We investigate the integrability of two-dimensional systems in which a particle moves under the influence of a force field in the interior of a given domain and moreover reflects elastically on the enclosure. A simple example is a particle bouncing on a parabola under the influence of gravity, but whole classes of such systems are obtained.

The approximations used by Wang in explaining the dynamic behavior of walls related to the Fréedericksz transition in nematic liquid crystals (Brochard-Leger walls) as solitary waves [Phys. Lett. 112A, 402 (1985); Phys. Rev. A 32, 3126 (1985); 34, 5179 (1986)] are so severe as to make the results dubious.

In this Comment we consider the conclusion drawn by Mees, Rapp, and Jennings [Phys. Rev. A 36, 340 (1987)] concerning the usefulness of the singular-system analysis of a trajectory matrix (obtained by applying Takens’s construction to time-series data). We point out that this is primarily due to their misinterpretation of our work, and to an assumption they apparently made concerning the conditions under which a map preserves the dimension of a set. We attempt to clarify the issues.

We reply to the Comment by Broomhead, Jones, and King [Phys. Rev. A 37, 5004 (1988), preceding paper]. We show that singular-value decomposition in the form that we describe is useful for reducing the effects of noise but not for dimension estimation.

We provide necessary conditions for the equilibrium of the process $A+B\to C$ where there is a steady input of $A$ and $B$ particles, or when back reactions $C\to A+B$ are allowed. There is an important distinction between inputs which conserve or do not conserve the particle number difference ($N_A-N_B$). For nonconserving input in finite volume or in low enough dimensions, the system never reaches equilibrium. For conserving input, as in the case of back reactions, the system may or may not reach equilibrium.

Two theorems are given governing the general quantum mechanical validity of Davydov Ansatz states.

Polarized triplet positronium, formed in the ground state with a polarized slow-$e^{+}$ beam, is used for an experimental test of CPT (charge-conjugation–parity–time-reversal) invariance. The angular correlation S^⋅k${^}_1$×k${^}_2$ was measured (where S is the positronium spin angular momentum and ‖${\mathrm{k}}_1$‖>‖${\mathrm{k}}_2$‖>‖${\mathrm{k}}_3$‖ are the momenta of the three decay γ rays). It is expected to have zero amplitude if CPT is conserved. No effect was found in the experiment at the 2.3% level of uncertainty in the coefficient of the angular correlation. Information gained from a study of the systematic effects, along with straightforward improvements in the apparatus, would allow a 0.1% measurement. Other possible angular correlations using polarized and aligned positronium, including tests of CP invariance, are discussed.

We compare different techniques for the computation of a long-time evolution and the S matrix in a Schrödinger system. As an application we consider a two-nucleon system interacting via the Yamaguchi potential. We suggest computation of the time evolution for a very short time using Padé approximants, the long-time evolution being obtained by iterative squaring. Within the technique of strong approximation of Moller wave operators (SAM) we compare our calculation with computation of the time evolution in the eigenrepresentation of the Hamiltonian and with the standard Lippmann-Schwinger solution for the S matrix. We find numerical agreement between these alternative methods for time-evolution computation up to half the number of digits of internal machine precision, and fairly rapid convergence of both techniques towards the Lippmann-Schwinger solution.

Partial cross sections for electron capture into specific n states are reported for 0.1- and 0.25-MeV/nucleon ${\mathrm{I}}^{\mathrm{q}+}$-${\mathrm{H}}_2$ collisions (q=12–18). The measured cross sections show pronounced differences when compared to theoretical calculations based on a number of models for bare incident ions on atomic hydrogen.

