Scattering amplitudes are extracted from (elastic scattering) differential cross sections under the constraint that the scattering function is unitary. A modification to the Newton iteration method has been used to solve the nonlinear equation that specifies the phase of the scattering amplitude in terms of the complete (0° to 180°) cross section. The approach is tested by using it to specify the scattering amplitude from simulated data and comparing the result with the amplitude found by using an exact iterated fixed point method of solution. The (modified) Newton method was then used to analyze the cross sections from neutron–α-particle scattering at low nuclear energies (<24 MeV) and from 1000-eV electron-water molecule scattering.

Differential, total, and momentum transfer cross sections for the elastic scattering of low- and intermediate-energy (0.2–100 eV) electrons by strontium and barium atoms were calculated in the relativistic polarized orbital approximation. A static part of the projectile-target interaction potential was generated by solving the Dirac-Hartree-Fock (DHF) equations for the isolated target. A polarization potential was obtained by solving the coupled DHF equations for the target perturbed by an electric field produced by the projectile. Only the dipole term in the polarization potential was included in scattering calculations. For low angular momenta (0≤l≤5) relativistic phase shifts were extracted by solving a continuum state DHF equation in an inner region, where exchange between the projectile and the target electrons was important, and then a relativistic variable phase (RVP) equation in an outer region, where exchange was negligible. For intermediate angular momenta (6≤l≤17) exchange was neglected and the phase shifts were calculated by solving the RVP equation in the whole configuration space. Higher (l≥18) phase shifts were obtained using the Born approximation and their contributions to scattering amplitudes and cross sections were evaluated analytically. At low energies (0.2–10 eV) our total cross sections for both strontium and barium atoms differ seriously from experimental data of Romanyuk, Shpenik, and Zapesochnyi (Pis’ma Zh. Eksp. Teor. Fiz. 32, 472 (1980) [JETP Lett. 32, 452 (1980)]). At energies up to 60 eV our differential cross section for barium differs both in magnitude and shape from experimental data of Jensen, Register, and Trajmar [J. Phys. B 11, 2367 (1968)] but quite satisfactorily reproduces shapes of curves measured recently by Wang, Trajmar, and Zetner [J. Phys. B (to be published)]. At energies above 80 eV the agreement between the present results and the data of Jensen, Register, and Trajmar is much more satisfactory.

We have observed coherence between the photoionization of the 2${\mathit{s}}^{\mathrm{-}1}$${(}^2$${\mathit{S}}_{1/2}$) and the 2${\mathit{p}}^{\mathrm{-}1}$${(}^2$${\mathit{P}}_{3/2}$) inner-shell vacancy states of argon, and between the 3${\mathit{d}}^{\mathrm{-}1}$${(}^2$${\mathit{D}}_{3/2}$) and the 3${\mathit{d}}^{\mathrm{-}1}$${(}^2$${\mathit{D}}_{5/2}$) inner-shell vacancy states of krypton. The method is based on the occurrence of interferences between photoelectrons and Auger electrons, resulting from the photoionization and subsequent Auger decay of the two states concerned. A parametrization is proposed that describes the observed interference effects reasonably well.

Quantal and semiclassical (WKB) methods of inversion have been used in an analysis of the elastic-scattering cross sections for 62.5-meV He atoms from Ne atoms by which an effective local interaction between those atoms is specified. The potentials obtained by the approximate method (WKB) differ from that found with the full quantal analysis. The quantal inversion potential is repulsive at short distances and becomes attractive at a radius of 2.695 Å. It has a minimum value of -1.981 meV at a radius of 2.98 Å.

An interference effect on angular correlation patterns due to the exchange of Auger and photoelectrons of the same energy is discussed. The detection in coincidence of Auger and photoelectrons may reveal a striking angular correlation pattern when a synchrotron light source is tuned so that the Auger and photoelectron energies are nearly equal. This effect is present even when only one electron is detected, but is strongly reduced by the averaging over the direction of the undetected electron.

Coherences of two photoexcited nondegenerate resonant states are investigated. The two autoionizing states decay by emission of Auger electrons to indistinguishable final states of the residual doubly ionized atom. The coherence produces observable effects when the incident photon is tuned so that the Auger electron in the first channel and the photoelectron in the second channel have comparable energies. Under these conditions the energy dependence of the cross section exhibits interference structure due to two paths to the same final state. We present a theoretical description of the effect. Cross section formulas for angular distributions and angular correlations are presented.

