Asymptotic solutions to the Hamiltonian have been developed for photon numbers and angular momenta that describe an atomic assembly interacting with a single-mode quantized electromagnetic field through dipole coupling. They have been used in the formulation of a multiphoton description of the Autler-Townes effect.

The decay of isolated quantum systems is studied. In particular, a specific model for the radiative decay of an excited atomic state is considered. The atom is taken to have two levels and is described by a current distribution $\overrightarrow{\mathrm{j}}(\overrightarrow{\mathrm{x}};1,2)$. Both the case in which the modes of the electromagnetic field are continuous and the case in which they are discrete are considered. Conditions on $\overrightarrow{\mathrm{j}}(\overrightarrow{\mathrm{x}};1,2)$ are found under which the decay law for the excited state is approximately exponential with a lifetime given by Fermi's golden rule. The current should be well localized, not too strong, and not too singular. The $2p\to 1s$ decay in hydrogen is examined in detail. It is also found that the existence of an approximately exponential decay law does not depend upon the ability to extend the resolvent operator of the system to a second Riemann sheet. The case in which the electromagnetic field is quantized in a cavity illustrates this point.

Conditions are found for the growth of a current in an electron swarm in gaseous media in the presence of intense, monochromatic radiation. For transport to occur by free-free absorption, it is necessary for the medium to have left- or right-handed chirality (as in a sample of chiral molecules), such that the radiative-dipole rate of absorption by the swarm is unequal for electron velocities $\overrightarrow{v}$ and $-\overrightarrow{v}$ relative to the photon direction.

We present solutions for two-photon optical transients from a three-level system which include the effects of (a) direct spontaneous emission to and from the nonresonant intermediate state and (b) phase-interrupting collisions. These effects are, in general, expected to be important for electronic transitions in the visible or ultraviolet region relevant for many two-photon transient experiments on free atoms. The steady-state absorption profile shows power narrowing and desaturation due to spontaneous relaxation. The two-photon delayed optical nutation signal is obtained explicitly. A perturbative calculation of optical nutation shows intensity-dependent damping. We find that for a particular case, namely, when the upper level spontaneous decay rate is twice that of the intermediate level, transient signals have especially simple forms and can be usefully employed for experimental determination of decay constants. The paper is a direct but nontrivial generalization of Schenzle and Brewer's corresponding investigation on one-photon transients.

It is shown that in superfluorescence in the presence of an intense laser which resonates with the lower atomic state involved in the superfluorescence and some other atomic state, quantum beats of a modified Rabi frequency exist. Experiments for observation of these quantum beats are suggested.

Self-induced-transparency phenomena in systems with multiple atomic or molecular species are investigated theoretically. It is shown that under certain conditions relating relative concentrations and transition probabilities that (in the absence of loss processes) complex highly structured solitons can propagate through the system. For some parameters the inversion of some of the species and the field envelope can have very many maxima. Under other (more typical) conditions it is shown that a chaotic infinite train of irregular maxima and minima can propagate.

The stationary convection instability of a superfluid mixture is considered. The criteria for the instability onset in a superfluid region of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ phase diagram and in different limiting cases are obtained. It is shown that in different regions of the phase diagram, depending on the magnitude of the kinetic coefficients, the stationary-instability criterion is similar to that of either the regular binary mixture with abnormal thermal diffusion, to the pure liquid, or to the compressible pure liquid. The stability is also strongly dependent on concentration and temperature, and the critical temperature gradient rises sharply with decreasing temperature and concentration. At very low temperature (below 0.5 K) and concentration (dilute solution) the superfluid solution becomes stable with respect to stationary convection. Asymptotic behavior of the criterion in the vicinity of the $\lambda$ line, the tricritical point and for infinitely dilute solutions is also estimated.

A new type of infinite-order perturbation treatment of the incoherent intermediate scattering function $F_s(\overrightarrow{\mathrm{k}},t)$ yields analytic expressions for the spectrum $S_s(\overrightarrow{\mathrm{k}},\omega )$ and the Van Hove self-correlation function $G_s(\overrightarrow{\mathrm{r}},t)$ valid at intermediate to very large values of the wave number $k$. Predictions of this "intermediate-$k$" theory agree quantitatively with the results of computer simulations of fluid argon for $k$ as small as 6.75 ${\mathrm{\AA }}^{-1\mathrm{}}$ at the triple point and 2 or 3 ${\mathrm{\AA }}^{-1\mathrm{}}$ away from the triple point. The present theory is qualitatively and quantitatively superior to competing large-$k$ theories and predicts a scaling of dynamical variables associated with $S_s(\overrightarrow{\mathrm{k}},\omega )$ that differs from that predicted by generalized Boltzmann-Enskog theory. The deviation of the Boltzmann-Enskog "scaling law" from experiment is fully accounted for in the present theory, with its new "scaling law." Relations between the "intermediate-$k$" model and previous models in various limits are discussed.

