}^{\mathrm{-}}$ and He, arising from different partitionings of the Hamiltonian operator for the same system; our findings for the order of merit of these series are in complete accord with previous numerical and theoretical studies. Furthermore, the theory has been applied to an idealized RS series modeled on a geometric progression, thereby gaining insight enabling one to correlate the rapidity with the regularity of convergence for actual RS series; in this context, the so-called doctrine of ‘‘small perturbations’’ has also been investigated, and, in corroboration of earlier work, it is concluded that the doctrine is an unreliable guide for selecting favorable partitionings of the Hamiltonian. To our knowledge, this is the first time that information theory has been applied to the study of perturbational convergence.

In this work a comparison between new experimental and quantum-mechanical results is performed for the reactions He+${\mathrm{H}}_2$${\mathrm{}}^{+}$(${\mathrm{v}}_{\mathrm{i}}$) →${\mathrm{HeH}}^{+}$(J${\mathrm{v}}_{\mathrm{f}}$)+H; $v_i$=0–4 in the energy range 1 eV≤$E_{\mathrm{tot}\le 2}$ eV, where $E_{\mathrm{tot}}$ is the total (vibrational plus relative translational) energy including the zero-point energy. It was found that the two features which characterize this system, namely, the strong enhancement of the reaction rate with initial vibrational energy (at fixed total energy) and the relatively weak dependence of the cross sections on translational energy, are moderately well reproduced by the quantum-mechanical infinite-order sudden approximation.

Potential energy curves of ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ symmetry have been calculated for the process ${\mathrm{C}}^{3+}$(2l)+H(1s) →${\mathrm{C}}^{2+}$(nln’l’${;\mathrm{}}^1$L)+${\mathrm{H}}^{+}$ by means of the spin-coupled valence-bond theory. Very large basis sets of Slater functions have been used in order to describe reasonably well a large number of states. A total of eleven states has been examined, the asymptotic energies of which match the experimental values closely: errors are 0.02–0.9 eV over a range of 45 eV. The only exception is the ${\mathrm{C}}^{2+}$(2s3d${;\mathrm{}}^1$D)+${\mathrm{H}}^{+}$ state where there is a discrepancy of 2 eV which we attribute to remaining deficiencies in the 3d basis set. The charge-transfer states ${\mathrm{C}}^{3+}$(2s${;\mathrm{}}^2$S)+H(1s)(state 7) and ${\mathrm{C}}^{3+}$(2p${;\mathrm{}}^2$P)+H(1s) (state 11) show very strongly avoided intersections with at least four other states. We conclude that charge-transfer studies of this system must take into account a minimum of five strongly coupled states. Later studies will concentrate on the ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ states and on the radial couplings.

New measurements for the total, single ionization of ${\mathrm{B}}^{2+}$ and ${\mathrm{O}}^{5+}$ by electron impact are reported with particular attention directed to the indirect contribution of excitation-autoionization. For ${\mathrm{B}}^{2+}$ these are the first measurements to our knowledge while for ${\mathrm{O}}^{5+}$ the present data improve on previous measurements. In both cases the direct total ionization cross sections are in good agreement with recent distorted-wave predictions of Younger, and the excitation-autoionization contribution is consistent with measurements for other Li-like ions. For ${\mathrm{O}}^{5+}$ an additional small increase in the cross section is observed at an energy well below the excitation-autoionization threshold; this feature may be attributable to resonance recombination followed by auto-double-ionization. For the Li-like ions ${\mathrm{Be}}^{+}$, ${\mathrm{B}}^{2+}$, ${\mathrm{C}}^{3+}$, ${\mathrm{N}}^{4+}$, and ${\mathrm{O}}^{5+}$, the ionization theory of Younger is used as a basis to subtract the direct ionization component from the total measured ionization cross sections in order to extract the 1$s^2$2s→${\mathcal{J}}_l$1s2s2l excitation cross section. The deduced inner-electron excitation cross sections are quantitatively compared with excitation theory including new close-coupling calculations for ${\mathrm{Be}}^{+}$ and ${\mathrm{B}}^{2+}$ presented here. For all cases except ${\mathrm{Be}}^{+}$, the close-coupling theory is in agreement with the deduced experimental excitation cross sections. These new results and analysis improve confidence in excitation theory for highly charged ions.

The method of complex-coordinate rotation is applied to investigate autoionization states of positronium molecules. Using elaborate Hylleraas-type wave functions in which all six interparticle coordinates are used, resonance parameters for the lowest S-wave resonant state are predicted for the first time. The resonant energy, measured in positronium-atom–positronium-atom scattering, and resonance width are determined as 4.28 eV and 0.11 eV, respectively.

