A theory of the influence of binary collisions on the line shapes associated with Doppler-free spectroscopy is presented. The specific calculation is for two-photon absorption through a real or virtual intermediate state, but the extension of the results to alternative level schemes is included. Collisions are treated quite generally at first, but, ultimately, a simple but reasonable collision model is adopted to properly account for both the "phase-interrupting" and "velocity-changing" aspects of collisions. It is shown that collisional processes can be used to distinguish between the "two-quantum" and "stepwise" contributions to the two-photon excitation rate. Moreover, it is demonstrated that systematic experimental line-shape investigations, in addition to providing tests of current collision theories, can lead to values for collision broadening and shift parameters, excitation transfer rates, magnetic substate relaxation rates, velocity-changing collision rates, and collision kernels. Consequently, Doppler-free spectroscopy can provide a new and important probe of collision effects in atomic and molecular systems.

Adjacent vibrational modes of different isotope species are coherently excited by an intense ultrashort light pulse. The free decay of the vibrational system is observed by coherent probe scattering of a second delayed interrogating pulse. Coherent superposition of the excited vibrational states gives rise to a beating effect of the collectively vibrating isotope components. The phenomenon is observed for the first time in several tetrahalides on a time scale of several ${10}^{-12\mathrm{}}$ sec. The experimental information obtained by the probing technique depends on the wave-vector geometry of the material excitation and the interrogating pulse: One individual vibrational component is studied under a selective $\overrightarrow{\mathrm{k}}$ condition while coherent superposition of the vibrational components is observed for nonselective $\overrightarrow{\mathrm{k}}$ matching. Our technique provides new information on the vibrational system which is not obtained by other experimental methods.

The concept of a two-photon coherent state is introduced for applications in quantum optics. It is a simple generalization of the well-known minimum-uncertainty wave packets. The detailed properties of two-photon coherent states are developed and distinguished from ordinary coherent states. These two-photon coherent states are mathematically generated from coherent states through unitary operators associated with quadratic Hamiltonians. Physically they are the radiation states of ideal two-photon lasers operating far above threshold, according to the self-consistent-field approximation. The mean-square quantum noise behavior of these states, which is basically the same as those of minimum-uncertainty states, leads to applications not obtainable from coherent states or one-photon lasers. The essential behavior of two-photon coherent states is unchanged by small losses in the system. The counting rates or distributions these states generate in photocount experiments also reveal their difference from coherent states.

The nodal expansion of the potential of average force is worked out systematically by iterating all the nonconvolution compact graphs from the order at which they appear first to infinity. For this purpose, we perform an exhaustive study of the asymptotic behavior of the bridge (without articulation points) graphs, and show that they decrease as $\frac{\beta e^{-\alpha r}}{r}$, with $\alpha >1\mathrm{}$ and $r$ in units of the Debye length ${\lambda }_D$. We demonstrate that the asymptotic $w_2\mathrm{}\left(r\right)\mathrm{}$ expansion is obtained from the resummation of the longest convolution chains [$l\ge 2(n-1\mathrm{})\mathrm{}$] with $n-1\mathrm{}$ two-bubbles and $0\le c\le n$ Debye lines, which allow for a systematic improvement of the usual hypernetted-chain (HNC) approximation with the replacement of one, two, or more two-bubbles by bridge graphs. Substantial simplification of the final expression is achieved with the aid of the $n$-bubble sum which decreases asymptotically faster than the Debye line. The onset of short-range order is shown to arise at the critical value ${\Lambda }_c=4.247\mathrm{}$ of the plasma parameter $\Lambda =\frac{e^2}{k_B}T{\lambda }_D$ in excellent agreement with the Del Rio-DeWitt calculations.

A nonlinear interaction term is added to the Schrödinger equation which makes it exactly equivalent to classical mechanics. In the hydrodynamic formulation of this equation, the usual classical theory is obtained. This theory is a Lagrangian density formulation of hydrodynamics and is used to calculate the density profile of superfluid helium in a line vortex. The theory can be canonically quantized, in the sense of quantum field theory, in terms of the density and velocity fields. The quantized theory is not equivalent to that which one would obtain if the quantization were done in the usual way in terms of the field operations ${\psi }^{*}$ and ($\psi$). The Schrödinger equation, with this interaction, has localized solutions with a definite energy and momentum and does not give quantized energy levels for a one-dimensional harmonic oscillator.

