We present a simple Fermi-gas model for the low-temperature Kapitza resistance (KR) of a nonmagnetic liquid-${\mathrm{He}}^3$—solid interface in which the vibrational quanta of the solid surface atoms are carried away by single fermion states. A one-dimensional calculation of the energy-exchange process is made assuming that a fermion interacts with a single solid atom through a Morse potential. For temperatures $T$ small compared to the Fermi temperature $T_F$, the KR $R$, is found to be of the form $R{T}^3=\frac{a_0}{\left\{1+\left[46{\left(\frac{k_f}{a}\right)}^2-1.8\mathrm{}\right]{\left(\frac{T}{T_F}\right)}^2\right\}}$ where $k_F$ denotes the Fermi wave vector and $a$ the inverse range parameter of the Morse potential. The constant of proportionality $a_0$ is generally independent of the nature of the fermion—solid-atom interaction potential and depends on the properties of the Fermi gas only through its dependence on the fourth power of $k_F$. As a function of increasing $T$, $R{T}^3$ decreases rapidly on account of the largeness of the ${\left(\frac{T}{T_F}\right)}^2$ correction. The theoretical results can therefore account for the pressure and temperature dependences of the KR of the liquid-${\mathrm{He}}^3$—cooper interface observed by Anderson et al. The success of the model tentatively suggests that in the phenomenon of the liquid-${\mathrm{He}}^3$ KR, the vibrational quanta of the surface atoms are carried away by individual quasiparticle states rather than by the zero-sound modes considered in the acoustic mismatch theory of Bekarevich and Khalatnikov.

A quantum statistical analysis of phase-locked coupled light beams is presented with the coupling mechanism between the individual modes provided by the time-modulated dielectric constant of the crystal inserted in the cavity. The intense electric field that drives the modulator is treated classically. A Hamiltonian including the modulator interaction is formulated and the Heisenberg equations of motion of the mode operators are solved utilizing a generating function of the mode operators. The evolution in time of the phase-space distribution functions for single and multiple modes is derived under various initial conditions. Initially coherent oscillating modes are shown to conserve their coherent character. Below threshold, the modes are assumed to be chaotic Gaussian. It is shown that when all modes have the same average number of photons, they remain uncorrelated Gaussian. When the average photon numbers are nonidentical, the field remains a pure noise field, but the various modes are correlated. The analysis of the resonant-case mode of operation, properly interpreted, leads directly to the case of nonresonant modulation.

The magnetic resonance of the NO molecule is observed using the 78-, 79-, and 119-μm lines of the ${\mathrm{H}}_2$O laser as the radiation source. The resonances in three cases are due to the $({}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}J=12.5)\to ({}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}J=12.5)$, $({}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}J=11.5)\to ({}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}J=11.5)$, and $({}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}J=12.5)\to ({}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}J=11.5)$ transitions, respectively. Most of them are magnetic dipole transitions, but a few electric dipole transitions are also observed. It is found that the calculated $g$ factors $g_{c2\mathrm{}}=\left(11.5\right)=g_{d2\mathrm{}}\mathrm{}\left(11.5\right)=-0.0064\mathrm{}$, $g_{c1\mathrm{}}\mathrm{}\left(11.5\right)=g_{d1\mathrm{}}\mathrm{}\left(11.5\right)=0.0272\mathrm{}$, $g_{c2\mathrm{}}\mathrm{}\left(12.5\right)=g_{d2\mathrm{}}\mathrm{}\left(12.5\right)=-0.0092\mathrm{}$, $g_{c1\mathrm{}}\mathrm{}\left(12.5\right)=g_{d1\mathrm{}}\mathrm{}\left(12.5\right)=0.0270\mathrm{}$, and the calculated $\Lambda$-doublet separations $f_{c2\mathrm{}}\mathrm{}\left(11.5\right)-f_{d2\mathrm{}}\mathrm{}\left(12.5\right)=243\mathrm{}$ MHz, $f_{c1\mathrm{}}\mathrm{}\left(11.5\right)-f_{d1\mathrm{}}\mathrm{}\left(11.5\right)=4323\mathrm{}$ MHz, are consistent with our experimental results. The hyperfine structure and the second-order effects are also in agreement with theoretical values. The average separation between the ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{3}{2}}^{}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi _{\frac{1}{2}}^{}{}_{}{}^{}$ states for a given $J$, which we call $X_J$, is found to be 126.4469±0.0005 and 127.5786±0.0005 ${\mathrm{cm}}^{-1\mathrm{}}$ for $J=11.5\mathrm{} \mathrm{and} 12.5$, respectively. The conventional spin-orbit coupling constant is found to be 123.1580±0.0010 ${\mathrm{cm}}^{-1\mathrm{}}$ when $J=12.5\mathrm{} or 11.5$. [The conventional spin-orbit coupling constant $A_c$, commonly referred to as $A$, is given by $A-\delta {(J+\frac{1}{2})}^2+\frac{1}{4}\gamma$ in our notation.] The coupling constant ${\mu }_S$ for the $\overrightarrow{\mathrm{S}}·\overrightarrow{\mathrm{N}}$ term is found to be -0.006±0.002 ${\mathrm{cm}}^{-1\mathrm{}}$.