A modified $R$-matrix technique is presented which determines the eigenvalues and widths of resonant states by the direct diagonalization of a complex, non-Hermitian matrix. The method utilizes only real basis sets and requires a minimum of complex arithmetic. The method is applied to two problems, a set of coupled square wells and the ${\Pi }_g$ resonance of ${\mathrm{N}}_2$ in the static-exchange approximation. The results of the calculation are in good agreement with other methods and converge very quickly with basis-set size.

The radially dependent quadrupole antishielding factors $\gamma \mathrm{}\left(r\right)\mathrm{}$ and $\beta \mathrm{}\left(r\right)\mathrm{}$ for ${\mathrm{Be}}^{2+}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{Zn}}^{2+}$ are calculated by using the nonorthogonal-Hartree-Fock perturbation theory (NHFPT) of Dalgarno. These results are important in view of the recent theory of Lodge on the electric-field gradient (EFG) in metals, which shows the dependence of EFG on both $\gamma \mathrm{}\left(r\right)\mathrm{}$ and $\beta \mathrm{}\left(r\right)\mathrm{}$. While in the literature, calculations of $\gamma \mathrm{}\left(r\right)\mathrm{}$ are available for some ions (other than ${\mathrm{Be}}^{2+}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{Zn}}^{2+}$), those of $\beta \mathrm{}\left(r\right)\mathrm{}$ are lacking to our knowledge. It is this deficiency which is being made up in the present paper by the calculations of $\beta \mathrm{}\left(r\right)\mathrm{}$ and $\gamma \mathrm{}\left(r\right)\mathrm{}$ for some of the divalent ions.

Collisions of very heavy ions at energies close to the Coulomb barrier are discussed as a unique tool to study the behavior of the electron-positron field in the presence of strong external electromagnetic fields. To calculate the excitation processes induced by the collision dynamics, a semiclassical model is employed and adapted to describe the field-theoretical many-particle system. An expansion in the adiabatic molecular basis is chosen. Energies and matrix elements are calculated using the monopole approximation. In a supercritical ($Z_1+Z_2\gtrsim 173$) quasiatomic system the $1s$ level joins the antiparticle continuum and becomes a resonance, rendering the neutral vacuum state unstable. Several methods of treating the corresponding time-dependent problem are discussed. A projection-operator technique is introduced for a fully dynamical treatment of the resonance. Positron excitation rates in $s_{\frac{1}{2}}$ and $p_{\frac{1}{2}}$ states are obtained by numerical solution of the coupled-channel equations and are compared with results from first- plus second-order perturbation theory. Calculations are performed for subcritical and supercritical collisions of Pb-Pb, Pb-U, U-U, and U-Cf. Strong relativistic deformations of the wave functions and the growing contributions from inner-shell bound states lead to a very steep $Z$ dependence of positron production. The results are compared with available data from experiments done at GSI. Correlations between electrons and positrons are briefly discussed.

A concise interpretation of the perturbation potential in the distorted-wave Born-approximation representation is given for state-to-state rearrangement collisions. We discuss the usefulness of the kernel and radial overlap distributions for understanding reaction mechanisms. For example, the cause of backward scattering in product angular distributions is explained from the study of the kernel distribution. The reaction zone is seen to be well defined by the domain of the kernel distribution with the exclusion of the region interior to the channel radii corresponding to the classical turning points in the initial- and final-arrangement channels. However, the domain of the overlap distribution sharply defines the reaction zone on the channel coordinate plane. Unlike the case of a few nucleon transfer reaction involving a massive target nucleus, wave-number matching alone is not a sufficient condition for yielding the maximum cross sections for the state-to-state rearrangement-collision processes of heterotriatomic systems.

Hydrogen atoms with principal quantum number $n=10\mathrm{}$ have been laser excited to states between $n=44\mathrm{} \mathrm{and} 67$ in the presence of a strong microwave field whose frequency $\omega$ was adjustable between 5.9 and 8.0 GHz. The excitation probability has been studied as a function of $n$, $\omega$, microwave field strength and the number of microwave photons absorbed.

