The Stark shifts of four transitions in cesium were measured using two atomic beams. One traverses through a uniform electric field and the other a field-free region. The atoms were excited using a ring dye laser, with the laser beam interacting with the atoms in the electric-field region frequency shifted by an acousto-optic modulator. The Stark shift was determined by measuring the electric field for which the atoms in both beams are simultaneously in resonance. The results for the 6${\mathit{P}}_{3/2}$→(10–13)${\mathit{S}}_{1/2}$ transitions are -59.36(14), -154.68(13), -356.57(29), and -745.43(61) MHz (kV/cm${)}^2$, respectively.

The total and total ionization cross sections for positron scattering on atomic hydrogen are calculated by applying the convergent-close-coupling method to the model where positronium-formation channels are omitted. This model accurately describes the physics of the scattering whenever the positronium formation cross section is negligible, in particular, above 100 eV for this system. The total ionization cross section results in this energy region are in excellent agreement with the recent measurements of Jones et al. [J. Phys. B 26, L483 (1993)], and so lie below the earlier measurements of Spicher [Phys. Rev. Lett. 64, 1019 (1990)], and the recent calculations of Acacia et al. [Phys. Rev. Lett. (to be published)]. The total cross section is in very good agreement with the recent measurements of Zhou et al. (unpublished) down to 30 eV.

We have observed conical emission from a dense, strongly driven ensemble of two-level atoms without noticeable self-focusing. We present the arguments that conical emission, unaffected by autocollimation, is due to cooperative, Čerenkov-like, spontaneous emission of collisionally perturbed, optically dressed atoms rather than to parametric wave mixing. Our results indicate the importance of many-atom correlations which must be taken into account when strong light interacts with dense media.

Feynman introduces the concept of negative probability in the context of Young’s double-slit experiment and in doing so sheds a new light on the problem. However, there are, as Feynman notes, conceptual problems as well as insights associated with this point of view. The micromaser which-path (Welcher-Weg) detector eliminates these conceptual difficulties. We also emphasize that the concept of negative probability yields useful insight into the Einstein-Podolsky-Rosen (EPR) problem.

We present a complete analysis of variance matrices and quadrature squeezing for arbitrary states of quantum systems with any finite number of degrees of freedom. Basic to our analysis is the recognition of the crucial role played by the real symplectic group Sp(2n,openR) of linear canonical transformations on n pairs of canonical variables. We exploit the transformation properties of variance (noise) matrices under symplectic transformations to express the uncertainty-principle restrictions on a general variance matrix in several equivalent forms, each of which is manifestly symplectic invariant. These restrictions go beyond the classically adequate reality, symmetry, and positivity conditions. Towards developing a squeezing criterion for n-mode systems, we distinguish between photon-number-conserving passive linear optical systems and active ones. The former correspond to elements in the maximal compact U(n) subgroup of Sp(2n,openR), the latter to noncompact elements outside U(n). Based on this distinction, we motivate and state a U(n)-invariant squeezing criterion applicable to any state of an n-mode system, and explore alternative ways of expressing it. The set of all possible quantum-mechanical variance matrices is shown to contain several interesting subsets or subfamilies, whose definitions are related to the fact that a general variance matrix is not diagonalizable within U(n). Definitions, characterizations, and canonical forms for variance matrices in these subfamilies, as well as general ones, and their squeezing nature, are established. It is shown that all conceivable variance matrices can be generated through squeezed thermal states of the n-mode system and their symplectic transforms. Our formulas are developed in both the real and the complex forms for variance matrices, and ways to pass between them are given.

We present a calculation of the second-order process of electron-positron pair creation by the electromagnetic fields of two relativistic heavy ions for impact parameter b zero. Total probabilities as well as differential ones are presented. A comparison with the results of the double equivalent-photon approximation (DEPA) shows explicitly the inapplicability of this approximation in the case of total probabilities. We discuss the creation of pairs with large invariant mass. The DEPA results are too high, which can be traced back to the mass singularity of the photon cross section at very small angles, giving a discrepancy, whereas the agreement between our result and DEPA is good for larger angles.

The moment of inertia of a physical system exhibiting irrotational flow is expressed as a series expansion in terms of the moments of the density distribution. The lowest-order contribution yields a simple relation with the quadrupole moment and is applicable to models of classical and quantum systems. The method is applied in some detail to the special case of the rotational magnetic moment of the hydrogen molecule.

Mathematical methods in optics show that the overall amplitude resulting from the infinite summation over all the various alternative paths that the light can take inside a Fabry-Pérot interferometer can directly be obtained by using a complex generalization of Einstein’s composition law for parallel velocities. Moreover, this result appears to be quite general. In fact, the reflection coefficient for any number of interfaces or quantum wells can be easily obtained by using the composition law. This suggests that a more general way to obtain the probability amplitude for an event which usually needs infinite summation on virtual paths (as in the Fabry-Pérot interferometer) is to compose amplitudes following Einstein’s addition law. I explore this problem and show how the composition law avoids divergences and guarantees the modulus of any total wave function to be less than (or equal to) unity. By examining its physical meaning in the light of probability theory, I also show that it provides an interesting expression for nonlocality and nonseparability.

