An analytic form for the nonrelativistic Coulomb propagator is derived, thus resolving a long-standing problem in Feynman’s path-integral formulation of quantum mechanics. Hostler’s formula for the Coulomb Green’s function is expanded according to the theorem of Mittag-Leffler, then Fourier transformed term by term to give the Coulomb propagator. The result is a discrete summation over the principal quantum number n, involving Whittaker, Laguerre, Hermite, and error functions. As is the case for other nonquadratic potentials, the Coulomb propagator does not have the canonical structure K=F exp(iS/ħ). Part of the expansion resembles a form derived by Crandall [J. Phys. A 16, 3005 (1983)] for the case of reflectionless potentials.

A study of post-collision interaction has been carried out experimentally for Auger-electron emission of rare-gas atoms following electron-impact ionization. Spectra of the Xe ${\mathit{N}}_5$${\mathit{O}}_{23}$${\mathit{O}}_{23}$ ${(}^1$${\mathit{S}}_0$), Kr ${\mathit{M}}_5$${\mathit{N}}_1$${\mathit{N}}_{23}$ ${(}^1$${\mathit{P}}_1$), and Ar ${\mathit{L}}_3$${\mathit{M}}_{23}$${\mathit{M}}_{23}$ ${(}^1$${\mathit{S}}_0$) Auger electrons have been measured changing the electron-impact energy from slightly above the threshold of the ionization to a few kilo-electron-volts. The Auger line shape has been analyzed using a profile formula that includes the finiteness of the velocities of all the cooperating electrons. Moreover, the analysis has partly considered the possible energy distribution of the scattered primary electron and the ejected secondary electron, due to the sharing of excess energy between them. The post-collision interaction effect is found to be absent at high excess energies.

Rubidium vapor, contained together with a buffer gas in a quartz cell located in a 4.75-T magnetic field, was irradiated with light from a pulsed dye laser producing selective excitation of each 6 ${}_{}{}^2{}_{}{}^{}$P Zeeman substate in turn. Collisions of the excited and polarized atoms with the ground-state He, Ne, or Ar atoms and the resulting Zeeman mixing produced a population of the whole Zeeman manifold and resulted in the emission of a Zeeman fluorescence spectrum that was resolved with a scanning Fabry-Pérot interferometer and recorded with a photomultiplier and a multichannel scaler. Measurements of the relative intensities of the fluorescence components in relation to the buffer-gas pressures yielded the absolute (thermally averaged) cross sections for Zeeman mixing and cross sections for relaxation of the atomic multipole moments for collisions with He, Ne, and Ar.

Requirements for the existence of isolated zeros in the generalized oscillator strength (GOS) for one-electron atoms and molecules are considered. It is shown that in certain limits the atomic GOS cannot be zero for any value of the momentum-transfer magnitude ħK≠0 unless it is zero for all values. A relationship between the existence of a zero and the angular momentum of the target’s states is pointed out for the atomic case and a numerical example is provided. The conditions for the existence of an isolated zero for a molecular GOS are derived and, using the atom case as a model, they indicate that one is unlikely for 0<K<∞ and the internuclear separation R restricted to 0<R<∞. Minima, or possibly zeros, in the molecular GOS occur in both experiment and theory. It is postulated here that these structures are minima and not zeros. They appear to be due to zeros in a matrix element related to the leading term of the small-K GOS expansion while higher terms remain finite. Several numerical examples are provided and the speculation is supported by the correlation of the GOS minimum as a function of K and R to a zero in the dipole oscillator strength. Attention is brought to the existence of zeros in the molecular dipole oscillator strength when a nodeless function appears in this matrix element, contrary to the atomic case, and an explanation for this difference is given.

A Schwinger-type variational principle for time-dependent interactions is developed for the S matrix using a separable operator approach. The S matrix has an implicit fractional form by which we mean that an integral equation has to be solved to compute the wave function. This principle shares the important features of the fractional form of Schwinger’s variational principle and reduces to it for time-independent interactions. We discuss the relationship with the Lippmann-Schwinger variational principle. The variational principle is generalized to treat direct and rearrangement processes in ion-atom collisions in both the time-dependent and time-independent representations. It is shown to yield the correct asymptotic form for capture. Using free states as trial functions, the channel-distorted strong-potential Born S matrix is obtained. The distortion potential is determined variationally and is found to have the correct form at large distances.

We have considered the dynamics of simple measuring devices coupled to quantized relativistic Heisenberg fields. We have defined localized observables and derived covariant equations for the joint probability distribution of the measured outcomes. The proposed formalism is based on standard field-theoretical terms. We have shown that our formalism yields the expected anticoincidence when two devices detect two wave packets of a single electron. Applications in the measurement theory of vacuum fluctuations have been suggested.

We present a numerical method for the solution of the Lippmann-Schwinger equation for electron-molecule collisions. By performing a three-dimensional numerical quadrature, this approach avoids both a basis-set representation of the wave function and a partial-wave expansion of the scattering potential. The resulting linear equations, analogous in form to the one-dimensional linear algebraic method, are solved with the direct iteration-variation method. Several numerical examples are presented. The prospect for using this numerical quadrature scheme for electron-polyatomic molecules is discussed.

