The logarithmic mean excitation energies that determine, for fast charged particles, the total inelastic-scattering cross section, the stopping power, and the straggling are bounded from above and below by simple expressions involving moments of the oscillator-strength distribution. A general condition under which the set of elementary inequalities gives tight bounds is indicated, and is illustrated in several examples. Effective oscillator-strength distributions that are constructed on the basis of variational principles lead to tighter bounds in terms of some of the moments and the oscillator strenths for some discrete excitations.

Rotational cross sections and rate coefficients for $e$-CO and $e$-HCN collisions have been calculated in the energy range relevant to dark interstellar clouds by using the close-coupling method. Gordon's technique has been used for solving the coupled Schrödinger equations. Initial rotational levels $j=0, 1, \mathrm{and} 2$ of CO and HCN have been considered. The rotational cross sections have been calculated in the energy range 0.0006 to 0.1 eV and the rate coefficients in the temperature range 5-100 K. The cross sections and rate coefficients thus obtained have been compared with Born and unitarized time-dependent perturbation calculations.

A quasielastic scattering scaling law for the most probable energy loss has been derived for ion-molecule scattering, and verified for ${\mathrm{Ne}}^{+}$ and ${\mathrm{Ne}}^0$ on ${\mathrm{H}}_2$, ${\mathrm{D}}_2$ in the small-angle, low-keV energy range. This scaling is shown to break down for the more fundamental collision ${\mathrm{D}}^{+}$ + ${\mathrm{H}}_2$. The neon and ${\mathrm{D}}^{+}$ results portray the importance of the valence forces in scattering, and show a breakdown of the concept of a two-center potential for ion-molecule scattering. A single electronically inelastic channel is found for this collision. The inelastic excitation of ${\mathrm{H}}_2$ by ${\mathrm{D}}^{+}$, in the same energy and angular range, is reported to yield a sharp universal reduced cross-section plot, similar to the ${\mathrm{He}}^{+}$ + ${\mathrm{H}}_2$ collision. This supports the existence of a quasimolecule that is formed during close encounters of the collision. No strong direct dissociation of the target ${\mathrm{H}}_2$ molecule is found.

Total cross sections for the reactions ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(2p\right)\mathrm{}$, ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {}_{}{}^4{}_{}{}^{}\mathrm{He}\left(1s2p{}_{}{}^{1,3}{}_{}{}^{}P\right)+{\mathrm{H}}^{+}$ are calculated in an impact-parameter formalism, for collision energies 0.5-30 keV, using a molecular approach. The molecular energies are calculated at large internuclear distances by a configuration-interaction method, and at short distances by a block-diagonalization method. The radial couplings between the molecular wave functions are evaluated exactly, and turn out to depend strongly on the choice of origin of electronic coordinates; as a consequence, the cross sections also depend on this choice. The effect of the anomalous rotational couplings which decrease like $R^{-1\mathrm{}}$ is shown to be negligible, and a method to integrate them is proposed in the Appendix. Choosing the center of mass as origin of electronic coordinates, we obtain good agreement with experimental data, but we find no a priori reason to favor this choice. As an important conclusion, the main effect of the so-called momentum-transfer problem, which is the origin dependence of the cross sections, is due to the form of the molecular wave functions at short internuclear distances.

A new method is proposed for the calculation of the total inelastic-scattering cross-section differential with respect to the solid angle for detection of scattered x rays from atomic or molecular targets within the Born approximation. The Born expression for the cross-section differential with respect to solid angle and energy loss is summed over energy loss for the cases of constant scattering angle and constant momentum transfer. The sums over final states required to derive the proposed formulas are carried out with an error of the order of the - 3.5 power of the maximum observable energy loss for both constant momentum transfer and scattering angle. The leading term in the expansion is the familiar Waller-Hartree result. All quantities involved can be calculated with a knowledge of the target ground-state electronic wave function. Problems encountered in the application of the theory to $\gamma$-ray scattering are discussed.

A total of eleven autoionizing ${}_{}{}^2{}_{}{}^{}P$ resonances has been observed by Ederer et al. in the lithium absorption spectrum below the $2{}_{}{}^3{}_{}{}^{}S{\mathrm{Li}}^{+}$ threshold. In this work, all eleven states have been calculated using a saddle-point technique. The results of this calculation agree with those of experiment. For the highest-eight resonances, the present results are higher by an average of 0.010 eV. The errors of the lowest-three resonances are slightly larger. A perturber which is presented in the observed spectrum is positively identified. The full effect of this perturber is studied with the concept of dynamic coupling. The oscillator strength and the various radial expectation values of these states are also calculated.