Cross sections for electron capture into the 2p level evaluated with use of the strong potential Born approximation are presented. While these 2p cross sections are smaller than cross sections for capture into the 1s and 2s levels at high velocities, nevertheless the Thomas peak is clearly evident at energies above 1 MeV in both the m=0 and ‖m‖=1 magnetic substates in atomic hydrogen. At energies above 10 MeV where the Thomas peak is important, cross sections for capture into m=0 and ‖m‖=1 are comparable. Consequently, the polarization fraction becomes negative at high energies in sharp contrast to Brinkman-Kramers results where the polarization fraction stays near its maximum value.

Electron-loss cross sections for hydrogenlike ions with atomic number $Z_1$ (2≤$Z_1$≤7) and with velocity v (0.3$v_0$≲v/$Z_1$≲6$v_0$; $v_0$ is the Bohr velocity) are investigated in collisions with ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, Ne, and Ar targets using the unitarized impact-parameter method. In order to describe the form factors of these targets, we use the modified Molière electron distributions where the parameters appearing in the Molière potential are slightly modified to fit the form factors obtained from Hartree-Fock wave functions in the small momentum-transfer region. Then we find the electron-loss cross sections sensitive to those parameters at high velocities. The scaling relations, characterized by the reduced cross section σ̃ (=$Z_1^m$σ) versus the reduced velocity ṽ (=v/$Z_1$), are presented, where m=2.8 for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$, 2.6 for Ne, and 2.4 for Ar. Here the molecular effect in ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ targets and the polarization of target electron clouds due to a projectile are both neglected. These scalings yield good agreement with the reported data, particularly when ṽ≲1.

United-atom 2pσ-2pπ rotational coupling in asymmetric collisions is influenced by the avoided crossing between the 2pσ and 2sσ orbits. We study this influence using the ${\mathrm{HeH}}^{+}$ system as a prototype. The time-dependent Schrödinger equation is solved numerically in the basis of ${\Sigma }_2$-${\Sigma }_3$-${\pi }_1$ molecular states. We find substantial population of the 2sσ state, in disagreement with estimates based on the Landau-Zener model. The ${\Sigma }_3$ level is populated directed by transitions near the avoided crossing at b=0.4 a.u. and indirectly by ${\Sigma }_2$-${\pi }_1$-${\Sigma }_3$ rotational coupling for b>0.4 a.u.

Using the hyperspherical wave functions of the high-lying doubly excited ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ states of He, we have calculated the generalized oscillator strengths between these excited states and the Born cross sections for electron-impact excitation of He in these excited states within the manifold of ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ states. Based on the rovibrator model of the doubly excited state, we predict theoretically that for these excitation processes a He atom tends to enlarge its size while keeping its shape, as a limber ‘‘e-${\mathrm{He}}^{2+}$-e’’ linear molecule, the same as that in the initial states.

We have formulated and applied a method for solving the low-energy electron-molecule collision problem. This method treats the scattering by the local and nonlocal parts of the interaction differently. A differential equation method is used to obtain a solution of the set of coupled equations which describe the scattering by the (nonspherical) local potential. The T-matrix expansion method is used to account for the scattering by the nonlocal part of the interaction. The method is tested by application to low-energy $e^{\mathrm{-}}$-${\mathrm{H}}_2$ and $e^{\mathrm{-}}$-${\mathrm{N}}_2$ scattering in the static exchange approximation.

Semiempirical polarization potentials with several cutoff functions are investigated for positron- and electron-atom interactions. A disposable parameter, an effective radius, in each cutoff function is adjusted so as to reproduce well-established reference values (scattering lengths and binding energies) in calculations. Striking regularities in fitted parameter values are found despite the very wide variety of cutoff functions examined. The parameter exhibits a strong dependence upon spin and angular momentum in the electronic systems, which is rationalized in terms of the Pauli exclusion principle. Simple semiempirical relations between the effective radii for positronic systems and those for the corresponding electronic systems are proposed, which enable one to find the parameter value for an electron by fitting a positron calculation to a reference value, or vice versa. In other words, the number of adjustable parameters is reduced to a single effective radius for each target regardless of the projectile.

The method for constructing model polarization potentials for electron- and positron-atom systems, previously presented for targets containing up to two electrons, is extended to neon and argon targets. The empirical character of the method is reduced to the determination of a single effective radius for each target, so that electron scattering calculations can be carried out by reference to positron scattering data, or vice versa. In this work, electron data are used to fix the value of the effective radius of each target, which is then used in positron scattering calculations. For electron scattering, exchange is approximated by a local effective potential with two adjustable parameters. The calculated elastic total and differential cross sections are nevertheless in excellent agreement with recent experimental values and are as accurate as the results from much more elaborate calculations.