The autoionization of the Ar 2${\mathit{p}}^5$nd resonances has been studied both experimentally and theoretically. The effect of the partial collapse of the 3d wave function between the initial and the final state has been investigated with regard to shake probabilities as well as to the structure of the final ionic configuration. The decay probabilities depend strongly on the principal quantum number both of the core-excited ${\mathrm{Ar}}^{\mathrm{*}}$ 2${\mathit{p}}^5$nd state and of the ${\mathrm{Ar}}^{+}$ 3${\mathit{p}}^4$n’d final state. One of the most striking features is that the 2${\mathit{p}}^5$nd→3${\mathit{p}}^4$ndεl decay is almost completely forbidden for n=4.

An exact formulation of the impulse approach (IA), or quantum-mechanical spectator model, is applied to atom-diatom collisions. Results are compared with previous work on the IA, which has always involved the peaking approximation (PA). The PA is seen to overestimate (underestimate) differential cross sections for processes involving projectile atom energy loss (gain). The internal consistency of the IA is explored by subjecting it to semidetailed balancing. For small scattering angles the IA is seen to be an inadequate theory, probably due to the neglect of double- and higher-collision terms in the multiple-collision expansion of the three-body T matrix. For large scattering angles, where the IA does appear to describe the scattering process accurately, the exact calculation is shown to give the same results as when only the energy-conserving on-the-energy-shell two-body processes are considered. An accurate approximation method is also developed for rapid computation of inelastic differential cross sections. Finally, the calculated results are compared with the experimental measurements, and the need to explore two-body potentials more complicated than the hard-core potential is pointed out.

Measurements of the asymmetry (Sherman) function for gold as a function of foil thickness have been made in a ‘‘classical’’ electron double-scattering experiment. Results are presented for incident energies of 50 and 120 keV at scattering angles of 45°, 60°, 75°, 105°, 110°, 115°, 120°, 125°, and 130°. The measurements were highly reproducible owing to the consistent method we used for coping with spurious asymmetries. Absolute values of the asymmetry function were determined using two identical foils of 222 μg/${\mathrm{cm}}^2$ at 120 keV and 71 μg/${\mathrm{cm}}^2$ at 50 keV. An analysis of the uncertainties at these calibration points shows that they are below 0.3%. Extrapolation of the data to zero foil thickness and comparison with theory are critically discussed.

The semiclassical, impact-parameter method, based on a 15-state molecular-orbital expansion, is employed to calculate the cross sections for charge transfer in ${\mathrm{Li}}^{3+}$-Li collisions. Electron-translation effects have been taken into account. In addition to total capture, cross sections for capture into individual states have also been calculated. The present results show qualitative agreement with the other available theory; details, however, are different. It is found that this reaction, through state-selective capture into the n=4 manifold of ${\mathrm{Li}}^{2+}$, may provide a useful mechanism to achieve population inversion necessary for short-wavelength lasers.

The spectrum and the wave functions of neutrons bound in the magnetic field of a thin rectilinear current filament are calculated analytically by solving a fourth-order Hamburger equation. Finite current cross sections are treated numerically: the bound states persist—a necessary prerequisite in view of possible experimental verifications of the theory. Two setups [(i) a superconducting wire and (ii) a Church trap] are proposed for obtaining these states experimentally. Some results on spin-1 magnetic surface states are presented.

The wavelength of the 2${\mathit{p}}_{3/2}$→1${\mathit{s}}_{1/2}$ transition in hydrogenlike ${\mathrm{Ni}}^{27+}$ has been measured with an accuracy of 13 ppm. Bare ${\mathrm{Ni}}^{28+}$ ions of 11.4 MeV/amu as emerging from a carbon stripper foil were decelerated to 8.4, 6.7, 5.2, and 3.1 MeV/amu and dressed in a thin target gas by electron capture. The x rays were measured with a crystal spectrometer in Johann geometry employing a position-sensitive x-ray detector. The 1s Lamb shift in hydrogenlike nickel has been found to be 5.07±0.10 eV in good agreement with theory.

Spectra of hydrogenlike iron Fe XXVI have been observed from Tokamak Fusion Test Reactor plasmas with a high-resolution crystal spectrometer. The experimental arrangement permits simultaneous observation of the Fe XXVI Ly-${\mathrm{\alpha }}_1$ and Ly-${\mathrm{\alpha }}_2$ lines and the associated dielectronic satellites, which are due to transitions 1snl-2pnl’ with n≥2, as well as the heliumlike 1${\mathit{s}}^2$${(}^1$${\mathit{S}}_0$)-1s4p${(}^1$${\mathit{P}}_1$) and both hydrogenlike Ly-${\mathrm{\beta }}_1$ and Ly-${\mathrm{\beta }}_2$ lines from chromium. Relative wavelengths and line intensities can be determined very accurately. The spectral data are in very good agreement with theoretical calculations. The observed spectra have also been used to estimate the total dielectronic recombination rate coefficient of Fe XXVI.