We report angle-resolved studies of projectile ${\mathit{L}}_{2,3}$-shell autoionization electron emission by bombarding a polycrystalline Al surface with 0.2–5-keV ${\mathrm{Ne}}^{+}$ ions. Several previously unresolved transition lines have been observed and assignment to Ne 2${\mathit{p}}^3$nln’l’n’’l’’ and ${\mathrm{Ne}}^{+}$ 2${\mathit{p}}^3$nln’l’ autoionizing states has been proposed. We found that the ${}_{}{}^3{}_{}{}^{}$P triplet is the dominant configuration for the excited Ne 2${\mathit{p}}^4$3${\mathit{s}}^2$ and its relative population depends sensitively on both the primary ion energy and incidence angle. Analysis of the electron spectra shows that most excited Ne particles are backscattered from the surface and decay in vacuum, rather than inside the solid.

We have measured keV secondary electrons induced by 2.5- and 3.5-MeV/u ions under Si〈100〉 and Si〈110〉 channeling-incidence conditions. From a comparison of the electron yields for the ions of equal velocity, the effective nuclear charges of the ions in glancing collisions with aligned Si atoms have been determined. The results indicate that ${\mathrm{He}}^{2+}$, ${\mathrm{B}}^{5+}$, ${\mathrm{C}}^{4+}$, ${\mathrm{C}}^{6+}$, ${\mathrm{O}}^{5+}$, and ${\mathrm{C}}^{8+}$ do not capture target electrons, while Si, S, and Cl ions capture or lose electrons depending on the incident charge state. For the heavy ions, the number of bound electrons in the charge equilibrium is greater than for the random case, for example, by 2–4 and 3–5 for 2.5-MeV/u Si and S, respectively.

The interaction of an atomic beam with three spatially separated linearly polarized standing-wave fields is considered, taking into account the magnetic degeneracy and hyperfine splitting of the atomic levels. A spatial modulation of the ground-state density matrix occurs, and is not washed out as a result of spontaneous decay from the upper states. The interaction with fields separated by a distance L results in a focusing of harmonics at distances L’=(m/n)L, where m and n are integers; the period of the matter gratings is λ/2n, where λ is the wavelength of the radiation field. For a beam having angular divergence θ, one can observe these higher harmonics independently from each other if L≫λ/θ. The gratings can be probed using a third standing-wave laser field in the focal plane of the harmonic under investigation. General expressions that allow one to calculate the probe absorption for atoms having arbitrary fine and hyperfine structure are derived. Explicit calculations for the alkali metals are presented. It is predicted that spatial modulations having periods 30–500 nm and modulation depths 2.5–50 % can be produced in this manner. The focusing of the spatial harmonics is interpreted in terms of a shadow effect.

In this paper, a quantum-field theory is employed to study the diffraction of an ultracold atomic beam by a crystalline solid surface. We show that the crystalline solid surface acts as a nonlinear atomic grating for an ultracold atomic beam with a Bose condensate. The nonlinearity in such a mechanical atomic grating is due to the phonon exchange between the atoms in the ultracold atomic beam via the surface lattice vibration. Such a phonon exchange leads to an attractive interatom interaction in the ultracold atomic beam, which results in the generation of correlated atomic pairs in momentum space. Such correlated atomic pairs have similar properties to the conjugate photon pairs in nonclassical light.

We have observed 10-MHz-wide energy-transfer resonances between colliding Na Rydberg atoms. The narrow linewidth allows us to apply a modest 5–40-G static magnetic field in addition to a static tuning electric field and resolve new resonances arising from magnetic-field-induced splitting of the Stark energy levels. When B is parallel to E, the nine resolved resonances observed with only an E field are further split into 144 possible resonances. However, only the 21 resonances corresponding to collisions in which the spins are unchanged are observable. When B is perpendicular to E, the spectrum of collisional resonances is similar to that of the vertical field case, except that the final spin states cannot be determined. With both parallel and perpendicular fields present, linear and quadratic terms of the B field interaction create more complicated spectra than with either case alone. The experimental spectra agree quantitatively with the spectra calculated using a simple Zeeman model of the energy levels.