Electron-attachment cross sections are calculated for the process $e^{\mathrm{-}}$+${\mathrm{SF}}_6$→${\mathrm{SF}}_6$${\mathrm{}}^{\mathrm{-}}$ in the energy range 1–200 meV. An electron scattering approximation is used in which diatomiclike potential energy curves near the equilibrium ${\mathrm{SF}}_6$ ground state are constructed from recent spectroscopic data. Excellent agreement is found over the entire energy range with experimental attachment cross sections at a temperature of 300 K for s-wave (l=0) scattering. The same calculation, with appropriate adjustment of the thermal populations, is used to calculate attachment rate constants k(ε¯) in the range 50–600 K for both s- and p-wave scattering. Comparisons are made with four independent sets of measured rate constants in the range 200–600 K, after adding an experimental estimate of the attachment rate for the process $e^{\mathrm{-}}$+${\mathrm{SF}}_6$→${\mathrm{SF}}_5$${\mathrm{}}^{\mathrm{-}}$+F. Good agreement is found with three sets of data, and poorer agreement with the fourth. The calculation shows that the true s-wave behavior of the rate constant, in which k(ε¯) is independent of ε¯, will be realized only at temperatures T less than 115 K, and that the observed constancy in the range 300–600 K is accidental. Theory predicts approximately a 9% increase in k(ε¯) as T is lowered from 300 to 200 K.

The collision strengths for the inelastic transitions among the lowest eleven LS states of C v are presented. Configuration-interaction wave functions are used to represent the eleven target states which are included in the calculation. The calculation for the lower partial waves (l≤11) are carried out using the R-matrix method. The contribution from higher partial waves is obtained in the close-coupling approximation with exchange terms omitted. The effective collision strengths have been calculated assuming a Maxwellian distribution of electron energies. Results are also presented for calculations in which the five lowest states were included. The present results are compared with the previous calculation of Pradhan, Norcross, and Hummer. Some significant differences are noted, particularly at lower temperatures for some transitions.

The nonadiabatic close-coupled theory of atomic collisions in a radiation field is generalized to include electron spin and is used to consider the weak-field Na–rare-gas (RG) optical collision Na${(}^2$$S_{1/2}$)+RG+nhν μNa${(}^2$${\mathrm{P}}_{\mathrm{j}}$)+RG+(n-1)hν. The effects of detuning and incident energy on the branching into the atomic Na 3$p^2$$P_{3/2}$ and 3p ${}_{}{}^2{}_{}{}^{}P_{1/2}^{}{}_{}{}^{}$ states are examined. The cross sections σ(j) are found to have a strong asymmetry between red and blue detuning as well as a complex threshold and resonance structure dependence on energy. A partial cross-section analysis of σ(j) shows a significant difference between contributions from states of e and f molecular parity. The theoretically calculated detuning dependence of the branching ratio into each fine-structure state is in good agreement with available experimental data for Na-Ar, Na-Ne, and Na-He, as well as the total absorption coefficient for the production of Na 3p atoms. The fine-structure branching ratio for thermal energy collisions shows considerable variation with a rare-gas collision partner, due to the different interaction potentials. For sufficiently high collision energy, the branching approaches a recoil limit which is independent of collision partner.

We present a semiclassical model to analyze a recent experimental study on the polarization dependence of associative-ionization (AI) collisions between two Na(3p ${\mathrm{}}^2$$P_{3/2}$) atoms and the resulting spatial distribution of product rotational angular-momentum vectors. The theory is based on the idea of a ‘‘locking radius’’ at which the quantization axis changes from space-fixed coordinates to the molecular frame, and the total AI yield is a sum of the contributions from different collision orbital configurations. The model calculation shows the consistency between the measurements of our earlier study and that of Kircz, Morgenstern, and Nienhuis. We also derive a theoretical expression for the spatial distribution of ${\mathrm{Na}}_2$${\mathrm{}}^{+}$ rotational angular-momentum vectors which reproduces the experimentally determined features. We conclude that the ${\sigma }^2$ orbital configuration approach is favored over ${\pi }^2$ by a factor of about 6, and locking takes place at R larger than 25 Å.

The trapped-ion measurements of Barlow, Dunn, and Schauer [Phys. Rev. Lett. 52, 902 (1984); 53, 1610 (1984)] on ${\mathrm{CH}}_3$${\mathrm{}}^{+}$${+\mathrm{H}}_2$ →${\mathrm{CH}}_5$${\mathrm{}}^{+}$+hνare reexamined. It is shown that they require the rate of the stabilizing radiative transition to be 3.5×${10}^4$ ${\mathrm{s}}^{\mathrm{-}1}$. This high rate is attributed to an electronic transition involving the state having ${\mathrm{CH}}_4$${+\mathrm{H}}^{+}$ or ${\mathrm{CH}}_3$+${\mathrm{H}}_2$${\mathrm{}}^{+}$ as its dissociation products.