Measurements have been made of the isotope shift $\sigma \left({\mathrm{D}}_2\right)-\sigma \left(\mathrm{HD}\right)$ over the temperature range 18 to 296 K in the density range 10 to 850 amagats (one amagat is density at STP). At 296 K in the zero-density limit our value for the shift is 0.0469±0.0005 ppm, an improvement by nearly two orders of magnitude over the existing uncertainty. The predicted but previously unobserved temperature dependence has been found. A density dependence has also been observed.

Mass-analyzed photoionization spectra have been obtained from beams of atomic iodine and atomic tellurium from their respective ionization thresholds to ∼ 19 eV. In each instance the ionization thresholds are confirmed. For iodine, most of the features in the autoionization resonance spectrum have been identified and assigned to several $s$- and $d$-like Rydberg series converging to the higher-ionization limits ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$, and ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ of the $5s^{2}5p^4$ configuration. For tellurium we also observe autoionization resonance features assigned to $s$- and $d$-like Rydberg series converging to the higher-ionization limits ${}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}$, ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ of the $5s^{2}5p^3$ configuration. In addition, a window-resonance series and additional peaks have been assigned as converging to the $5s5p^4{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}$ state of ${\mathrm{Te}}^{+}$, with quantum defect of ∼0.5 (modulo 1). In both elements, the $d$-like series exhibits anomalous resonance profiles similar to those in the heavier noble gases, with quantum defects of ∼0.4 (modulo 1). The $s$-like series has quantum defects of ∼0.0 (modulo 1). Some comparisons are made with many-body calculations on the related chlorine atom.

The $\Xi a$ method, in which the self-interaction integrals are explicitly calculated, and the remaining portion of the charge density ${\rho }^{\prime }$, is scaled in the same way as in the $X\alpha$ method, has been applied to atoms from Li to Ar. The total $\Xi a$ atomic energy is made equal to the total atomic energy for the Hartree-Fock (HF) limit, to give a set of parameters $a_{\mathrm{HF}}$. The $a_{\mathrm{HF}}$ generally increase as $Z$ increases, in contrast to the behavior of ${\alpha }_{\mathrm{HF}}$ in the $X\alpha$ theory. The plot of $a_{\mathrm{HF}}$ against $Z$ reflects the atomic shell structure. Energy results for several small-$Z$ atoms show that the atomic one-electron energy in the $\Xi a$ method, compared to those from the $X\alpha$ method, are much closer to the HF results. Within the $\Xi a$ scheme, calculated atomic energies using $a_{\mathrm{HF}}$ are compared with those calculated using ${\alpha }_{\mathrm{ta}}$, the average theoretical $\alpha$ value from the $X\alpha$ theory.

The $5d7d{}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ state of barium is configuration mixed with the 6snd Rydberg series. This work examines the larger-$r$ behavior of the Rydberg character of the mixed-state wave function by projecting it experimentally onto a series of known Rydberg states, $6P_{\frac{1}{2}}\mathrm{nd}$, $J=3\mathrm{}$. Results agree with calculations based on the quantum-defect characterization of the wave function. This work also presents an analytical approximation to the radial-wave-function overlap integral between Rydberg states of arbitrary energy.

Frequency-modulation spectroscopy has been employed to monitor the absorption and dispersion changes induced by the optical saturation of nonzero velocity groups of ${\mathrm{I}}_2$ molecules. The use of a high modulation frequency markedly increases the sensitivity of this form of saturation spectroscopy and allows convenient access to molecular velocities well above the thermal average.

Many-body perturbation theory is applied to calculate double-electron photoionization for helium. While lowest-order results show reasonable agreement with experiment, it is found that certain higher-order correlation effects are significant. Techniques are presented for approximating these effects in a calculation which is first order in electron correlations.

A comprehensive set of theoretical $L$-shell Auger and total widths, and Coster-Kronig and fluorescence yields is presented for atomic numbers $18\le Z\le 100$. These quantities are based on ab initio relativistic calculations. Agreement with experimental values is fair for ${\omega }_1$ and generally good for ${\omega }_2$, ${\omega }_3 (Z\ge 54)$, $f_{23} (Z\ge 60)$, $\Gamma \left(L_2\right)$, $\Gamma \left(L_3\right)$, and for $\Gamma \left(L_1\right)$ in the range $49\le Z\le 75$. Discrepancies in $\Gamma \left(L_1\right)$ for $Z<\mathrm{}49\mathrm{}$ point toward the need for a many-body calculation of low-energy $L_1-L_{2,3}{M}_{4,5}$ Coster-Kronig transitions. There is a pronounced need for measurements of ${\omega }_3$ and $f_{23}$ of elements lighter than Xe.