We describe a detailed account of an experiment demonstrating light-induced stabilization against photoionization. The choice of initial state and atom is discussed in relation to the laser wavelength and laser pulse duration. In combination with a 100-fs, 620-nm probe pulse, the optimum choice is the circular 5g state in neon. A picosecond pump laser was used to prepare this Rydberg state. Initially, the population in this state was probed with a nanosecond laser pulse. Subsequently, the nanosecond probe pulse was replaced by an intense, (sub)picosecond pulse and the photoionization signal was studied. When the probe intensity is several times ${10}^{13}$ W/${\mathrm{cm}}^2$ a decrease in yield with respect to a less intense pulse with the same fluence is observed, which indicates stabilization. The results are in accordance with recent theoretical predictions.

We present a general procedure for accurate nonperturbative treatment of the angular distribution and partial widths for multiphoton above-threshold detachment (ATD) of atoms or negative ions in intense laser fields. The procedure consists of the following two steps: (1) The resonance wave function is determined by means of the non-Hermitian Floquet Hamiltonian method. The Floquet Hamiltonian is discretized by the complex scaling generalized pseudospectral method recently developed by Yao and Chu [Chem. Phys. Lett. 204, 381 (1993)]. No computation of potential matrix elements is required, and the kinetic-energy matrix elements can be evaluated analytically. (2) The angular distribution and partial rates are calculated, based on an exact differential expression, and a procedure is developed for the backrotation of the total complex resonance wave function to the real axis. The method is applied to the study of multiphoton ATD of ${\mathrm{H}}^{\mathrm{-}}$ in strong fields at 10.6 μm. An accurate one-electron model potential [Laughlin and Chu, Phys. Rev. A 48, 4654 (1993)], which reproduces the known ${\mathrm{H}}^{\mathrm{-}}$ binding energy and the low-energy e-H(1s) elastic scattering phase shifts, is employed. At this low frequency, the resonance wave functions can be obtained efficiently and rather accurately by means of a nonperturbative adiabatic approach recently developed by Telnov [J. Phys. B 24, 2967 (1991)]. This adiabatic theory is also valid in the limit of weak fields, and its validation is justified by its agreement with the exact perturbation calculations for the seven- and eight-photon detachment of ${\mathrm{H}}^{\mathrm{-}}$. Detailed results for the angular distribution and partial widths for multiphoton ATD of ${\mathrm{H}}^{\mathrm{-}}$ are presented for the moderately strong laser intensity regime (${10}^{10}$–${10}^{11}$ W/${\mathrm{cm}}^2$) at 10.6 μm.

The problem of integrating the time-dependent Schrödinger equation (TDSE) describing the interaction of a polyelectronic atom with a laser pulse is treated by expanding the time-dependent wave function Ψ(r,t) in terms of wave functions ${\mathrm{\Phi }}_{\mathit{n},}$E computed for discrete, autoionizing, and scattering states separately. The TDSE is transformed into a system of coupled first-order differential equations with time-dependent coefficients, whose number (in the thousands), necessary for convergence to be reliable, depends mainly on the degree of the contribution of the continuous spectrum, as a function of the frequency and strength of the field. This approach allows the systematic incorporation of the significant electronic structure, electron correlation, and spectral characteristics of each N-electron system under investigation. Furthermore, since the free-electron function is computed numerically in the polarized core potential of the remaining (N-1)-electron atom, properties such as the angular distribution and partial above-threshold ionization (ATI) of the photoelectron are directly computable. We present results from the application of our methods to H and ${\mathrm{Li}}^{\mathrm{-}}$. For the applications to H, which served as testing grounds for the method, the state-specific wave functions for discrete and continuum states were obtained numerically, for n and l up to 12 and 5, respectively, and for positive energies up to ɛ=34 eV with l up to 6. When comparisons with other time-independent and time-dependent results are possible, very good agreement is observed. On the other hand, our calculations do not confirm recent experimental results on absolute ionization rates for laser pulses of 248 nm. For ${\mathrm{Li}}^{\mathrm{-}}$, our results on ATI for photon energy ħω=1.36 eV demonstrate the effects of initial-state electron correlation and of final-state field-induced coupling of open channels (the Li 1${\mathit{s}}^2$2s ${}_{}{}^2{}_{}{}^{}$S and 1${\mathit{s}}^2$2p ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$), as a function of field intensity.

