Recent experimental results on laser-induced breakdown of liquid ${\mathrm{He}}^4$ have been interpreted by assuming that unbound electrons collide mainly with thermal rotons between the $\lambda$ temperature and 1.5°K. Previous experimental results on the behavior of hot electrons injected into liquid helium suggest that the collision frequency $\nu$ of the unbound electrons and their lifetime $\tau$ before they are trapped into bubbles are relatively temperature-independent between 4.2 and 1.35°K in contrast to the above-mentioned assumption. An alternative explanation is offered to the recent results based on an assumed temperature-dependent ejection of electrons from the bubbles.

We have analyzed the thermodynamic behavior of a system of fermions by use of a model Hamiltonian. On introducing a certain weakly singular term into the interaction, we find that nonclassical values for some of the critical-point exponents result.

This paper gives the details of pulse delay in self-induced transparency in S${\mathrm{F}}_6$ with a C${\mathrm{O}}_2$ laser at 10.5915 μ. Results show that the propagation of intense C${\mathrm{O}}_2$ laser pulses in S${\mathrm{F}}_6$ can be described by self-induced transparency.

Widths and shifts of Stark-broadened, neutral atomic lines have been measured using a gas-driven shock tube. Stark widths are given for 35 isolated lines or blended multiplets of carbon, oxygen, neon, silicon, phosphorus, sulphur, chlorine, and argon. Shift data are presented for 15 of these features. Electron densities are determined from both ${\mathrm{H}}_{\beta }$ profiles and pressure-temperature data. Estimated accuracy is 8-25% for the widths and 15-40% for the shifts. Results are compared with theoretical predictions and other measurements.

The importance of quasibound resonances is emphasized, with special reference to alkalinoble-gas systems. A modified WKB method for calculating the distribution and properties of quasibound resonances as well as of bound states is reviewed and applied to calculations of KAr and RbAr ground states. The calculated distribution of states in a Lennard-Jones 6-10 potential agrees precisely with the exact results of Mahan and Lapp. Inclusion of quasibound resonances is found to increase the total number of states by about $\frac{2}{3}$. Tunneling lifetimes much larger than typical collisional destruction times are found for most resonances.

The Brueckner-Goldstone many-body perturbation theory has been applied in a calculation of hyperfine structure (hfs) of sodium in the ground (${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$) state. Our result for $A$ (as in $A\overrightarrow{\mathrm{I}}·\overrightarrow{\mathrm{J}}$) is 857.8001±6 Mc/sec, in good agreement with the experimental result of 885.8131±0.0001 Mc/sec. The major contributions beyond the restricted Hartree-Fock result of 622.6430 Mc/sec arise from diagrams describing the exchange core-polarization effect. This contributes 139.6665 Mc/sec, in agreement with the existing unrestricted Hartree-Fock (UHF) and moment-perturbation (MP) results. All diagrams involving two orders of correlation interactions and associated ladders were calculated and were found to contribute 95.49 Mc/sec. Higher-order diagrams involving three or more orders of correlation interaction were investigated and found to be of minor importance in affecting the hfs constant of soidum.

Total $\gamma$-ray attenuation coefficients have been measured at nine energies in the range of 88 keV to 2.75 MeV for the following elements: Be, C, Mg, Al, S, Ti, Fe, Ni, Cu, Zn, Zr, Nb, Mo, Ag, Sn, La, Gd, Hf, W, Au, Pb, Th, U, and Pu. Radioactive isotopes were used as sources of monoenergetic $\gamma$ radiation in a narrow-beam-collimated geometry. Experimental errors are less than 1%.

