Calculations of total cross sections for the scattering of low-energy electrons by ${\mathrm{Li}}_2$ have been performed in the fixed-nuclei approximation. These calculations employed a parameter-free model of the correlation-polarization interaction and an essentially exact treatment of the exchange.

The differential cross section (DCS) d${\sigma }^{\mathrm{el}}$/dΩ for the elastic scattering of electrons by homonuclear diatomic molecules in the first Born approximation at scattering angles equal or near zero is derived here by an expansion method. This method gives d${\sigma }^{\mathrm{el}}$/dΩ=α+β$K^2$+γ$K^4$+.. ., where α,β,γ are constants, and K is the momentum transfer. For ${\mathrm{H}}_2$, the value α with vibrational corrections is calculated with use of the most accurate wave function given by Kolos and Wolniewicz (KW) and the values for the constants β and γ are evaluated from the Davidson and Jones (DJ) wave function. The resulting DCS’s at small scattering angles are given for comparison with experiment. The disagreement between theory and experiment for ${\mathrm{H}}_2$ is found when the scattering angle is less than 15 mrad at 25 keV (i.e., K=0.6 a.u.). The disagreement is very similar to the ones reported in the studies of Compton scattering and (e,2e) reaction spectroscopy. The disagreement between theory and experiment at scattering angles near zero for ${\mathrm{N}}_2$ are also reported. New experimental data for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ at very small scattering angles may be needed in order to establish the disagreements reported here. The DCS for ${\mathrm{N}}_2$ at large scattering angles is also calculated using an accurate multiconfiguration self-consistent-field first-order configuration-interaction (MCSCF-FOCI) wave function. Good agreement within experimental resolution at large scattering angles is found for ${\mathrm{N}}_2$ for the difference function ΔN(K) and for the DCS. This is contrary to the recent study of ${\mathrm{H}}_2$ where discrepancies were reported at large scattering angles. The calculated total cross sections for ${\mathrm{N}}_2$ are in good agreement with the experimental data at low incident energies is the hundred-electron-volt range.

An analysis of infrared radiation in the potential scattering of a Dirac electron was presented by Bloch and Nordsieck [Phys. Rev. 52, 54 (1937)], in their now classic work, to illustrate how divergence difficulties are removed by nonperturbative treatment of the radiation of soft photons. It is shown here how an improved low-frequency approximation can be obtained which provides a small correction to the Bloch-Nordsieck sum rule for the scattering cross section, while still requiring as input only physical (on-shell) values of the amplitude for scattering in the absence of the radiation field. The calculation is based on a variational determination of the radiative amplitude with trial functions chosen in accordance with the Bloch-Nordsieck approximation. An extension of the model scattering problem is introduced which allows for potentials with a Coulomb tail. The applicability of the approximation procedure to the analogous problem of relativistic scattering in a low-frequency external field is pointed out.

The van der Waals interaction energy between two closed-shell systems can be approximated as the sum of the Hartree-Fock (HF) and dispersion interaction energies. The dispersion energy is given as a power series in $R^{\mathrm{-}n}$ when the interaction potential is expanded in the multipole operators of the asymptotic systems. This series is convergent only if the overlap of the systems is explicitly considered. This paper will describe the calculation of the induced-dipole–induced-dipole dispersion interaction including the anisotropic damping due to charge overlap. The He-${\mathrm{H}}_2$, Ne-${\mathrm{H}}_2$, and Ar-${\mathrm{H}}_2$ systems were considered and the van der Waals potentials were constructed with use of available HF interaction potentials.

Homonuclear associative ionization, also known as the Hornbeck-Molnar process, has been investigated in a crossed-beam experiment for the collision He($5^3$P)+He with use of a time-of-flight technique. Excited states were produced from metastable He($2^3$S) with use of a tunable cw source of coherent light. The density distribution of the He($5^3$P) atoms in the interaction zone was investigated by a highly sensitive photoionization method. The combination of these techniques with a crossed-beam geometry allowed the kinetic-energy dependence of the cross section to be investigated with a very good resolution in the range 20–200 meV. The experimental curve exhibits structures similar to that calculated by Cohen for the excited states $3^3$P and $4^3$P. The interpretation of our results has been performed by an extension of Cohen’s model to the present case, considering bound-bound transitions between quasidiabatic states of ${\mathrm{He}}_2^{\mathrm{*}}$, and assuming a 100% ionization rate for the states penetrating into the continuum. The shape of the experimental curve is well reproduced by the contribution due to channels of ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ symmetry, which is found to be preponderant, and the validity of Cohen’s model is thus demonstrated. Two different processes are found to occur in different regions of the kinetic-energy range separated by a narrow transition zone. The limits of the latter are the diabatic threshold [crossing energy of the repulsive entrance channel ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ $5^3$P with the ionization limit ${\mathrm{He}}_2$${\mathrm{}}^{+}$(${\mathrm{X}}^2$${\mathrm{\Sigma }}_{\mathrm{u}}^{+}$)], and the asymptotic energy of the first attractive channel ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$ $6^3$D.

