The negative-ion mobility in liquid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ has been determined in the range 17-300 mK. The pressure dependence of the mobility up to 2 atm was also studied.

The multiple-quantum and rotating-field descriptions of resonant transitions requiring two frequencies are compared. Transitions combining features of both descriptions have been observed.

The time development of the coherence properties of a beam of light interacting linearly with a gas of two-level atoms maintained at fixed population levels is determined. For initially coherent light, the results obtained differ from those of a previous theory.

The $K$ shell of aluminum and the $M$ shell of hafnium have been excited using H, He, N, O, and Ar ions in the energy range 70-400 keV. The appearance of an excitation mechanism is observed for N, O, and Ar projectiles, which results in ionization cross sections several orders of magnitude greater than those predicted by a direct-scattering interaction such as is assumed for H and He ions. The results are examined in the light of the electron promotion mechanism of molecular-orbital theory as suggested by Der et al. The similar increases in cross sections for the hafnium $M$ shell and the aluminum $K$ shell using incident ions heavier than He suggest that an electron promotion mechanism does not provide a satisfactory explanation of the anomalous cross sections. It is felt that other factors, such as polarization of the relevant atomic shells of both the target atom and the projectile at close impact distances, must be considered in terms of the direct-scattering theory.

The formulation of the van der Waals (VDW) interaction between atoms in terms of frequency-dependent polarizabilities is extended to the problem of the long-range contribution to the hyperfine pressure shift in optical-pumping experiments. The requisite perturbed-energy expression for the present problem involves two orders of VDW interaction and one order of magnetic hyperfine interaction. This expression is recast in terms of integrals involving requisite frequency-dependent response functions which are evaluated using the Brueckner-Goldstone many-body technique applied earlier to VDW energy calculations. Specific applications are made to H-He and H-Ne systems. The fractional shift $\frac{\Delta \mathcal{A}}{{\mathcal{A}}_0}$ of the hyperfine constant is expressed in the form of $\frac{D_{\mathrm{H}X}}{R^6}$, where $R$ (a.u.) is the separation between H and $X$ atoms. The values we obtain for $D_{\mathrm{H}X}$ are 13.34 and 26.13 for $X=\mathrm{He} \mathrm{and} \mathrm{Ne}$, respectively. This analysis removes one of the important uncertainties in hyperfine-pressure-shift calculations, namely, the influence of correlation effects on the long-range part of $\frac{\Delta \mathcal{A}}{{\mathcal{A}}_0}$.

It is shown that the law of corresponding states can be applied to sublimation pressure curves of rare-gas solids. The vapor pressure ($P$) and temperature ($T$) below the triple point are written in terms of the usual reduced variables $P^{*}=\frac{P{\sigma }^3}{\epsilon }$ and $T^{*}=\frac{\mathrm{kT}}{\epsilon }$, where $\epsilon$ and $\sigma$ are Lennard-Jones potential parameters. It is then demonstrated that a single curve fits the $P^{*}$, $T^{*}$ data for Ar, Kr, and Xe over the 5-decade range in $P^{*}$ for which measurements have been made, $2\times {10}^{-8\mathrm{}}\le P^{*}\le 2\times {10}^{-3\mathrm{}}$ and $0.36\le T^{*}\le 0.72$. The equation of the curve for Ar, Kr, and Xe is $\ln P^{*}=5.\mathrm{}302-\frac{8.206}{T^{*}}$. The sublimation pressure curve for Ne is different from that of the heavier rare gases because of zero-point energy effects. The equation of the Ne curve is $\ln P^{*}=4.\mathrm{}287-\frac{7.077}{T^{*}}$, over about 3 decades in $P^{*}$. The historical background of the law of corresponding states and its derivation by De Boer et al. from quantum-mechanical first principles are presented in a way natural to this problem. It is shown that extension of the law of corresponding states to the solid-vapor phase transition is natural and proper. As a corollary, the sublimation pressure for radon is predicted as ${log}_{10}P\left(\mathrm{Torr}\right)=7.868-\frac{1034}{T}$.

The polarization model for the excited states of He I is reconsidered in the framework of modern perturbation theory. The central potential exerted on the optical electron by the ionic core is obtained in an unified way, and its first three terms — Coulomb, dipole, and quadrupole — are shown to account quantitatively for the binding energy of the excited levels ($n,l$) with $n>~3$ and $l>~2$. The usual dipole approximation is then established on firm grounds and appears to be sufficient for practical uses of the polarization model.

Numerical solutions to the $S$-limit equations for the helium ground state, excited triplet state, and the hydride-ion ground state are obtained with the second and fourth difference approximations. The results for the ground states are superior to previously reported values. The coupled equations resulting from the partial-wave expansion of the exact helium atom wave function are solved giving accurate $S,P,D,F$, and $G$ limits. The $G$ limit is -2.903 51 a.u., compared to the exact value of the energy of -2.903 72 a.u.