Hyperfine-structure anomalies of the stable ytterbium isotopes ${\mathrm{Yb}}^{171}$ ($I=\frac{1}{2}$) and ${\mathrm{Yb}}^{173}$ ($I=\frac{5}{2}$) have been measured in the two lowest-lying ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ states of the Yb atom. For the ${\mathrm{}\left(4f\right)\mathrm{}}^{14}6s6p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level $\Delta =-0.367\mathrm{}\left(9\right)\%$, while for the ${\mathrm{}\left(4f\right)\mathrm{}}^{13}5d{\mathrm{}\left(6s\right)\mathrm{}}^2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level $\Delta =+0.084\mathrm{}\left(22\right)\%$. The former result is the first conclusive evidence that the Nilsson model can account for the distribution of nuclear magnetism in highly deformed nuclei. The second result, in conjunction with the first, can be used to establish the amount of unpaired $s$-electron spin density in a state explicitly lacking in unpaired $s$ electrons. If we neglect other forms of configuration interaction, we calculate that the core-polarization magnetic field produced by the $5d$ electron at the nuclear site is -1.7×${10}^5$ G. Byproducts of our work have been the lifetimes of the two excited electronic states. We find $\tau \left(6s6p{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=7.6\mathrm{}\left(8\right)\mathrm{}\times {10}^{-7\mathrm{}}$ sec and $\tau \left(f^{-1\mathrm{}}d{s}^2{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)=1.7\mathrm{}\left(2\right)\mathrm{}\times {10}^{-8\mathrm{}}$ sec.

The variational solutions to the Rayleigh-Schrödinger inhomogeneous equations are derived by simple matrix algebra. It is shown how the approximate perturbation energies and wave functions obtained in this way obey the same type of equations as the exact ones. This permits the formulation of a variation-iteration theory convenient for numerical applications. Results for the He-like ions show that the conventional linear series is less suitable than the present method in obtaining accurate energies. The use of inner projection techniques leads to an efficient calculation of Padé approximants to the energy series, which show remarkable convergence properties.

A many-body procedure applied earlier to helium is utilized here to study the response of a neon atom in its ground state to a time-dependent electric field. The theory of the method, omitted in the helium paper for reasons of brevity, is included here. Our results for the frequency-dependent polarizabilities $\alpha \left(\omega \right)$ lead to refractive indices $n\left(\omega \right)$, in excellent agreement with experiment. As a by-product of the calculation, we obtain [from the poles of $\alpha \left(\omega \right)$] excitation energies for $2p\to \mathrm{ns}$ and $2p\to \mathrm{nd}$ transitions in good agreement with experiment.

The zero-field hyperfine structure of the metastable $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state of ${\mathrm{He}}^3$ has been measured by the optical pumping magnetic resonance method. The hyperfine transitions in a weak magnetic field were observed at low temperature in order to achieve narrow linewidths. Discussions of the theory of the hyperfine structure, the theory of the experiment, the apparatus, and the experimental procedure are presented. The final value for the hyperfine structure is 6739 701177 ± 16 Hz on the $A-1\mathrm{}$ time scale. The fractional pressure shift of the hyperfine structure is (-7.4±3.0)×${10}^{-9\mathrm{}}$/Torr. The theoretical and experimental values for the hyperfine structure are compared, and the dependence on the nuclear structure is discussed.

The helium double-photoionization cross section has been evaluated using a Hylleraas wave function for the ground state in order to include correlation between the atomic electrons more directly than in previous calculations. Good agreement is found between the present results, the experimental data, and the theoretical work of Byron and Joachain. An interpretation of the differential electron spectrum is used to motivate an asymptotic calculation of the double-photoionization cross section which agrees well with the more exact treatment at high energies.

The rotational intensity distribution was measured for ${}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}-{}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ electric dipole transition which occurs only by violating the spin-selection rule. The photographic intensities, obtained using a 5-m two-mirror vacuum spectrograph, were reduced by means of the Seidel function and the intensity alternation which exists for homonuclear molecules with $\Lambda =0\mathrm{}$. The results are in disagreement with theoretical intensity distributions.