To probe the configuration mixing between the Ba $6snd{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}D_2^{}{}_{}{}^{}$ Rydberg series and the $5d7d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ perturber we have observed the radio-frequency transitions between the $5d7d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ state and the $6s28s{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, $6s24f{}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$, and $6s24f{}_{}{}^1{}_{}{}^{}F_3^{}{}_{}{}^{}$ states using a delayed-field-ionization approach. The transitions are observed in the presence of small (∼1 V/cm) electric fields, and from the Stark shifts of the transitions we are able to estimate the ${}_{}{}^1{}_{}{}^{}D$ and ${}_{}{}^3{}_{}{}^{}D$ Rydberg fractions of the $5d7d$ state. Our measured zero-field term separations tie together previous optical measurements of the various Rydberg series involved. In addition, we have measured the lifetimes of the $6snd$ states in the vicinity of the $5d7d$ perturber to estimate the fraction of $5d7d$ character in each of the Rydberg states. The values we find for the configuration mixing are in reasonable agreement with those determined by a multichannel-quantum-defect-theory analysis of the optical spectrum of the even-parity $J=2\mathrm{}$ states of Ba.

Effects due to the interaction of 300 K background radiation with $\mathrm{Xe}\mathrm{}\left(\mathrm{nf}\right)\mathrm{}$ Rydberg atoms are reported. Transitions to nearby $d$ and $g$ levels are observed. When the ambient photon density is reduced to that appropriate to liquid-nitrogen temperature by cooling the apparatus, a corresponding reduction in the transition rates to these levels is observed. The transition rates are found to be consistent with those predicted by use of quantum-defect theory.

Using various projectile ions incident on an ${\mathrm{N}}_2$ gas target, we have determined cross sections for the ${\mathrm{N}}_2^{+}$ 3914-Å emission in coincidence with charge transfer from ${\mathrm{N}}_2$ molecules to the projectiles. Ions of H and the inert gases, each in the energy range 10 to 100 keV, were used. As in charge transfer in which target and projectile are left in the ground state, the velocity at which the maximum cross section occurs increases as the magnitude of the potential energy change increases. Unlike the ground-state case, the value of the cross section at a fixed velocity is significantly greater for an exothermic reaction than for an endothermic reaction having the same magnitude of $\Delta E$.

Separated-beam experiments for both the Doppler-free two-photon and saturated absorptions are under consideration. In the Doppler-free two-photon absorption, the experimental arrangement is important. Such important has not been recognized before. Three different arrangements are discussed here. In the first one, the separated-beam experiment is not coherent and the Ramsey fringe variation cannot be observed. In the second, the transit-time broadening is present and the Ramsey fringe variation depends on the atom's time of flight as well as the transit time. Finally, in the third arrangement, the transit-time broadening is eliminated and the Ramsey fringe variation depends on the atom's time of flight alone. These examples have shown that in the Doppler-free two-photon absorption, the elimination of the transit-time broadening is through a mechanism other than the beam separation. In the saturated absorption the situation is quite different. Even in the presence of transit-time broadening, the Ramsey fringe spacing depends only on the atom's time of flight.

The inefficiency of detectors of low-energy photons permits a loophole in the experimental refutation of local hidden-variables theories by observations of polarization correlations. A specific local hidden-variables model of Clauser and Horne shows that a hypothetical selectivity of detectors can yield the counting rates predicted by quantum mechanics. We therefore derive a new Bell-type inequality, which takes detection inefficiency into account. The loophole can then be blocked by observing spin correlations of atom pairs in an electronic singlet state, if both spin analysis and detection are sufficiently efficient. We propose to create Na atom pairs in the electronic singlet state, by using the induced Raman effect to excite ${\mathrm{Na}}_2$ molecules in the electronic ground state $X{}_{}{}^1{}_{}{}^{}{\Sigma }_g_{}^{+}{}_{}{}^{}$ to the continuum of the electronic ground state. Two laser beams are to be used, one for excitation to a virtual intermediate state in $A{}_{}{}^1{}_{}{}^{}{\Sigma }_u_{}^{+}{}_{}{}^{}$, one to induce the downward transition to the final state. The ensemble needed to test the new inequality consists of those pairs which enter the respective collimating apertures of two Stern-Gerlach analyzers.

