By heterodyning together the outputs from two stable He-Ne $3.39-\mu$ lasers, we have measured the power spectrum of the laser field over a wide range of output powers. By combining this high-gain laser transition with a very lossy laser cavity, the quantum phase noise contribution to the laser linewidth could be made dominant at low output powers. The laser spectrum was then found to be nearly Lorentzian with a bandwidth inversely proportional to output power, in good agreement with a modified form of the Schawlow-Townes laser linewidth formula. Weak quantum-noise-excited sidebands were also observed in the beat spectrum of a He-Xe $3.508-\mu$ laser. These were identified with a resonance in the He-Xe laser amplitude-fluctuation spectrum.

By the superposition of Bethe's wave functions, using the Lieb's solution for the system of identical bosons interacting in one dimension via a $\delta$-function potential, we construct the wave function of the corresponding system enclosed in a box by imposing the boundary condition that the wave function must vanish at the two ends of an interval. Coupled equations for the energy levels are derived, and approximately solved in the thermodynamic limit in order to calculate the boundary energy of this Bose gas in its ground state. The method of superposition is also applied to the analogous problem of the Heisenberg-Ising chain (not the ring).

A detailed proof is given for the validity of substituting a $c$ number for the zero-momentum-state operators in the quantum-field-theory approach to the many-boson problem at a finite temperature. We use a modification of the method of Kromminga and Bolsterli, and add slightly to their work for the ground-state case. The case in which the bosons which condense are themselves composite particles, as in superconductivity, is treated in this method by the artifice of coupling to a fictitious elementary boson and then letting the coupling become infinitely weak; the self-consistent formulation of Schrieffer for superconductivity can be obtained in this way.

Charge-exchange collisions of ${\mathrm{H}}^{-}$ ions in a Cs vapor target have been studied for incident ${\mathrm{H}}^{-}$-ion energies of 2-30 keV. The cross sections ${\sigma }_{-0\mathrm{}}$ and ${\sigma }_{-+}$ have been obtained. The cross section ${\sigma }_{-0\mathrm{}}$ has the value (2.1 ± 0.3) × ${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at 5 keV and decreases slowly as the energy increases. The cross section ${\sigma }_{-+}$ has the value (2.4 ± 0.3) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 5 keV and increases rapidly as the energy increases.

The Breit interaction is reviewed with applications to heavy atoms in mind. Generalizations of the Breit interaction which avoid expansion in powers of the electron velocities are discussed. Two-particle matrix elements of the Breit interaction and its generalizations are given in a form convenient for numerical applications. Expressions are derived for evaluating configuration-averaged atomic energy shifts for the Breit interaction and its generalizations. Numerical results for the energy shifts of atomic ground states are presented for selected atoms in the range $Z=2\mathrm{}$ to $Z=102\mathrm{}$; interpolated values of the energy shifts are given graphically for all atoms in the range considered. A breakdown of the interelectron contributions to the Breit energy shift is given for Ne and for $K$ electrons in Hg. "Frozenorbital" calculations of Breit corrections to electron binding energies in Hg are given. The binding of $K$ electrons in W, Hg, Pb, and Rn including the generalized Breit interaction with rearrangement are determined; when considered together with Lamb shift and correlation effects, these calculations reduce the discrepancy between theoretical and experimental $K$ binding energies to about 0.1 Ry.

Exchange and polarization effects are included in an $e-{\mathrm{D}}_2$ interaction potential. Cross sections for rotational excitation by electron impact for energies less than 1.0 eV are calculated for 0 → 2, 1 → 3, and 2 → 4 transitions in ${\mathrm{D}}_2$. For energies less than 0.5 eV, theoretical results are found to be in agreement to within 8% with results deduced from swarm experiments by Gibson.

An experimental study of the additivity of the phase shift or perturbation energies produced by foreign-gas perturbers in collision with an optical atom is made by measuring the shift and the half-width of the second to the seventh doublet of the Cs absorption series, under various pressures and with various concentration ratios of a mixture of He and Ar. The shift produced by the mixture is found to be about the average of the shifts of the separate gases. The broadening of the fourth absorption doublet of Cs produced by the mixture of He and Ar is about $\frac{3}{4}$ of the sum of broadenings due to the constituents.

The electrical conductivity of Rb-N${\mathrm{H}}_3$ solutions has been measured over the concentration range 2-27 MPM (mole percent metal) at temperatures between 190 and 240 K. The conductivity is lower than for any other alkali-metal solution. Evidence for phase separation below 205 K is given.

It is possible for an isotropic object to have an interaction energy of form $-{\alpha }_E{E}^2-{\alpha }_M{H}^2-2\mathrm{}{\alpha }_X\mathrm{E}·\mathrm{H}$ in a weak constant electromagnetic field, with a nonvanishing crossed polarizability ${\alpha }_X$. The Feinberg-Sucher formula for the van der Waals potential between two such bodies, $A$ and $B$, accordingly generalizes uniquely to $r^{-7\mathrm{}}{\left(4\mathrm{}\pi \right)}^{-1\mathrm{}}[-23({\alpha }_E^A{\alpha }_E^B+{\alpha }_M^A{\alpha }_M^B)+7({\alpha }_E^A{\alpha }_M^B+{\alpha }_M^A{\alpha }_M^B{\alpha }_E^B)-60\mathrm{}{\alpha }_X^A{\alpha }_X^B]$ as a consequence solely of invariance under duality rotations.