X-ray emission from the molecule ${\mathrm{H}}_2$S is strongly polarized following excitation of a sulfur K-shell electron to an unoccupied subthreshold molecular orbital with a polarized x-ray beam. Changes in the polarization of the emission spectrum are observed as the incident beam’s energy is swept across the subthreshold absorption resonance. The previously unresolved absorption resonance is shown experimentally to be primarily associated with a molecular orbital of ${\mathit{b}}_2$ symmetry, but with a high-excitation-energy component due to an orbital with ${\mathit{a}}_1$ symmetry. Satellite emission intensity is shown to depend on the primary photon energy and is therefore associated with multivacancy effects and not with contamination, as previously suggested.

The response of ground-state spin coherence to narrow-band periodic optical excitation is studied theoretically and experimentally. The dependence of the induced oscillating magnetization on the transverse magnetic field and on the frequency of the laser radiation is calculated for a four-level model system from a Bloch-type equation, yielding a two-dimensional resonance line. The application of this two-dimensional high-resolution Zeeman and optical spectroscopy is demonstrated experimentally in the case of the ${\mathit{D}}_1$ line of atomic rubidium vapor. Resolution in the kilohertz range is achieved, which allows clear spectral separation of the two isotopes ${}_{}{}^{85}{}_{}{}^{}\mathrm{Rb}$ and ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$, showing overlapping lines in the conventional optical absorption spectrum.

A plane-wave pulse passing by a charged particle can leave the particle with momentum and energy different from that before the arrival of the pulse. The mechanism for transmitting this momentum and energy is nonradiative and involves the interference of the electromagnetic fields of the particle and wave. A focused pulse (with a finite beam waist) cannot transfer momentum and energy in this way. However, if a charged particle is mechanically restrained and then released inside a focused pulse, momentum can be transferred nonradiatively to the particle through the mechanical restraining force. We use these considerations to further clarify the source of the large drift momentum that photoelectrons have been observed to acquire in recent experiments on atomic ionization by strong low-frequency fields, we discuss the energy quantization condition and we illuminate the distinction between the low-frequency regimes for scattering and ionization processes. We also show that atomic stability in a high-frequency field is a consequence of the difficulty of transferring momentum. Finally, we briefly examine the distribution of drift momentum in two-color processes, illustrating the role of the ponderomotive shift and the sensitivity to the phase at which ionization occurs.

Photodetachment of negative ${\mathrm{H}}^{\mathrm{-}}$ ions in parallel and crossed static electric and magnetic fields is considered for the case of photon polarization parallel to the electric field. The final-state interaction between the electron and the H atom is included in the framework of the zero-range-potential approximation combined with the frame transformation theory. The cross section shows modulations caused by the electric field that are enhanced by the magnetic field. Singular behavior of the cross section at Landau thresholds due to the magnetic field can be strongly suppressed by a weak electric field. Final-state interaction effects in the case under consideration are significant for very strong magnetic fields B≥60 T.

We report a detailed investigation of excited-state alignment-to-orientation conversion in the presence of an external magnetic field. This counterintuitive phenomenon occurs under intermediate-coupling conditions. A weak, linearly polarized, cw laser beam was used to excite and align the Na 3${\mathit{P}}_{3/2}$ state in an atomic beam along the z direction. The degree of circular polarization of the resulting fluorescence was detected along the z direction as a function of magnetic-field strength. The spectrally integrated transitions originating from individual F levels of the 3${\mathit{S}}_{1/2}$ state yield a maximum circular-polarization fraction of ∼40%; integrating the circular polarization over all the allowed 3${\mathit{S}}_{1/2}$-3${\mathit{P}}_{3/2}$ transitions gives rise to an ∼8% effect. The results are predicted by the Breit formula, which is in excellent agreement with our observations.

A combined complex rotation and Feshbach-projection method is implemented within Z-dependent perturbation theory to obtain the lowest-order contribution to the width and shift of autoionizing states of two-electron atoms. This approach relies on the fact that in the complex rotation method, it is the open-channel part of the wave function that produces the imaginary component of the energy. Calculation of this part of the wave function involves the solution of a simple one-electron differential equation which, in lowest order, can be obtained to any desired level of accuracy. Use of the complex rotation method here simultaneously yields the lowest-order contributions to both the width and shift. It also simplifies the calculation by making this wave function square-integrable while simultaneously rotating the interacting continuum away from the real energy axis, thereby eliminating the degeneracy in zeroth order between the doubly excited states and the adjacent continuum. In the present paper, the lowest-order contributions to the width and shift for the 50 lowest singlet and triplet autoionizing P states below the n=2 threshold are calculated. These results represent the limiting values of the width and shift for high Z in the nonrelativistic approximation. The dependence of these results on the level of excitation N is studied. Comparisons to total values for the isoelectronic series are made, indicating that even for relatively low values of Z, these lowest-order results can yield useful estimates of the total widths and shifts. This approach is particularly useful for states with extremely narrow widths, as these are difficult to calculate accurately with other methods. Hence, the lowest-order estimates obtained here give useful information for such states, even for small values of Z.