In a recent ${\mathrm{Ar}}^{+}$-Ar collision study by Thomson et al., the lack of correlation between the energy of the emitted Auger electron and the number of coincident slow electrons was interpreted as evidence that the lifetime of the $L_{23}$ inner-shell vacancy resulting from such collisions was not significantly longer than the lifetime of the $M$-shell autoionizing states. In this paper, Auger-electron energy and $L_{23}-MM$ nonradiative lifetime calculations for the argon atom and its ions are used to demonstrate that this conclusion is not justified on the basis of the coincidence results reported.

Comments by F. P. Larkins about our fast-electron-slow-electron coincidence study of the ${\mathrm{Ar}}^{+-}$ Ar collision appear to raise a question on the validity of our evidence that some outer-shell autoionizing states may have lifetimes comparable with those of inner-shell vacancies. In this reply, his argument is examined, and it is found that the inclusion of $L_{2,3}-M_1{M}_{2,3}$ and $L_{2,3}-M_1{M}_1$ transitions, as Larkin suggests, complicates the analysis, but does not alter the basic conclusion we originally reached.

We have reanalyzed some results on rare-gas diamagnetic susceptibilities using different theoretical models to calculate a correction used in analyzing the experimental data. We find the final experimental susceptibility to be very model dependent. We conclude that the original scattering data does not allow for a well-defined experimental determination of diamagnetic susceptibility.

The possibility of cooling solid ${\mathrm{He}}^3$ by adiabatic magnetization is discussed using the antiferromagnetic nearest-neighbor spin-½ Heisenberg linear chain as a reference system. The lack of a phase transition is not important in this discussion since the locus of maximum cooling generally lies outside (i.e., is unrelated to) the $T-H$ phase boundary, contrary to previous predictions using mean-field and spin-wave theories. Exact calculations on linear chains demonstrate a potentially useful degree of equilibrium cooling. The results are in qualitative agreement with earlier spin-wave arguments, although the details of the energy spectrum are more complicated than is assumed in spin-wave theory.

Earlier experiments on the He II-He I transition in a heat current have been repeated in several different flow geometries in an attempt to discover the reason for discrepancies among results of various observers. Detailed analysis of the data has allowed us to suggest a mechanism which may account for the apparent inconsistencies.

A recent model for electron transport in disordered systems is used to examine the behavior of electron mobility near the critical point in neon. It is found that the electron may prove a useful probe of critical behavior in this case.

Local laser-beam intensity fluctuations were observed and related to the scattering in the data of multiphoton ionization of atoms and molecules.

$\frac{K\beta }{K\alpha }$ x-ray transition-probability ratios for 16 elements in the range $18\le Z\le 39$ were measured with a high-resolution Si(Li) detector. The $K$ vacancies were produced by a heavily filtered bremsstrahlung beam from a commercial x-ray tube. Our results agree qualitatively with the theoretical calculations of Scofield but are consistently about 15% higher.

Measured values of the relative intensities of several $L$ fluorescent x rays are reported for 13 elements ranging from cerium through plutonium. A solid-state Si(Li) spectrometer and a Bragg-diffraction spectrometer were used to analyze the x-ray excited fluorescence from thin samples. Corrections were made to the measured relative intensities for sample absorption, air absorption, and spectrometer efficiency. The accuracy of the measurements varies from ±5 to ±15%. The results are compared with those from the Scofield calculations.