The theory of transient stimulated Raman scattering has been extended to include an arbitrary shape of the laser pump pulse. It is shown that the maximum Stokes gain depends on the total energy content per unit area of the pump pulse, and not on the instanteous intensity for an exciting pulse of short duration. The Stokes pulse has a leading edge which rises sharply to a maximum, where the maximum occurs with some delay with respect to the maximum of the pump pulse. The trailing edge follows the decay of the pump. In a nondispersive medium, the gain is not reduced by frequency broadening of the laser output, while in a dispersive medium, considerable gain reduction is expected. Numerical results for various laser-pulse shapes and spectral distributions are presented.

The mean excitation potential of helium has been determined to be 42.7 ± 0.6 eV by measuring the ranges of monoenergetic particles in a helium bubble chamber. Special care was taken to minimize systematic errors in the measurement of track lengths. The result obtained is independent of assumed corrections to the Bethe-Bloch equation at low velocity, but a discussion of such corrections is presented. Two existing theoretical estimates of 41.5 and 41.8 eV are in fair agreement with the measured value.

Recently, we have reported variational solutions to Schrödinger's equation for C${\mathrm{H}}_4$, N${\mathrm{H}}_3$, ${\mathrm{H}}_2$O, and HF, using a Hamiltonian which included the kinetic-energy operators of the protons. The results of these calculations implied the existence of protonic spectra similar to the electronic spectra. We show here that the selection rules which apply to electrons also apply to the protons. Furthermore, we find a two-particle-transition operator which allows an electron and a proton or two protons to be simultaneously excited with intensities proportional to the square of $\frac{k{m}_p}{M}$, where $k$ is the wave number of the light, $m_p$ is the mass of the proton, and $M$ is the total mass of the molecule. For completeness, the effects of the radiation field on the coordinates of the c. m. are given also.

The power spectrum of the radiation emitted by a driven collision-damped two-level system is evaluated. The driving field, which is treated classically, is assumed to oscillate harmonically near the atomic resonance frequency, and its intensity is allowed to assume arbitrary values. The collisions are assumed to be strong, i.e., to instantaneously thermalize the state of the atom. The limiting forms of the power spectrum of the radiated field are discussed for the cases of low and high excitation of the atomic system.

A method of analysis of all level positions in multiple strongly perturbed series of levels is presented and illustrated by examples from the rare gas and Ba spectra. The method is suggested by Seaton's multichannel quantum defect theory but is presented here as an empirical approach. It emphasizes the dependence of a perturbation on the periodicity of the perturbing series and aims at extracting significant information from experimental data in compact form; this goal will be pursued in later works.

A series of Zeeman resonances has been measured in the $2{}_{}{}^3{}_{}{}^{}P$ state of ${\mathrm{He}}^4$, using the optical-microwave atomic-beam magnetic-resonance technique. The results were analyzed in terms of relativistic and motional contributions to the Zeeman effect, and are presented in the form of corrected $g$ factors: $g_{S^{\prime }}=g_S-(76.0\mathrm{}\pm 2.4)\times {10}^{-6\mathrm{}}$, $g_{L^{\prime }}=g_L+(3.8\mathrm{}\pm 9.0)\times {10}^{-6\mathrm{}}$, and an additional factor $g_x=(4.0\mathrm{}\pm 25.0)\times {10}^{-6\mathrm{}}$. These are compared with theoretical calculations using quasi-hydrogenic radial wave functions which give $g_{S^{\prime }}=g_S-(79.9\mathrm{}\pm 3.5)\times {10}^{-6\mathrm{}}$, $g_{L^{\prime }}=g_L+(1.1\mathrm{}\pm 1.5)\times {10}^{-6\mathrm{}}$, and $g_x=-(3.2\mathrm{}\pm 4.4)\times {10}^{-6\mathrm{}}$. The values of the experimental $g$ factors are $g_S^1=2.002\mathrm{}2432\pm 0.0000224$, and $g_L^1=0.\mathrm{}999867\pm 0.000009$. The validity of the theory and the consistency of the data are discussed. The experimental results were used to reduce the quoted uncertainty in a previously reported fine-structure measurement. The new result is $E\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)-E\left(2\mathrm{}{}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}\right)=2291.\mathrm{}196\pm 0.005$ MHz.