Experimentally, the transitions between ${}_{}{}^3{}_{}{}^{}\mathrm{P}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{D}$ terms of ${\mathrm{Cl}}^{+}$ have been observed in the inelastic collision between ${\mathrm{Cl}}^{+}$ and Ar. The transfers are modeled through Landau-Zener types of processes at the points where the potential-energy surfaces of the electronic states of ${\mathrm{ArCl}}^{+}$ cross. The potential-energy curves of ten electronic states of ${\mathrm{ArCl}}^{+}$ arising from Ar${(}^1$S)+${\mathrm{Cl}}^{+}$${(}^3$P), Ar${(}^1$S)+${\mathrm{Cl}}^{+}$${(}^1$D), and ${\mathrm{Ar}}^{+}$${(}^2$P)+Cl${(}^2$P) dissociations are computed using the complete active-space multiconfiguration self-consistent field method followed by first-order configuration-interaction calculations. In addition, relativistic configuration-interaction calculations are carried out for the low-lying states of ${\mathrm{ArCl}}^{+}$, with the objective of computing spin-orbit effects. These calculations reveal the existence of three bound states ${(}^3$Π, ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{})$ for which spectroscopic constants and dipole moments are obtained. The ground state is a ${}_{}{}^3{}_{}{}^{}\mathrm{\Pi }$ state with a dissociation energy of 0.32 eV, while the excited ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ is bound at least by 1.81 eV with respect to Ar${(}^1$S)+${\mathrm{Cl}}^{+}$${(}^1$D). The calculations predict that ${\mathrm{ArCl}}^{+}$ is stable and long lived. The Mulliken population analysis of the electronic states of ${\mathrm{ArCl}}^{+}$ reveals considerable charge transfer from Ar to ${\mathrm{Cl}}^{+}$ in the ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{}^{+}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }$ states.

The charge-transfer reaction of helium ions with xenon was investigated with a crossed-beam apparatus at collision energies of 5.1, 29, and 97 eV. In agreement with luminescence studies of the same reaction, the dominant product observed is the 6s ${}_{}{}^4{}_{}{}^{}P_{1/2}^{}{}_{}{}^{}$ state of ${\mathrm{Xe}}^{+}$. A deconvolution technique which removes the contribution of this near-resonant state was used to investigate the contribution of other excited states and the ground state to the observed scattering diagram. A highly structured scattering-contour diagram was revealed which allowed positive identification of several excited-state products. These states are formed directly by charge transfer rather than by cascading from higher states; they also exhibit angular-specific and quantum-state-specific scattering. A propensity rule to conserve electronic angular momentum (ΔJ=0) is also inferred.

Differential cross sections are reported for the elastic scattering of 344-, 411-, 444-, 723-, 779-, 868-, 964-, 1005-, 1086-, 1112-, 1275-, and 1408-keV γ rays through scattering angles from 2° to 45° by targets of Cu, Mo, Sn, Ta, Pb, and U. The results have been compared with two sets of theoretical cross sections for Rayleigh plus nuclear-Thomson plus Delbruck scattering. The first set was interpolated from the tables of P. P. Kane et al. [Phys. Rep. 140, 75 (1986)], which are based upon exact S-matrix amplitudes for inner-shell Rayleigh scattering and use of modified form factors and photoelectric cross sections for outer-shell Rayleigh scattering; the second set was based upon modified-form-factor Rayleigh amplitudes for all electron shells. The measured cross sections agree to closer than 10% with the Kane et al. calculations and indicate that for larger scattering angles, higher photon energies, and heavier target elements the modified form factor overestimates Rayleigh scattering. At small scattering angles there is no evidence for any systematic discrepancy between experiment and the cross sections of Kane et al.

A fully relativistic electron-impact ionization cross section is calculated as a triple partial-wave expansion of the first Born scattering amplitude. The target atomic ion is described by a Dirac-Fock approximation, a jj subconfiguration average method is used to calculate the scattering algebra, and the radial partial waves (ɛlj) are computed in distorted-wave potentials. The resulting general computational scheme is applied to electron-impact ionization of ${\mathrm{U}}^{89+}$. The fully relativistic cross-section results are compared with those obtained from both nonrelativistic and semirelativistic theories.