Both quantum mechanics and Markov-process theory deal with dynamical systems whose behaviors can be predicted only probabilistically. The question therefore arises as to whether Markov-process theory, a theory that is firmly rooted in the common-sense laws of probability, can provide a generally adequate mathematical framework for quantum mechanics, a theory whose predictions often seem to defy common sense. It is shown here that the measurable behavior of a certain elementary quantum system that oscillates between two discrete states cannot be modeled as a Markov process. That this will also be true for most other quantum systems is shown to follow from the same property of quantum mechanics that is responsible for the so-called quantum Zeno effect. The conclusion that quantum behavior cannot generally be modeled as a Markov process underscores the truly mysterious nature of quantum mechanics when viewed in common-sense terms.

By differentiating the Schrödinger equation and separating the real amd imaginary parts, one obtains the Madelung hydrodynamic equations, which have inspired numerous classical interpretations of quantum mechanics. Such interpretations frequently assume that these equations are equivalent to the Schrödinger equation, and thus provide an alternative basis for quantum mechanics. This paper proves that this is incorrect: to recover the Schrödinger equation, one must add by hand a quantization condition, as in the old quantum theory. The implications for various alternative interpretations of quantum mechanics are discussed.

We have computed the partial and total widths with interchannel coupling for the 1s3s3p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ and 1s3${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P states for Z=2–5 and 10, by solving the corresponding complex matrix equations constructed from square-integrable N-electron functions with numerical and analytic real and complex orbitals. The correlated wave functions are computed by the state-specific method. Oscillator strengths for one- and two-electron transitions from the metastable 1s2s2p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state suggest that the states are reachable in ${\mathrm{He}}^{\mathrm{-}}$ and in Li directly, (1s3${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P), or via the 1s2${\mathit{p}}^2$ ${}_{}{}^4{}_{}{}^{}$P state (1s3s3p ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$). The effect of interchannel coupling on the partial widths in the case of the ${}_{}{}^4{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$ state is considerable. On the contrary, interchannel coupling has no significant effect on the total widths. This computational result is discussed formally.

We discuss a stationary version of the coupled-cluster response theory using multideterminantal model space. This brings in all the attendant advantages of a stationary theory for quasidegenerate cases.

The probability distribution of a two-level ion confined in a time-dependent nonlinear trapping field and driven by a radiation field is calculated using an alternative treatment based on a singular asymptotic expansion. It is assumed that the ion is excited by electromagnetic radiation and relaxes back irreversibly by spontaneous emission. The present calculations reproduce the quantum results of the laser cooling of ions in static traps in the heavy-particle limit, and previous classical treatments for the confinement and cooling of ions in radio-frequency traps.

An analysis is presented for the evaluation of atomic integrals of the form F${\mathit{r}}_1^{\mathit{i}}$${\mathit{r}}_2^{\mathit{j}}$${\mathit{r}}_3^{\mathit{k}}$${\mathit{r}}_{23}^{\mathit{l}}$${\mathit{r}}_{31}^{\mathit{m}}$${\mathit{r}}_{12}^{\mathit{n}}$ ${\mathit{e}}_1^{\mathrm{-}\mathrm{\alpha }\mathit{r}}$-β${\mathit{r}}_2$-γ${\mathit{r}}_3$d${\mathbf{r}}_1$d${\mathbf{r}}_2$d${\mathbf{r}}_3$. General formulas are worked out for the two cases (i) l=-2, m≥-1, n≥-1, and (ii) l=-2, m=-2. A series solution for both cases is obtained. The Levin u transformation and the Richardson extrapolation techniques are employed to obtain a reasonable number of digits of precision for the integral with minimum CPU requirements.

This paper describes the determination of the ionization threshold of rubidium Rydberg atoms in crossed electric and magnetic fields. An experimental setup is used that allows one to count separately Rydberg atoms which ionize in the region of optical excitation, and those which leave the excitation region in a bound state. The obtained spectra allow one to determine the energy and the width of the ionization threshold. For different values of the electric-field strength E the influence of the magnetic field B on the ionization threshold was investigated. It was found that the scaled electric field ε=${\mathit{EB}}^{\mathrm{-}4/3}$ and the scaled energy ω=${\mathit{WB}}^{\mathrm{-}2/3}$ with excitation energy W are sufficient in order to describe the observed ionization threshold. This is remarkable since ε and ω are the classical parameters of the system. For ε≳1.5 (atomic units), i.e., a weak magnetic field, the ionization energy does not depend on B and can be explained classically by direct-path ionization. In the regime 1.5≥ε≥0.2, the energy and the width of the ionization threshold increase with increasing magnetic-field strength.