It is pointed out that the unitary ${\Gamma }_8$ matrices for the octahedral double group obtained from the representation $U^{\frac{3}{2}}$ satisfy a symmetry property which is responsible for certain relations between Wigner coupling coefficients. In addition, it is noted that, out of the infinite number of ways to construct bases for the two ${\Gamma }_8$ representations contained in ${\Gamma }_8\times {\Gamma }_4$ or ${\Gamma }_8\times {\Gamma }_5$, the coupled bases determined by diagonalizing either of two invariants are the only ones to satisfy certain other symmetry relations between Wigner coupling coefficients.

Perturbation diagrams of the Brueckner-Goldstone expansion are partially summed to derive a Bethe-Goldstone equation for the short-range correlations in solid helium. The three corresponding two-body wave equations used in binding-energy calculations by Guyer, by Horner, and by Ebner and Sung are critically compared with the present one by means of the theory of $t$-matrix propagator perturbations. This provides qualitative explanations for the discrepancies between these published calculations and experiment.

It is shown that the $T^{-2\mathrm{}}$ dependence of the mobility is valid for all terms in the variational calculation. Moreover, the drag effect is separated in all orders, its contribution being an additional term in the expression for the mobility. Assuming the hard-sphere model for the impurity, first-order corrections are calculated.

Light shifts and line narrowings due to real transitions in alkali atoms have been calculated for well-resolved $\Delta m=0\mathrm{}$, $\Delta F=1\mathrm{}$ transitions between ground-state sublevels. The shifts vary in a systematic way for the various $\Delta m=1\mathrm{}$ transitions. Resonant increases in the magnitude of the shift occur in the neighborhood of certain critical magnetic fields. The calculations are in excellent agreement with the recent experimental results of White, Hughes, Hayne, and Robinson.

The interaction of hydrogenic atoms with a weak constant magnetic field is discussed in detail. The Breit Hamiltonian, minimally coupled to the external magnetic field, is treated in several different ways. First, approximate eigenfunctions are obtained in the nonrelativistic nucleus approximation. These wave functions are used to treat perturbatively the residual terms dependent on the magnetic field, and to identify the magnetic moment of the bound electron in the ground state. The corrections previously given by us, of relative order ${\left(Z\alpha \right)}^2$, $\frac{{\left(Z\alpha \right)}^{2}m}{M}$, $\alpha {\left(Z\alpha \right)}^2$, and $\frac{\alpha {\left(Z\alpha \right)}^{2}m}{M}$, are confirmed including lowest-order radiative corrections. Next, a unitary transformation of the complete Breit Hamiltonian is made in order to simplify further the calculation of small corrections to the electron and nuclear $g$ factors. The physical origin of this unitary transformation, which is similar to a gauge transformation, is discussed extensively, and it is shown that the transformed Hamiltonian for a neutral system commutes with $\overrightarrow{\mathrm{P}}$, the momentum conjugate to the center-of-mass position $\overrightarrow{\mathrm{X}}$. This new Hamiltonian, which treats the electron and the nucleus on equal footing, is then transformed by means of the Chraplyvy-Barker-Glover reduction. The electron and the nuclear $g$ factors are calculated, this time including terms of relative order $\frac{{\left(Z\alpha \right)}^2{m}^2}{M^2}$ and $\frac{\alpha {\left(Z\alpha \right)}^2{m}^2}{M^2}$. These computations yield the magnetic moments for hydrogenic atoms in their ground state. The theoretical results are summarized and compared with recent experiments.

An accurate method for solving the one-electron Schrödinger equation for small molecules is presented. For $\mathrm{Li}_2^{}{}_{}{}^{+}$, the valence-electron-core interaction is treated as an effective potential found by fitting the atomic energy levels. The intermolecular potentials for six low-lying electronic states of $\mathrm{Li}_2^{}{}_{}{}^{+}$ are calculated. For the ground state ${\sigma }_{g1\mathrm{}}$, a binding energy of 1.30 eV is found at a separation of 3.08 Å and a vibration frequency of 277 ${\mathrm{cm}}^{-1\mathrm{}}$. From the intermolecular potentials, three cross sections are calculated for Li ions scattering from Li atoms: (i) elastic scattering, (ii) charge transfer, and (iii) inelastic scattering leaving the atom in a $2p$ excited state. This last process proceeds through a curve crossing of the ${\sigma }_{u1\mathrm{}}$ and ${\pi }_{u1\mathrm{}}$ states at $R=5.95\mathrm{}{a}_0$.

A variational perturbation method is used to evaluate the first-order wave functions of ${\mathrm{H}}^{-}$ and ${\mathrm{Li}}^{+}$ in the presence of a monochromatic electromagnetic field. These functions are utilized to calculate the dynamic polarizabilities and refractive indexes of ${\mathrm{H}}^{-}$ and ${\mathrm{Li}}^{+}$ ions. Converged results are obtained for both systems. The converged static polarizability of ${\mathrm{H}}^{-}$ in the present calculation is shown to be 206.0 a.u., which compares favorably with previous theoretical calculations. The wavelength for the ${\mathrm{Li}}^{+}1{}_{}{}^1{}_{}{}^{}S-2{}_{}{}^1{}_{}{}^{}p$ transition from the dynamic polarizability calculation, 199.16 Å, is compared with the exact theoretical value of 199.32 Å.