Precision calculations of the energies of the $\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ states of He and ${\mathrm{H}}^{-}$ are carried out with a Hylleraas-type wave function and are the lowest variational results yet obtained. The associated wave functions are used to calculate the mass polarization of the state. With the reduced mass correction, the wave numbers of the transitions $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}-\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ in He and $\mathrm{}\left(2s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P_{}^0{}_{}{}^{}-\left({2p}^2\right){}_{}{}^3{}_{}{}^{}P_{}^e{}_{}{}^{}$ in ${\mathrm{H}}^{-}$ are found to be 312 222 and 3783 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively. This former value is in disagreement with the experiment of Kruger (1930) who obtained 312 118 ${\mathrm{cm}}^{-1\mathrm{}}$. The discrepency between the experimental and theoretical values of 100 ${\mathrm{cm}}^{-1\mathrm{}}$ is large enough to encourage renewed experimental observation.

The positron annihilation lifetime spectra in nitrogen have been measured by a new apparatus consisting of two time-to-amplitude converters. The annihilation of positrons in nitrogen as a function of nitrogen densities from 2 to 45 amagats has been investigated. The free annihilation rate is found to be 5.80 ± 0.07 μ${\sec }^{-1\mathrm{}}$ ${\mathrm{amagat}}^{-1\mathrm{}}$, and the $o-\mathrm{P}\mathrm{s}$ quenching rate, 0.22 ± 0.06 μ${\sec }^{-1\mathrm{}}$ ${\mathrm{amagat}}^{-1\mathrm{}}$. Both rates are found to be linear for densities up to 45 amagats. A distinctive shoulder has been observed in the positron annihilation lifetime spectra for nitrogen with densities less than 10 amagats. The shoulder width is estimated to be 14 ± 3 nsec amagat. The value of $Z_{\mathrm{eff}}$ for free-positron annihilation at thermal energy is found to be 30. The value of $Z_{\mathrm{eff}}$ for free-positron annihilation at energy about 0.5 eV or higher is estimated to be only about 23.

The effect of a homogeneous electric field on the protonic coordinates of neutral hydrides is shown to be identical to the effect on the electronic coordinates. For ionized hydrides, the effects on the protonic coordinates are shown to be proportional to (1 —$\frac{N{m}_p}{M}$) where $m_p$ and $M$ are the protonic and total mass, respectively, and $N$ is the degree of ionization. A homogeneous magnetic field affects the protonic coordinates through terms proportional to $\frac{{\mathcal{H}}^2{m}_p}{M}$ and $\frac{N_e{\mathcal{H}}^2{m}_p^2}{M^2}$, where $\mathcal{H}$ is the strength of the field and $N_e$ is the number of electrons in the molecule. The terms of first order in $\mathcal{H}$ are found to be negligible for the protonic coordinates. The effects of both the electric and magnetic fields on the motion of the center of mass are also given. We show that in the presence of a homogeneous magnetic field in the $z$ direction, the center of mass of neutral atoms or molecules will vibrate in the $\mathrm{xy}$ plane with a frequency of $\omega ={\left(\frac{N_e{q}_e{}_{}{}^2{}_{}{}^{}\mathcal{H}_{}^2{}_{}{}^{}}{4M{m}_e{c}^2}\right)}^{\frac{1}{2}}$, where $c$ is the velocity of light.

The electron momentum density (EMD) of the electrons in the helium atom and hydrogen molecule were measured by Compton x-ray scattering. The results for helium, in both the liquid and gaseous state, are in agreement within the statistical accuracy of the experiment with Hartree-Fock calculations of the EMD. For the hydrogen molecule the effects of binding on the EMD are clearly observed. There is disagreement between Hartree-Fock calculations of the EMD for the hydrogen molecule and the measured EMD. This disagreement is attributed to non-Hartree-Fock electron-electron interaction effects, which are sizable in the ${\mathrm{H}}_2$ molecule. In addition, for these systems, further proof of the validity of the impulse approximation is obtained by an accurate measurement of the Compton shift.

A systematic study has been made of the ionization cross sections for ion excitation of the $M$-shell x rays of elements with $Z$ in the region $72\le Z\le 92$. Protons, $\mathrm{H}_2^{}{}_{}{}^{+}$ ions, and $\alpha$ particles with incident energies ranging from 60 to 400 keV were used to excite the $M$ lines of Hf, Ta, W, Au, Bi, and U. The $Z$ dependence of the proton-excited x-ray yield for these elements, although differing sharply from previously published $M$-shell results, is shown to be consistent with the $Z$ dependence for proton excitation of the $K$ and $L$ shells reported in earlier papers. Finally, we have compared the ionization cross sections of $\mathrm{H}_2^{}{}_{}{}^{+}$ ions at incident energy $E_0$ with those for protons at incident energy $\frac{1}{2}{E}_0$, and found that within 30% they are in the ratio 2: 1.

The atomic-beam magnetic-resonance technique has been used to measure the hyperfine structure of the $4f^{10}6s^2{}_{}{}^5{}_{}{}^{}I_{8,7}^{}{}_{}{}^{}$ atomic states of ${\mathrm{Dy}}^{161,163}$. Values of the hyperfine-interaction constants $A$, $B$, and $C$, corrected for hyperfine interactions with other states, are given for both atomic states of each isotope. It is found that for the nuclear ground states of ${\mathrm{Dy}}^{161,163}$, $\frac{{\mu }^{163}}{{\mu }^{161}}=-1.400\mathrm{}\left(3\right)\mathrm{}$, and, less accurately, ${\mu }^{163}=+0.65\mathrm{}\left(6\right)\mathrm{}{\mu }_N$, $Q^{163}=+2.51\mathrm{}\left(30\right)\mathrm{} \mathrm{b}$, ${\mu }^{161}=-0.46\mathrm{}\left(5\right)\mathrm{}{\mu }_N$, $Q^{161}=+2.37\mathrm{}\left(28\right)\mathrm{} \mathrm{b}$. The electron $g$ factor $g_J$ is measured for the atomic states $4f^{10}6s^2{}_{}{}^5{}_{}{}^{}I_{8,7,6}^{}{}_{}{}^{}$ and also for the lowest $J=8\mathrm{}$ level of $4f^{9}5d6s^2$ at 7565 ${\mathrm{cm}}^{-1\mathrm{}}$. The lifetime of this level cannot be appreciably less than 2 msec, the transit time for the atom in the apparatus.