In that regime the observed ionization behavior is qualitatively consistent with the assumption that the excited states are coupled to the continuum via free-electron states which exist at and beyond the classical ionization saddle point, those states corresponding to classical drift trajectories. At ε≊0.2, the ionization energy takes a maximum value, and in the range 0.2≥ε≥0.06, with increasing magnetic field, both the energy and the width of the ionization threshold decrease again. A further increase of the magnetic-field strength changes the tendency a second time: for ε<0.06, both the ionization energy and the width increase again. In this high-magnetic-field regime the ionization energy was explained by classical drift trajectories which almost completely surround the Coulomb center and extend into the continuum. Wave functions of corresponding drift states were calculated using a Born-Oppenheimer approximation. The coupling between the inner-configuration-space volume and the drift states, which leads to ionization, vanishes in the classical limit.

We employ an alternative technique for determining the Lorentzian linewidth based upon the simultaneous measurement of the vapor transmission and group-velocity delay outside the Doppler core of an optically dense transition. We apply this technique to measure the cross sections for broadening of the intercombination lines of calcium, 4${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→4s4p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$, and strontium, 5${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→5s5p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1$, by collisions with argon, neon and the ground-state neutral vapor. We compare our measured results with calculated values as well as previously determined values by other workers.

Thirteen core-excited lithium doublet states of the ${}_{}{}^2{}_{}{}^{}$P, ${}_{}{}^2{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, ${}_{}{}^2{}_{}{}^{}$D, and ${}_{}{}^2{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ symmetries are calculated with a multiconfiguration-interaction wave function. A variation method is used for the bound states whereas the saddle-point and saddle-point complex-rotation methods are used for the autoionizing states. A restricted variation method is used for the saturated wave functions. Fine structures, relativistic corrections, and mass polarization corrections are calculated. The quantum electrodynamic corrections are also estimated. The absolute term energy is predicted with an uncertainty which is much smaller than that in the literature. Among these core-excited states, ten doublet-doublet transitions and one doublet-quartet transition have been measured. The largest error bar for the transition energy has been 6.2 ${\mathrm{cm}}^{\mathrm{-}1}$ whereas others range from 0.5 to 3.3 ${\mathrm{cm}}^{\mathrm{-}1}$. Our predicted transition wavelengths agree with the experiment for 10 of the 11 transitions. The only discrepancy is about 2 ${\mathrm{cm}}^{\mathrm{-}1}$. In the case where there is a disagreement between different experiments, our results show a clear preference in the comparison. The transition rates calculated in this work suggest that other spectral lines may also be observed in future experiments.

The results of highly accurate calculations are presented for all nine of the known bound P states (L=1) and D states (L=2) of the six three-body muonic molecular ions (mesomolecules): ppμ, pdμ, ptμ, ddμ, dtμ, and ttμ. The mass shift (mass gradient) was determined for each ion for the lowest P and D states and for the first ‘‘vibrationally’’ excited P states. The threshold mass ratios ${\lambda }_{\mathit{t}}$=${\mathit{m}}_{\mathit{Y}}$/${\mathit{m}}_{\mathit{X}}$ for the lowest bound P and D states in symmetric systems such as ${\mathit{X}}^{+}$${\mathit{X}}^{+}$${\mathit{Y}}^{\mathrm{-}}$ were determined, with improved accuracy, to be ${\lambda }_{\mathit{t}}$(P)=0.237 34 and ${\lambda }_{\mathit{t}}$(D)=0.0891.

The simple expression 〈v’‖fΔ${\mathit{U}}^{\mathit{n}}$g‖v’〉 is offered tg are some operators which couple the vibrational levels v’ and v’’ of two interacting electronic states and ΔU=U’-U’’ is the difference of the corresponding internuclear potentials. The rigorous quantum proofs as well as semiclassical justification of this formula are presented and its absolute accuracy is estimated in a closed functional form. Invariant properties and spectroscopic applications of the sum rule, including the evaluation of lifetimes, fine-structure (Λ-doubling) constants, and Landé factors, are discussed.

The recently introduced coupled-cluster effective-Hamiltonian (CC-EH) approximation is used to calculate the ${\mathit{C}}_6$ dispersion constants for selected interatomic potentials. The formal relationship between ${\mathit{C}}_6$ and an integral over the dynamic polarizability evaluated at imaginary frequencies is used in the calculations, and a discussion of its computational implementation within the CC-EH framework is presented. For the long-range interaction between two ground-state beryllium atoms, the calculated dispersion constant is in good agreement with the full-configuration-interaction result. The applicability of the method to both closed- and open-shell systems is demonstrated by calculations of ${\mathit{C}}_6$ for interactions involving the ground states of both ${}_{}{}^1{}_{}{}^{}$S alkaline-earth-metal and ${}_{}{}^2{}_{}{}^{}$S alkali-metal atoms. The results of these calculations are in acceptable agreement with recommended values for most examples. However, significant discrepancies between the present estimates and empirical upper and lower bounds are observed for all systems containing calcium atoms. This observation, as well as previous criticism of calculations that were used in establishing these bounds, suggests that a reexamination of the empirical estimates is warranted.