We have investigated fine-structure–changing collisions of short-lived (20-ns) ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$ atoms in the {α}≡{(2p${)}^5$(3p)} multiplet with ground-state He atoms. A newly designed cross-beam apparatus allows the measurement of accurate polarized cross sections $Q_{l\leftarrow k}^{\Vert M_k\Vert }$ for the {α${\mathrm{\}}}_k$→{α${\mathrm{\}}}_l$ transition. In the experiment, the initial {α${\mathrm{\}}}_k$ state is prepared with a well-defined asymptotic orientation $M_k$ of its electronic angular momentum J, through excitation of metastable ${\mathrm{Ne}}^{\mathrm{*}}$ atoms with a polarized laser. The reported transitions are mainly between states in the {α${\mathrm{\}}}_4$,5,6,7 group (Paschen numbering), at approximately 100 meV center-of-mass energy. Some of these exhibit very strong polarization effects, with differences between $Q_{l\leftarrow k}^{\Vert M_k\Vert }$ and $Q_{l\leftarrow k}^{\Vert M_k^{\mathcal{’}}\Vert }$ of up to a factor 4. Fully quantum-mechanical coupled-channel calculations on a diabatic basis, with the ${\mathrm{Ne}}^{\mathrm{*}\mathrm{*}}$-He model potentials of Hennecart and Masnou-Seeuws as input, prove successful in reproducing experimental results. Cross-section behavior may be qualitatively understood from the presence of avoided crossings between the adiabatic potentials, indicative of strong radial coupling. The restraint of reflection symmetry is strongly felt here. In addition, the effects of rotational coupling can be readily identified.

The absolute cross sections for two-electron photoionization have been measured for ${\mathrm{K}}^{\mathrm{-}}$ from 70 meV below to 250 meV above the threshold by measuring product ${\mathrm{K}}^{+}$ ions. To minimize complications from the photodetachment and field ionization, the electric field strength used to separate ${\mathrm{K}}^{+}$ ions was limited to 300 V/cm, which ionizes only Rydberg neutral atoms with n≥30. The data fit to σ∼$E^m$ (E is the total energy of the two electrons) yielded m=1.16±0.05 with a reduced ${\chi }^2$=0.69, in agreement with the Wannier theory m=1.127 [G. H. Wannier, Phys. Rev. 90, 817 (1953)]. However, a nearly equally satisfactory fit can also be made to the oppositional theory of A. Temkin [Phys. Rev. A 30, 2737 (1984)].

Absolute two-photon absorption cross sections have been measured for the np ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$,1,0←2p ${}_{}{}^3{}_{}{}^{}\mathrm{P}_2^{}{}_{}{}^{}$ transitions in atomic oxygen (n=4 and 5) using the technique of two-photon–excited fluorescence. For the n=4 transition at 200.6 nm the integrated cross section is ${\mathcal{J}}_{J\mathcal{’}}$${\sigma }_0^{\mathrm{}\left(2\right)\mathrm{}}$(J’←2) =(4.8±2.4)×${10}^{\mathrm{-}36}$ ${\mathrm{cm}}^4$. The corresponding number for the n=5 transition at 192.5 nm is (0.$7_{-0.5}^{+0.7\mathrm{}}$)×${10}^{-36}$ ${\mathrm{cm}}^4$. These numbers are in moderately good agreement with ab initio calculations presented previously [Phys. Rev. A 34, 199 (1986)] for n=4 and in this paper for n=5. Calculations are also reported for the 4f ${}_{}{}^3{}_{}{}^{}F_4^{}{}_{}{}^{}$,3,2←2p ${}_{}{}^3{}_{}{}^{}\mathrm{P}_{\mathrm{J}\mathcal{’}\mathcal{’}}^{}{}_{}{}^{}$ transition at 194.2 nm. Atoms in the np ${}_{}{}^3{}_{}{}^{}P$ excited states produce positive ions and electrons upon collisions with ${\mathrm{O}}_2$. In each case, Penning ionization and associative ionization are possible, and cannot be distinguished.

Total rate constants for collisional ionization by ${\mathrm{O}}_2$ at room temperature are (2±1)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\sec }^{\mathrm{-}1}$for n=4 and (4±3)×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$${\sec }^{\mathrm{-}1}$ for n=5. Einstein A coefficients are calculated for all allowed fluorescence transitions originating from the 4p ${}_{}{}^3{}_{}{}^{}P$ and 5p ${}_{}{}^3{}_{}{}^{}P$ electronic states. For each state, the sum of the calculated Einstein A coefficients agrees well with the experimental zero-pressure decay rate. Rate constants for collisional removal of population from these states by the background gas (which is mostly ${\mathrm{O}}_2$) are 1.5×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$${\sec }^{\mathrm{-}1}$ for n=4 and 7.2×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\sec }^{\mathrm{-}1}$ for n=5. The photoionization cross section for atoms in the 4p ${}_{}{}^3{}_{}{}^{}P$electronic state is (3±2)×${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$. For atoms in the 5p ${}_{}{}^3{}_{}{}^{}P$ state the photoionization cross section is less than 1×${10}^{\mathrm{-}17}$ ${\mathrm{cm}}^2$.