We have investigated collisions which result in the formation and destruction of the $\left(1s{\sigma }^2\right)X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ ground state and the $\left(1s\sigma 2p\pi \right)c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ long-lived electronically excited state of molecular hydrogen. The molecules were formed by electron capture by 1- to 42-keV/nucleon ${\mathrm{H}}_2^{+}$ or ${\mathrm{D}}_2^{+}$ ions in Mg vapor. The resulting yields of ${\mathrm{H}}_2\left({}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)$, ${\mathrm{H}}_2\left({}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}\right)$, H, and ${\mathrm{H}}^{+}$ are reported as a function of Mg-target thickness. Also reported are cross sections for total loss and ionization of the ${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ states of ${\mathrm{H}}_2$ in collisions with ${\mathrm{H}}_2$ gas.

The Onsager symmetry relations, used in conjunction with appropriate linear transformations of the hydrodynamic variables, allow one to analyze the distribution of the eigenvalues of the hydrodynamic matrix and to establish symmetry characteristics of its diagonalizing matrices. The implications of these results for the analysis of the spectral distribution of the polarized component of scattered light are pointed out.

The minimax theorem for the eigenvalues of Hermitian operators is reviewed and its inverse (maxmini) theorem is derived. The connection between the Hylleraas-Undheim theorem (HUT) and the minimax theorem is clarified, and an extension of the HUT to compound resonance states is obtained. Thus, rigorous upper bounds on the resonance energies may be obtained without the explicit use of the exact open-channel projection operators. The exchange and rearrangement problems are also considered.

Ab initio calculations have been performed for states of C${\mathrm{H}}^{+}$ which arise from atomic ${\mathrm{C}}^{+}\left({}_{}{}^2{}_{}{}^{}P\right)$ and $\mathrm{H}\left({}_{}{}^2{}_{}{}^{}S\right)-X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, $A{}_{}{}^1{}_{}{}^{}\Pi$, ${}_{}{}^3{}_{}{}^{}\Pi$, and ${}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$. Potential curves have been constructed over a wide range of internuclear distances. All computed energies are believed to be within 1 eV of their exact nonrelativistic Born-Oppenheimer value, and all energy differences are believed to have an accuracy of better than 0.3 eV. Results, with known experimental values in parentheses, are $R_e\left(X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\right)=2.136\mathrm{}$ (2.137) a.u.; $D_e^0\left(X{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}\right)=4.11\mathrm{}$ (4.21) eV; $R_e\left(A{}_{}{}^1{}_{}{}^{}\Pi \right)=2.232\mathrm{}$ (2.333) a.u.; $T_e\mathrm{}(X-A)=249\mathrm{}70$ (24146) ${\mathrm{cm}}^{-1\mathrm{}}$; $R_e\left({}_{}{}^3{}_{}{}^{}\Pi \right)=2.130\mathrm{}$ a.u. No evidence is found for a quasibound ${}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ Rydberg state, although such behavior has been predicted for isoelectronic BH.

Accurate numerical Hartree-Fock (HF) self-consistent-field (SCF) wave functions have been obtained for ${\mathrm{Ce}}^{3+}\left(4\mathrm{}{f}^1\right){}_{}{}^2{}_{}{}^{}F$, ${\mathrm{La}}^{2+}\left(4\mathrm{}{f}^1\right){}_{}{}^2{}_{}{}^{}F$, ${\mathrm{Yb}}^{3+}\left(4\mathrm{}{f}^{13}\right){}_{}{}^2{}_{}{}^{}F$, ${\mathrm{Tm}}^{2+}\left(4\mathrm{}{f}^{13}\right){}_{}{}^2{}_{}{}^{}F$, and ${\mathrm{Yb}}^{2+}\left(4\mathrm{}{f}^{14}\right){}_{}{}^1{}_{}{}^{}S$ rare-earth ions. In each case, the virial theorem is satisfied to at least six digits and the $P_{\mathrm{nl}}$ radial functions are self-consistent and without "tail-oscillations" to three decimal places. Several HF parameters are also evaluated with these wave functions.

Principal-series oscillator strengths and ground-state photoionization cross sections are computed for sodium, potassium, rubidium, and cesium. The degree of polarization of the photoelectrons is also predicted for each atom. The core-polarization correction to the dipole transition moment is included in all of the calculations, and the spin-orbit perturbation of valence-$p$-electron orbitals is included in the calculations of the Rb and Cs oscillator strengths and of all the photoionization cross sections. The results are compared with recent measurements.