Polarization measurements have been made as a function of foil-tilt angle for the He I transitions $2s{}_{}{}^3{}_{}{}^{}S-3p{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}\left(3889\mathrm{} \AA \right)$ and $2p{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}-4d{}_{}{}^3{}_{}{}^{}D\left(4471\mathrm{} \AA \right)$. Particular attention was paid to the systematic effects that can enter into the analysis of such data from the decreasing time resolution as the foil-tilt angle is increased. It is shown that particle scattering at the foil is the main source of systematic error, but that this error can be eliminated by appropriate analytic techniques. The forms of the variation of the relative Stokes parameters with tilt angle are found to be very similar to those previously found for the corresponding singlet transitions, although the magnitudes of the alignment and orientation parameters are generally different for the singlets from the values we find for the triplets. The present results for $3p{}_{}{}^3{}_{}{}^{}P_{}^o{}_{}{}^{}$ are shown to be reasonably consistent with those recently published by Burns et al., provided that the necessary correction for decreasing time resolution at high tilt angles is included.

It is shown that the momentum-translation approximation (MTA) for the treatment of the interaction of bound states with a plane-wave field can be developed in at least five different ways. This multiplicity of approaches is used to exhibit some of the basic features of the approximation, as well as to contrast it with a gauge transformation, with which it is sometimes confused. Validity conditions are $\frac{\mathrm{ea}{a}_0\omega }{E}\ll 1$, $\omega a_0\ll 1$ (where $a$ is the amplitude of the vector potential in the Coulomb gauge for a plane wave of circular frequency $\omega$, $E$ is a characteristic bound-state energy, and $a_0$ is a characteristic size of the bound system), and an absence of intermediate near resonances in a transition. The momentum-translation technique predicts replica states very directly, but level shifts are found only by a method equivalent to perturbation theory. A general formalism is developed for transitions caused by linearly or circularly polarized applied plane-wave fields, in which a second field may or may not be involved. In first order, the MTA always reduces exactly to first-order perturbation theory, but when treated in their entireties, it is shown that a perturbation series and a momentum-translation series are rearrangements of each other. All the criticisms which have been directed at the MTA are reviewed and evaluated. The principal limitations of the MTA are found to be the difficulty of treating problems with intermediate near resonances, and the absence of a systematic way to improve on the basic approximation. The strengths of the MTA are its simple analytical form, its good accuracy when there are no intermediate near resonances, and the fact that high-order multiphoton processes are treated as easily as first-order processes.

The relativistic transition energies and electric-dipole oscillator strengths in length and velocity forms are calculated for ions of the boron sequence. Transitions from the $2s2p^2$, $J=\frac{1}{2}, \frac{3}{2}, \mathrm{and} \frac{5}{2}$ excited states to the $2s^{2}2p$, $J=\frac{1}{2} \mathrm{and} \frac{3}{2}$ levels of the ground state are considered. The magnetic-dipole transition studied relativistically is that between the $J=\frac{1}{2} \mathrm{and} \frac{3}{2}$ levels of the ground state. The trends in the relative importance of relativistic contributions and correlation effects along the isoelectronic sequence for the different transitions are discussed. A more detailed study of the various effects contributing to the excitation energies and oscillator strengths of Fe xxii, and comparison with other available results for this ion is carried out.