A covariant formulation of classical electrodynamics is given for nonviscous, compressible, nondispersive, polarizable, and magnetizable fluids. The part of the Lagrangian density accounting for the various interactions to be existent in such fluids under the influence of the electromagnetic fields is constructed rather intuitively by introducing two four-vector variables, one to describe the states of polarization and the other to describe those of magnetization. The energy-momentum conservation law can be derived separately for the material and the field subsystems. The energy-momentum tensor of the total system cannot be split in a unique way into the material and the field parts. However, physically reasonable ways of splitting can be found so as to give one and the same result as to the electromagnetic radiation pressure in electromagnetic fluids. This pressure is shown to be $\frac{(\overrightarrow{\mathrm{D}}\times \overrightarrow{E})}{4\pi {\left(\mu \nu \right)}^{\frac{1}{2}}}$, in agreement with experiment. This indicates that the pressure observed in experiment consists almost entirely of the "true" electromagnetic radiation pressure. For the sake of consistency, the mechanical pressure arising both from the electro- and magnetostrictive forces and the forced motions of the fluid particles under the influence of the electromagnetic radiation fields is also estimated and found, in fact, to be negligible in ordinary experimental conditions.

Liquid ${\mathrm{Rb}}^{+}$${\mathrm{Br}}^{-}$ has been investigated by molecular dynamics for comparison with neutron inelastic scattering results. The properties of ${\mathrm{Rb}}^{+}$ and ${\mathrm{Br}}^{-}$ on the one hand and those of the nuclei of Rb and Br on the other offer rather special features for such a parallel investigation. The results reported here use the Born-Mayer type of interaction between nonpolarizable ions. Based on a molecular dynamics study of a rather small, 122-ion system, our conclusion is that such a force model is probably inadequate for a satisfactory explanation of the neutron scattering data; we also conclude that allowing for ion polarization will impove the situation. Thus detailed studies of the equation of state have to be complemented with dynamical studies of molten salts before one can draw conclusions about the dependability of the Hamiltonian used for the system. Our results for $g_{++}$ and $g_{--}$ show a shoulder to the right of the first maximum. This feature has also been observed in neutron experiments on NaCl and in Monte Carlo calculations on "hard sphere" molten salts. As has already been reported, the calculated and observed static structure factors are in fair agreement. However, a detailed comparison shows more marked features in the calculated results than have been found experimentally. From the density fluctuations a velocity of sound has been deduced which is considerably larger than the only available experimental value. A comparison of the frequency characteristics of the density fluctuations at various wavelengths with neutron scattering data shows that at certain wavelengths there are large discrepancies which are, at least in part, related to the inadequacy of the rigid-ion model Hamiltonian used for these calculations.

Recently, small particles have been shown to exhibit a melting temperature which depends on the particle size. The various possible experimental methods have been compared and measurements of the melting points of small gold particles have been made using a scanning electron-diffraction technique. This method was applied to particles having diameters down to 20 Å. Consideration of the size distribution over an entire sample makes it necessary to carry out a careful analysis of the experimental results in order to deduce the melting temperature of particles having a well-defined diameter. The experimental results are quantitatively in good agreement with two phenomenological models. The first model describes the equilibrium condition for a system formed by a solid particle, a liquid particle having the same mass, and their saturating vapor phase. The second model assumes the preexistence of a liquid layer surrounding the solid particle and describes the equilibrium of such a system in the presence of the vapor phase. In order to permit a better comparison between both models, a new expression for the thermodynamic equilibrium condition has been derived in the present work. In the case of the first model, the agreement was obtained using only the physical constants of massive gold. In applying the second model, however, one is compelled to assume the existence of a liquid layer having a thickness of about 6 Å.