The $\frac{K{\beta }_3}{K{\beta }_1}$ transition probabilities have been measured for the following elements: ${}_{49}{}^{}{}_{}{}^{}\mathrm{In}$, ${}_{50}{}^{}{}_{}{}^{}\mathrm{Sn}$, ${}_{52}{}^{}{}_{}{}^{}\mathrm{Te}$, ${}_{58}{}^{}{}_{}{}^{}\mathrm{Ce}$, ${}_{65}{}^{}{}_{}{}^{}\mathrm{Tb}$, ${}_{73}{}^{}{}_{}{}^{}\mathrm{Ta}$, ${}_{75}{}^{}{}_{}{}^{}\mathrm{Re}$, ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{82}{}^{}{}_{}{}^{}\mathrm{Pb}$, ${}_{90}{}^{}{}_{}{}^{}\mathrm{Th}$, ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$, ${}_{93}{}^{}{}_{}{}^{}\mathrm{Np}$, ${}_{94}{}^{}{}_{}{}^{}\mathrm{Pu}$, and ${}_{95}{}^{}{}_{}{}^{}\mathrm{Am}$. This has been accomplished using a spectrometer with a bent quartz crystal in conjunction with a Ge(Li) detector. The measured transition probabilities for elements of medium atomic numbers are in good agreement with calculations based on the relativistic Hartree-Slater potential, while in the region of high atomic number the measured values seem to favor theoretical values obtained assuming a Coulomb potential with the electron screening effect prescribed by Burns.

Dipole and quadrupole polarizabilities and shielding factors of lithium and lithium-negative ion have been evaluated using Sternheimer's procedure. Unusually large values for quadrupole polarizabilities of lithium-negative ion are reported. The dipole polarizability of boron is also calculated and compared with the other calculations.

The linewidths of $Q\left(0\right)-Q\left(4\right)\mathrm{}$ in the electric-field-induced fundamental band of ${\mathrm{H}}_2$ are measured with 0.027-${\mathrm{cm}}^{-1\mathrm{}}$ resolution for pressures between 4.4 and 35 atm. The widths are found to vary linearly with density, with negligible contributions from the Doppler effect because of collision narrowing. The values obtained for the broadening coefficients at 300°K are, in order of increasing $J$: 2.78, 1.83, 3.05, 4.60, and 3.26 in units of ${10}^{-3\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$/amagat. These values are 20-30% larger than previous results from Raman data. The linewidth calculations of Van Kranendonk are revised to include the effective rotational constants of ${\mathrm{H}}_2$, and the results are compared with experiment. The agreement is fair when the anomalously small calculated width for $Q\left(1\right)\mathrm{}$ is excluded.

We consider theories in which a kinetic-energy correction $\left(\frac{\lambda h^2}{32{\pi }^{2}m}\right)\left[\frac{{\left(\nabla \rho \right)}^2}{\rho }\right]$ ($\rho =\mathrm{density}$) is added to the usual Thomas-Fermi term. A treatment based on the WKB method and expected to be valid for large $\mathcal{r}$ shows $\lambda =1\mathrm{}$ here, as found experimentally. For small $\mathcal{r}$, $\lambda =1\mathrm{}$ is needed to give proper behavior of $\rho$, but other arguments suggest that the Thomas-Fermi term be dropped here.

Accurate numerical solutions have been obtained for Schrödinger's equation for a two-particle system interacting through a static screened Coulomb potential (SSCP) $V\left(\mathcal{r}\right)=-\frac{Z{e}^2{e}^{-\frac{r}{D}}}{\mathcal{r}}$. The numerical integration of the wave equation uses a one-dimensional difference method which is simple, accurate, and efficient. Solutions have been computed for 45 eigenstates, $1s$ through $n=9\mathrm{}$, $l=8\mathrm{}$, yielding the eigenfunctions and energy eigenvalues for a wide range of $D$, the screening length which characterizes the range of the interaction. Under screening, all energy levels are shifted away from their unscreened values toward the continuum, the energy increasing as $D$ decreases. For each $n$, $l$ eigenstate, there is a finite value of the screening length $D_0(n, l)$, for which the energy becomes zero. The value of $D_0$ for the ground state of a two-particle bound system in a potential of this type, such as the Debye or Yukawa potential, is 0.83991 $\frac{a_0}{Z}$ in agreement with certain previous studies. The total number of different energy levels is finite for any finite $D$, and is approximately linearly dependent on $D$. The number of bound $s$ states $g^{*}$ is given by the relation ${\left(g^{*}\right)}^2=1.2677\mathrm{}$ $\frac{\mathrm{DZ}}{a_0}$. For given $n$, the $l$ degeneracy is destroyed, lowest $l$ levels lying lowest in energy. At sufficiently high $n$, this behavior results in level crossing, high $l$ levels of eigenstate $n$ having higher energies than low $l$ levels of eigenstate $n+1\mathrm{}$. This produces increasingly complex deviations of the level order from the unscreened order, commencing with the $5s-4f$ cross-over. Because of the displacement of high $n$ states into the continuum, the density of states in the SSCP for any finite $D$ is lower than in the unscreened potential, especially near the continuum.