A new and unusual phenomenon which we call light narrowing is reported and discussed in this paper. We discovered this effect in dense, spin-polarized cesium vapor optically pumped with a cw blue dye laser beam tuned to the second resonance $D_1$ line (4593 Å). We observe a significant narrowing of the radio-frequency power-broadened magnetic resonance lines (linewidths narrow by as much as a factor of 2.5) when the intensity of the circularly polarized incident dye laser beam is increased by either focusing the beam or by the removal of attenuating filters from the focused beam. The magnetic resonance linewidths in spin-polarized cesium vapor were measured over a wide range of cesium number densities (5×${10}^{12}$ ${\mathrm{cm}}^{-3\mathrm{}}$ ≤[Cs]≤1×${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$). This corresponds to cesium spinexchange rates of 4.5×${10}^3$ to 9×${10}^6$ ${\sec }^{-1\mathrm{}}$. For low cesium number densities (5×${10}^{12}$ <[Cs]<3×${10}^{14}$ ${\mathrm{cm}}^{-3\mathrm{}}$) the light-narrowing effect is large (a factor of 2.5) and independent of [Cs]. In the region of 3×${10}^{14}$ to 1×${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$ in number densities, the light-narrowing effect decreases with increasing [Cs]. At high cesium number densities ([Cs]> 1×${10}^{15}$ ${\mathrm{cm}}^{-3\mathrm{}}$) this light-narrowing effect almost completely disappears. In the limit of low-radio-frequency power the magnetic resonance linewidths for focused and unfocused dye laser beam are nearly the same. Experimental observations on this new effect are presented in detail. In the latter part of this paper a self-contained theoretical treatment of the light-narrowing effect is developed. Using Bloch equations in the presence of optical pumping, spin relaxation (diffusion, electron randomization), rapid spin exchange, and radio-frequency magnetic field, expressions for magnetic resonance line shapes are derived. In general, we find good agreement between our experimental results and the theory.

Pulsed dye lasers are used to excite sodium atoms into a coherent superposition of high Rydberg $\mathrm{nd} ({}_{}{}^2{}_{}{}^{}\mathrm{D}_{\frac{3}{2}}^{}{}_{}{}^{},{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{})$ states. Analysis of the field ionization behavior of these atoms reveals the time evolution of the superposition state. Rapid application of a weak electric field projects different components of the superposition state onto states having identifiably different field ionization behavior. Analysis of the signal from subsequent field ionization as a function of the time of weak-field application reveals fine-structure quantum beats. These beats result from the time development of the original superposition state. Measurements of the fine-structure quantum beat frequency are presented for the principal quantum numbers $n=32, 34, 35, 36, 38, \mathrm{and} 40$.

In this paper we develop the interrelationships between the steady-state and transient behavior for cw-pumped Kerr-like conjugators in which the optical Kerr effect is considered to respond instantaneously. We use Laplace-transform techniques to develop an expression for the conjugate response to input pulses of arbitrary form. For stable conjugator operation (in which the cw conjugate reflectivity is finite for all input frequencies), the expression reduces to an antilinear Fourier-transform relationship, which is readily adaptable to computer simulation. The cw filter function of Pepper and Abrams [Opt. Lett. 3, 312 (1978)] is found to play a central role. We show, both numerically and analytically, that our calculated delta-function response agrees with that previously published. We numerically demonstrate temporal spreading and reshaping when the conjugator transit time becomes equal to or longer than the duration of the input pulse, and we show numerically the perfect chirp reversal for sufficiently thin conjugators and the deviations from perfect chirp reversal upon increasing the thickness of the conjugator. These numerical results can be understood in terms of the bandwidth of the associated cw filter function.

We discuss the construction of population equations for driven quantum systems in contact with dissipation mechanisms in the limit where the strength of the driving force is sufficiently weak that a suitable Born expansion can be carried out in powers of the coupling constant of the coherent interaction. The Zwanzig projector technique and the application of an appropriate eigenfunction-expansion method due to Weidlich lead to an elegant derivation of population equations. If the decay rates of the irreversible processes allow the application of the Markoff approximation, ordinary first-order differential equations for the level populations can be derived. The transition rates are constructed explicitly in terms of the coherent Liouville operator and the Weidlich eigenfunctions.

The dynamics of collisionless infrared multiphoton absorption in S${\mathrm{F}}_6$ was studied using picosecond C${\mathrm{O}}_2$ laser pulses. It was found that at this new regime of light-matter interaction at very high laser intensities, the absorption in the quasicontinuum has a considerable intensity dependence. The deviation from an energy fluence scaling law was found to begin at about 200 MW/${\mathrm{cm}}^2$. Above this intensity, the multiphoton interaction between the laser and the molecule should be described by the full coherent Schrödinger equation rather than by the usual master rate equations. A novel method of preheating the S${\mathrm{F}}_6$ molecules is also described and the saturation behavior of these preheated molecules is measured with the picosecond pulses.

We present a study of the dynamics of traversing an avoided energy level crossing. A pair of Stark levels of Rydberg states of lithium are used as a test system for measuring the diabatic transition probability. The experimental conditions are close to those assumed by the Landau-Zener theory. Possible corrections to the Landau-Zener theory are analyzed, and applications of the results to pulsed-field ionization are discussed.