A complete quantitative discussion is given of the experiments in which muonium was discovered through studies of the depolarization of muons in gases and of the Larmor precession of muonium in argon in a static magnetic field. Also described are the observation of the hfs interval $\Delta \nu$ of muonium in its ground state and the determination of $\Delta \nu$ to an accuracy of about 50% through the use of a static magnetic field. A theoretical discussion is given of muonium formation in gases, including polarization effects. The experimental results on the Larmor precession of muonium prove that close to 100% of the muons stopping in pure argon gas form muonium. The experimental results on muon depolarization in other gases, together with the theoretical considerations, suggest that abundant muonium formation should occur when muons are stopped in most gases; the case of S${\mathrm{F}}_6$ appears anomalous in that, at most, only small formation of muonium is indicated. A discussion of the energy levels and decay characteristics of muonium is given. This is the first in a series of papers on the muonium atom and on its interactions in gases.

The theory of atomic lifetime measurements is developed on the basis of the quantum theory of radiation. The effect of coherent emission on the shape of the decay curves is studied in detail. It is shown that the light intensity will oscillate in time when two closely spaced levels decay coherently. Oscillations due to interference between fine-structure levels of the hydrogen atom in particular are discussed.

An experimental study of normal and stimulated Raman emission in diamond is presented, including measurements of linewidth, intensity, and angular distribution of radiation having a frequency shift of 1332.0 ${\mathrm{cm}}^{-1\mathrm{}}$. The diamond crystal formed a Raman resonator; excitation was by a giant-pulse ruby laser. The dependence of normal Stokes emission on laser intensity and the threshold for oscillation were investigated. A value for the Raman gain ($g=6.9\mathrm{}\times {10}^{-3\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$ per MW/${\mathrm{cm}}^2$) was calculated from the measured linewidth ($\Delta \nu =2.04\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$) and cross section for scattering, and found to be in good agreement with a value determined from the threshold for oscillation. The angular distributions of anti-Stokes and Stokes emission and absorption for parallel and convergent laser light are also in good agreement with theory: The emission cone angles are strongly dependent on the angle of convergence of the incident light, and it is established that the preferred directions for emission are those making use of the most intense first-order Stokes radiation which is peaked in the forward direction within the Raman resonator.

Stationary Gaussian optical fields are also often called thermal fields because they are generated by natural or thermal sources. By using the amplitude of the field, we show that thermal fields are only a particular case of the more general class of Gaussian fields. Such nonthermal Gaussian fields can be obtained experimentally, and we calculate some properties, concerning particularly the effect of Hanbury Brown and Twiss, photocounting, and coincidence experiments. We show that the thermal fields are the less chaotic or incoherent Gaussian fields. Finally, we introduce pseudo-Gaussian fields which appear in some experiments of diffusion with laser light. They are non-Gaussian fields, but their intensity has the same properties as that of a Gaussian field.

A detailed study of the correlation energy of Ne has been made in order to analyze the nature of the configuration-interaction (CI) method in ab initio calculations. Both the Bethe-Goldstone method of Nesbet and the total-pair-excitation-block method (TPEB) were examined. A series of calculations was made using both "atom-centered" and "shell-centered" basis sets. The most detailed calculations gave - 0.333 a.u. (88%) for the correlation energy by the TPEB method, and - 0.396 a.u. (104%) by the sum-of-the-pairs technique. The difference between these two values is mainly the so-called pair-pair interactions, which have been considered too small to be important to other investigators. A series of perturbation calculations on the triple and quadruple excitations gives ∼ 1.5% of the total correlation energy. A complete CI calculation with a very limited basis set was done on the $p$ block of Ne. The results of this calculation are in agreement with our total-atom calculation, except that now the TPEB calculation gave about 98.5%, and the sum of the pairs about 115% of the complete CI result. The effect on the pair correlation energy of a unitary transformation of the outer-shell occupied self-consistent-field orbitals was also studied. Only a small difference in the results was obtained.