It is shown how the concepts of scattering length and effective range, previously introduced for low-energy scattering from a potential V(r) in a plane, correspond to the well-known parameters in three dimensions. This is done by considering low-energy scattering in a general dimension n≥2 and subsequently showing that both the n=2 and n=3 cases fit naturally in such a generalized treatment. Furthermore, our previous work is extended to long-range potentials, decreasing faster than 1/$r^{n+1\mathrm{}}$. The method used is based on the properties of a local scattering length a(r) for the potential V(r) cut off at radius r and an equivalent hard-sphere radius a(r,k) for k≠0. Some applications and illustrative examples are given.

The concepts of scattering length a and effective range $r_e$ previously introduced for low-energy scattering from a potential V(r) in a plane and in higher dimensions are extended to include a 1/r potential (strength parameter γ). Both a and $r_e$ have the physical significance of being equal to the radius of an equivalent hard sphere giving rise to the same O($k^0$) and O($k^2$) terms in the expression for the phase shift. The method used is based on the properties of the ‘‘local scattering length’’ a(r,γ) for the potential V(r) cut off at radius r and an ‘‘equivalent hard-sphere radius’’ a(r,k,γ) for wave number k≠0. It is shown that these quantities have a smooth behavior for γ→0 and for dimension n→2.

The Thomas peak, which dominates the electron-capture cross section in the high-velocity limit, has the mathematical form of a simple resonance. However, this resonance occurs as a function of the momentum transfer (rather than energy), corresponding to a negative shift in the impact parameter (rather than time).

This paper contains an analysis of a new model of collisional broadening of spectral lines in which the effect of the velocity-changing collisions is treated within the Boltzmann-Lorentz model, borrowed from the kinetic theory of gases. The simultaneous occurrence of the velocity modulations and the effects of interaction during the collisions is investigated in detail.

The results of a search for metastable dissociations of ${\mathrm{Ar}}_2$${\mathrm{}}^{+}$ produced in an ion source via associative ionization are presented. The metastable fragmentations were studied with a double-focusing mass spectrometer by decoupling the acceleration and analyzer fields. The number of metastable transitions occurring in the observable time window between 3.1 and 7.9 μs after ion formation increases with electron energy in the ion source and is ≊100 times larger than the number of metastable transitions observed previously for ${\mathrm{Ar}}_2$${\mathrm{}}^{+}$ produced by electron ionization of ${\mathrm{Ar}}_2$. Decomposition pathways consistent with ab initio potential diagrams are presented.

Sub-Doppler molecular-beam laser Stark spectroscopy has been employed to produce high-contrast Rabi oscillations in the ${\nu }_3$ band of ${\mathrm{CH}}_3$F. By varying the intensity of the cw ${\mathrm{CO}}_2$ laser, up to five complete oscillations were observed before the phenomenon was washed out by rapid-passage effects and damping mechanisms. Besides being useful in clarifying key features of coherent ir molecular-beam spectroscopy, the observation of Rabi oscillations provides one of the most accurate means of directly measuring transition dipole moments. Analysis of the present data on three rovibrational transitions, Q(1,1) -1←0, P(1,0) 0←0, and R(1,1) 0←1, has yielded a rotationless transition dipole moment of 0.21±0.01 D for the ${\nu }_3$=1←0 vibration. This result is in agreement with values estimated from both band-intensity and absorption-coefficient data in the literature.

In photodissociation of a homonuclear diatomic molecule, conservation of linear and angular momenta requires that each atomic fragment follow identical but oppositely directed trajectories with respect to the molecular center of mass. For certain values of the incident photon energy, one of the atoms will be electronically excited while the other will be in its ground state. When a detector records the undispersed fluorescence from the decay of the excited atom it cannot distinguish which trajectory the excited atom followed and hence whether the photon possesses a blue or red Doppler shift corresponding to recoil towards or away from the detector. According to the principle of superposition in quantum mechanics, the wave function of the photon must be a sum over two paths corresponding to emission from an excited atom in either of the two recoil directions. Detection of such photons gives rise to an interference between the probability amplitudes for the two paths that is manifested in the output from the photodetector as a beat frequency. Since photodissociation of an ensemble of molecules gives rise to a distribution of recoil directions relative to the electric vector of the incident radiation, a range of beat frequencies must be present in the detected signal. This paper gives a calculation of expected output voltage waveforms from a photodetector viewing atomic fluorescence excited by molecular photodissociation. Expressions are given for partial Fourier transforms of the photodetector signals. The results show that the shape of the voltage waveforms depends strongly on the asymmetry parameter for recoil of the photofragments and on whether or not the magnetic sublevels of the excited atomic state are created in a coherent superposition.

In a recent spectroscopic study [D. E. Holmgren et al., Phys. Rev. A 31, 677 (1985)], many metastable core-excited quartet levels in Na i have been identified, and based on calculated decay rates (both radiative and autoionizing) some of these levels have been suggested for use in an extreme ultraviolet (xuv) laser. In order to test the theoretical calculations we have used the beam-foil technique to determine experimental lifetimes for eight quartet levels in the core-excited configurations 2$p^5$3s3d and 2$p^5$3s4s. The agreement between theory and experiment is within a factor of 2, but with systematic discrepancies.