The generating functional for many-time correlation functions for a dilute gas is shown to satisfy the nonlinear Boltzmann equation for space and time scales large compared to corresponding molecular dimensions. The result is used to investigate the behavior of triplet space and time correlation functions. Corrections to the Markovian approximation are found, due to coupling of solutions to the linearized kinetic equation by the nonlinear Boltzmann operator.

We have measured the hyperfine structure of the $5{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${}_{}{}^{23}{}_{}{}^{}\mathrm{Na}$ by radiofrequency spectroscopy. We find the magnetic dipole coupling constant to be $A=77.6\mathrm{}\pm 0.2$ MHz.

The polarization-model calculation of the hydrogenic HeI excited states $l\ge 2$ is reexamined. Compact expressions for the $〈nl\left|R^{-m}\right|nl〉$ matrix elements allow the elimination of spurious irregularities. The agreement with recent sophisticated calculations is greatly improved.

Two-photon absorption can produce a coherent oscillating atomic polarizability in a macroscopic vapor. If this vapor contains an ensemble of atoms having different transition frequencies, the beat frequencies between the polarizabilities of the two species can be detected in the time domain. Energy-level splittings can be determined which are too small to resolve in the frequency domain and are not accessible to quantum beats.

Recent experimental and theoretical works on the infrared absorption at the far wings are reviewed, and it is shown that the high-frequency or short-time property of the dipole-dipole autocorrelation cannot be adequately obtained by the statistical many-body model, as claimed by Sorgen and Ben-Aryeh.

Calculations of positions of the first three ${}_{}{}^2{}_{}{}^{}S$, ${}_{}{}^2{}_{}{}^{}P$ autoionization states of lithium are reported. The results agree with experimental values (available in four of the six cases) to almost four-place accuracy. A comment is included concerning the current status of quasiprojection optical-potential scattering calculations for non-resonant $e-\mathrm{He}$ phase shifts.

Using the linked-cluster many-body perturbation procedure we have evaluated the magnetic hyperfine constant $A$ in the spin-Hamiltonian term $A\overrightarrow{\mathrm{I}}·\overrightarrow{\mathrm{J}}$ of manganese atom. The nonrelativistic value of $A$ is found to be -90.8 ± 3.0 MHz, composed of -152.6 MHz from the exchange core polarization (ECP) effect and 61.8 MHz from a combination of consistency and correlation effects. We have also made a relativistic calculation of the ECP effect and used this to make estimates of the relativistic effects on (1, 1) and (0, 2) diagrams. On combining these relativistic results with those from nonrelativistic theory and including the calculated Casimir contribution of -4.3 MHz discussed by Sandars and Beck, our net theoretical value for the hyperfine constant $A$ turns out to be -74.1 ± 3.0 MHz, which is in the good agreement with the experimental results of -72.422 ± 0.002 MHz. Physical explanations are discussed for the trends of the contributions from various effects and their variations from shell to shell.

We derive variational equations for optimization of the orbitals of arbitrary multiconfiguration wave functions. Expressing the transformation matrix connecting the set of orthonormal trial vectors and the set of final optimal orbitals as an exponential matrix of independent rotation angles allows a simple derivation of the coupled variational equations to arbitrary order. We include the explicit results through third order which are sufficient for cubic convergence in the iterative solution of the optimum orbitals. The equations were programmed (including all terms), and applications to Hartree-Fock and generalized valence bond wave functions of the carbon atom, ${\mathrm{FeO}}_2$, and ${\mathrm{NiCH}}_2$ are reported.

The $g$ factor of the ${}_{}{}^2{}_{}{}^{}\Sigma$ Van der Waals molecule KAr has been measured relative to the $g$ factor of free potassium using molecular-beam magnetic-resonance techniques. A theoretical treatment of the $g$ factor of the molecule is presented that predicts the $g$ factor to be shifted from the value for the free potassium atom by an amount proportional to the ratio $\frac{\gamma }{B}$, where $\gamma$ and $B$ are the spin-rotational and rotational constants of the molecule, respectively. The experimental results show the molecular $g$ factor to be less than the value for free potassium by approximately 25 ppm, in agreement with the prediction.