The theory of spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ relaxation due to hyperfine coupling in ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ and due to spin-rotation coupling in ${}_{}{}^3{}_{}{}^{}\mathrm{He}_2^{+}{}_{}{}^{}$ is presented. Comparison is made between the theory and recent experiments which utilized spin-polarized ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ as a charged-particle beam target. The theory predicts that at low He pressures applying a magnetic field significantly reduces the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ depolarization rate due to formation of ${}_{}{}^3{}_{}{}^{}\mathrm{He}_2^{+}{}_{}{}^{}$. At high He pressures the relaxation rate decreases with pressure. In addition, charge-transfer processes with foreign gases suppress ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ depolarization by reducing the ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_2^{+}{}_{}{}^{}$ concentrations.

The dc Stark shift of the cesium D lines is observed in the low-field limit where the induced shift is small compared with the various hyperfine splittings. On the D2 line, modification by the electric field of the dipole transition rates to the various excited-state hyperfine levels must be taken into account in order to interpret our results. From our observations the following atomic polarizabilities in units of ${10}^{\mathrm{-}24}$ ${\mathrm{cm}}^3$ are deduced: ${\mathrm{\alpha }}_0$(${6\mathrm{P}}_{1/2}$)-${\mathrm{\alpha }}_0$(${6\mathrm{S}}_{1/2}$)=143.8±1.4, ${\mathrm{\alpha }}_0$(${6\mathrm{p}}_{3/2}$)-${\mathrm{\alpha }}_0$(${6\mathrm{S}}_{1/2}$)=187.3±1.9, and ${\mathrm{\alpha }}_2$(${6\mathrm{P}}_{3/2}$)=-38.6±1.2.

Recent experiments with single atomic ions isolated in electromagnetic traps have demonstrated abrupt changes in observed fluorescence intensities, which have been interpreted as evidence for quantum jumps as the atom changes energy levels. This presents the seeming paradox of discontinuously changing observables from a system whose dynamical evolution is governed by the continuous optical Bloch equations. In this paper I present an analysis of the dynamics of a model three-level atom interacting with two laser fields in terms of the dressed states of the atom-laser system. These dressed states are eigenstates of a Hamiltonian which includes laser-atom interactions, and thus they simplify the discussion of the time evolution of the combined laser-atom system. This dressed-state description is particularly useful in the regime in which both laser intensities are strong enough to saturate their respective transitions. I calculate the radiative lifetimes of the different species of dressed states and the branching ratios for decay to other dressed states, and demonstrate the consequences of these quantities for the observed fluorescence pattern. The calculated duration of bright and dark periods shows a pronounced dependence on the detunings of the lasers.

We report measurements of the temporal decay of sodium Stark resonances over regions of interference narrowing and compare with calculations using Wentzel-Kramers-Brillouin quantum-defect (WKB-QD) Stark theory. The measurements are performed with a beam of sodium atoms in a uniform electric field of ∼3.2 kV/cm excited via the 3 ${}_{}{}^2{}_{}{}^{}P$ state to ∼285 ${\mathrm{cm}}^{\mathrm{-}1}$ ($n^{\mathrm{*}}$∼20) below the zero-field ionization threshold, and hence substantially above the classical saddle-point energy. For mixed states at level crossings, the discrete-continuum couplings interfere, yielding resonances that are stabilized against ionization over a small interval of the field. Measurements of the maximum lifetimes of ‖m‖=1 levels here are not limited by laser bandwidth, as were our previous spectral observations of m=0 resonances. For three narrowing regions studied here, the observed maximum lifetime values of 127–191 nsec are 10–20 % less than values obtained from WKB-QD calculations, while experimental error limits are ∼5%. After considering estimates for competing processes, namely radiative decay and transfer by blackbody radiation, a slight discrepancy remains.