The cross section of neutral sodium has been calculated from threshold at 5.14 eV to 250 eV with use of many-body perturbation theory. The calculations use LS coupling and include resonance effects due to single excitations of 2p and 2s electrons. Near threshold the results are very sensitive to electron correlations. Our results are compared with previous theoretical calculations and experimental measurements.

We report the energies and autoionization rates of the Ba 6png, J=3 and J=5 states which we have obtained by multistep laser spectroscopy. The observed 6png states have small quantum defects (0.03), and widths of 0.05 $n^{\mathrm{-}3}$. The J=3 and J=5 series converging to the ${\mathrm{Ba}}^{+}$ 6$p_{1/2}$ limit are degenerate while the two J=3 and two J=5 series converging to the ${\mathrm{Ba}}^{+}$ 6${\mathrm{p}}_{3/2}$ limit are easily distinguished. The splittings are in good agreement with the electric quadrupole splittings calculated by assuming nonpenetrating ng orbitals. The autoionization rates are also in accord with estimates assuming nonpenetrating orbitals.

A high-efficiency x-ray spectrometer has been constructed with use of a curved crystal and a position-sensitive detector mounted along a Rowland circle. Results obtained for the Cl K absorption and fluorescent Kβ emission of molecular ${\mathrm{CH}}_3$Cl show previously unobtainable details. The gas target is excited by primary radiation from a demountable conventional x-ray tube. The use of different anode materials and the insertion of filters between x-ray source and target allow some variation of the primary excitation energy. By monitoring emission spectra for different primary excitation energies, we are able to attribute the newly observed absorption features to multivacancy excitations. Such modulations in the suprathreshold absorption cross section would complicate the extraction of structural information in an extended x-ray-absorption fine-structure (EXAFS) analysis.

The ionization of Na atoms by 8-GHz electric fields from principal quantum number n=16–42 exhibits a threshold for the ‖m‖=0 and 1 states of E≊1/3$n^5$, and two thresholds for the ‖m‖=2 states of E≊1/9$n^4$ and E≊1/21$n^4$ depending upon the n state. The ‖m‖=0 and 1 thresholds show a departure from a 1/$n^5$ scaling at high n which we interpret as being due to the fact that the relatively slower atomic frequencies at high n no longer match the 8 GHz microwave frequency. The E=1/21$n^4$ ‖m‖=2 threshold has not to our knowledge been observed before, and we interpret it as arising from the ionization of the highest energy, or blue, Stark state at the classical limit for ionization.

The quantum-statistical model for a three-level atom interacting with two radiation fields is studied. The mean atomic occupations and photon numbers are obtained under different initial conditions of one coherent field and one chaotic field or both chaotic or coherent fields, with the atom in upper or lower states. Through numerical summation, it is shown that the effects of coherent sources and chaotic sources are different even for low intensities. Meanwhile the effects of detuning on this interaction are discussed.

An algorithm [G. F. Thomas and W. J. Meath, J. Phys. B 16, 951 (1983)] for evaluating the evolution operator of a multilevel system dipole interacting with either a continuous-wave or Gaussian-pulsed source, based on its Riemann product integral representation in conjunction with Frazer’s method of mean coefficients, is appraised and extended. Our extension allows for the inclusion of spontaneous decay or a dissociation (or ionization) channel and useful relations are derived for the eigenvalues of the evolution operator for both the continuous wave and the Gaussian pulse. For the latter we now admit an arbitrary phase in the field and we derive a simple relation for cascading the state amplitudes of the system over the duration of an arbitrary number of identical phase-coherent pulses. As part of our appraisal, improvements in the implementation of the algorithm are provided. For a two-level system, the evolution operator is given as the chronologically ordered product of readily computed 2×2 matrices while for multilevel system it is conveniently evaluated using a resolvent method based on Leverrier’s algorithm for computing the Bateman matrices. The asymptotic behavior of the evolution operator and the fluence in the direction of propagation for both the continuous-wave and the Gaussian-pulsed sources are explored. Applications to model two-level systems illustrate the influence of the source’s phase and interaction duration on resonant and nonresonant transition probabilities, respectively. The saturation of a two-level system by a train of resonant phase-coherent Gaussian pulses is demonstrated.

A nonperturbative analysis (in one of the fields) of the Rayleigh-type optical-mixing signal in an absorbing medium shows that it is more sensible to saturation than the effect that could be expected from ‘‘absorption saturation arguments.’’ We also report the observation of such high-order effects in the organic dye malachite green. We have found that an effective two-level system model with a longitudinal relaxation time of 1.1±0.2 ps, a transverse relaxation time of 0.13±0.05 ps, and a transition moment of 1.2 D account for the deviation from the third-order regime. However, the frequency region of the data that follows the predicted spectral deformation is power dependent and it shrinks as power increases.