Confinement of ion clouds in an rf octupole ion trap is investigated with particular emphasis on the trapping stability, which is position dependent. Excitation spectra of trapped clouds of ${\mathrm{Ba}}^{+}$ ions are observed, and the kinetic energy of ion clouds is derived. The spatial extension of ion clouds is measured, providing the basis for an experimental study of the trapping stability. For ion clouds in an rf octupole trap the mean kinetic energy is smaller and the spatial extension is larger than in comparable Paul traps.

One-photon ionization from the 6s27d ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}_2$ state in barium is measured with short (0.25–2.7 ps), high-intensity laser pulses. Fermi’s golden rule predicts that only the fluence (time-integrated intensity) determines the yield. We observed a decrease in the yield for fixed-fluence pulses shorter than the Kepler orbit time of the Rydberg electron (2.2 ps). This is explained semiclassically: The wave function of a Rydberg electron performs a Kepler-like orbit. Only the wave function near the core can be ionized. Not all of the wave function nears the core during a short pulse, and therefore the wave function far away from the core is stable against ionization. A quantum-mechanical calculation based on Raman transitions over the continuum agrees well with experimental observations and the semiclassical explanation.

Effects of the atomic Zeeman degeneracy on the resonance fluorescence spectrum of a closed two-level atom with arbitrary ground-state angular momentum ${\mathit{J}}_{\mathit{g}}$ and excited-state, angular momentum ${\mathit{J}}_{\mathit{e}}$ are studied in detail. Especially interesting are the narrow structures due to the spontaneous Raman scattering and the incoherent Rayleigh scattering. Results for the cycling transition of a Cs atom are presented as part of the examples.

Calculations based on coupled Mathieu-Coulomb equations indicate that the transition from transient to stationary chaos for two ions in a Paul trap near the edge of the stability region is due to a boundary crisis. Numerical simulations reproduce the long-lived chaotic transients observed in ion trap experiments, obeying the power-law dependence T(q)∝(${\mathit{q}}_{\mathit{c}}$-q${)}^{\mathrm{-}\gamma }$ where T is the average transient lifetime and q the dimensionless trap voltage. The unstable, periodic orbits which are fundamental to a heteroclinic boundary crisis were identified and the intersection of their invariant manifolds in the four-dimensional phase space was located, yielding a prediction for ${\mathit{q}}_{\mathit{c}}$, the transition point between transient and stationary chaos, that agrees well with the experimental value. This provides a theoretical understanding of a transition which previously has been a subject of controversy. Finally, a heuristic derivation is given for the critical exponent γ, based on the stability properties of the mediating periodic orbits. Thus solutions of the deterministic, time-dependent equations of motion can be used to accurately describe the duration of transient two-ion chaos near criticality, with only a single free scale factor.

We numerically solve an effective single-atom Hartree-Fock master equation in order to investigate the effects of spontaneous emission on atomic Thirring solitons and atomic gap solitons. We show that spontaneous emission detrimentally effects the existence of Thirring solitons, as expected from the fact that they only occur on resonance. In contrast, gap solitons, which can also exist off resonance, survive in the presence of spontaneous emission in weakly allowed transitions, albeit at high atomic densities. This result is illustrated in the case of the [2 ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$⇆2 ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$]- intercombination line of magnesium.

We investigate the effect of injected squeezed vacuum on the phase and intensity fluctuations of a laser. By using a stochastic simulation of the Langevin equations, we find that the phase diffusion noise of a laser with injected squeezed vacuum can be transiently reduced by a factor of 2, in agreement, with earlier predictions. Further, we find that the laser linewidth is broadened. The key observation is that the phase-diffusion rate is time dependent. We find that the steady-state intensity fluctuations are increased by the injected squeezing, in qualitative (but not quantitative) agreement with an earlier prediction. The problem of locking is examined. We find that the injected squeezed vacuum does not cause the laser to lock to any particular phase. We present an approximate solution of the Fokker-Planck equation in steady state, and a simple geometrical, vector kick model from which most of our results can be obtained.