Nonrelativistic energies and mass-polarization shifts of $3S-10S$ states of He were calculated with 40- to 80-term Rayleigh-Ritz expansions in $r_1$, $r_2$, and $r_{12}$. Pekeris's calculated values of relativistic shifts were used in making comparisons with experimental values. Except for $8{}_{}{}^1{}_{}{}^{}S$, the calculated ionization energies are less than the experimental values (in agreement with variational principle) by amounts ranging from 0.01 ${\mathrm{cm}}^{-1\mathrm{}}$ upward.

It is argued that Hartree-Fock (HF), and certain HF-like, calculations provide upper bounds to energies of certain atomic autoionization states, defined as eigenfunctions of Feshbach's $\mathrm{QHQ}$. A detailed discussion and supporting calculations are given for the $2s^2{}_{}{}^1{}_{}{}^{}S$ state of helium. The $Q$-space constraint can be satisfied by assignment of a suitable value to an orbital-expansion parameter. A slightly higher, and hence upper-bound, value of energy is obtained by instead maximizing energy with respect to this parameter. It is argued that a HF calculation can be reduced to such a parameter-maximization process, on the assumption that the solution is unique. Several autoionization states in two-electron atoms are discussed, and it is noted that the HF energy bounds are useful for some such states but are useless for others because of configuration mixing. The general approach is not inherently limited to two-electron atoms, and a similar argument is given for the lowest ${}_{}{}^2{}_{}{}^{}S$ autoionization state of a three-electron atom.

The polarization of the $L{\alpha }_1$ characteristic x rays of mercury has been measured with respect to the emission plane. A mercury-vapor-target x-ray tube was used with a jet density such that most electrons encountered only a single exciting collision. A quartz crystal ($23\overline{5}4$) plane which diffracted the $L{\alpha }_1$ line (1. 241 20 ${\mathrm{\AA }}^{*}$) at an angle $2\theta ={104}^{\circ }$ was used as the analyzer. The observed polarization was (- 14±4)%.

A nonperturbative approach to the theory of transition probabilities is presented. The results of this theory are employed to investigate the validity of the assumptions inherent in the perturbative approach. For this purpose, the simple examples of absorption of radiation (first-order process) and Raman scattering (second-order process) are used. The method proposed, which is based upon finite-difference techniques, represents an accurate solution of the time-dependent Schrödinger equation in a given representation and has many advantages over methods based upon the perturbation series.

When charged particles interact with the noble gases, energy is radiated in the vacuum ultraviolet (VUV) region of the electromagnetic spectrum. Some recent measurements of the absolute yield of VUV energy per cm of proton track length show that this quantity $\frac{d\epsilon }{\mathrm{dx}}$ is an appreciable part of the total stopping power $\frac{\mathrm{dE}}{\mathrm{dx}}$. Here, we show by direct comparisons and by arguments based on the principle of conservation of energy that the Jesse effect (Penning ionization) in helium, neon, and argon is associated with radiation energy in the VUV region.

Interactions between a highly excited atom and another atom in the ground state with nonzero electron affinity lead to a splitting of highly excited levels. This situation provides a mechanism which modifies spectral lines of a Rydberg series. Electronic transitions between components of the quasi molecular level due to interatomic motion are analyzed on the basis of the adiabatic theory. The width of a spectral line near the edge of the series is expressed in terms of the electron affinity of the perturbing atom and other calculable quantities. Comparison of the present theoretical result and experimental data for K and Cs shows that this mechanism is as significant for linewidths as the Fermi process for line shifts.

A relative cross section for simultaneous excitation and ionization of the helium atom is derived from the sudden approximation. It is shown to agree with that obtained from the velocity form of the cross section in the Coulomb approximation. It is connected to the asymptotic cross section of Kabir and Salpeter through the cusp condition at the nucleus. An analysis of the influence of ground-state correlations on the asymptotic double-excitation cross section is carried out.

Phenomena of coherent resonant propagation can be considered as resulting from the cooperative interaction of a certain number of excited two-level systems. It is shown that these phenomena can be characterized by a specific "maximum cooperation number" and by the associated "cooperation time." These are defined for the superradiant state, but their meaning and usefulness can be extended to other situations. The alternative description of of superradiance as a spontaneous or as a stimulated effect is also discussed and it is shown that with the help of the new concepts, the Dicke quantum perturbative treatment can be reconciled with the semiclassical theories.

Accurate numerical methods are applied to the vibronic problem resulting from two interacting intersecting harmonic curves. Two examples are considered, corresponding to either degenerate or nondegenerate electronic states. The energies are obtained with (a) the zeroth-order Born-Oppenheimer approximation; (b) the so-called adiabatic approximation, which includes the diagonal corrections to (a); (c) the full vibronic procedure. Several features in the correlation diagrams giving the energies as a function of the configuration-interaction matrix element are given an explanation. We also note that, in the model treated here, inclusion of the diagonal corrections does not always lead to an improvement of the energies.

Spin-exchange optical pumping has been used to measure the hyperfine pressure shift of atomic nitrogen in helium, neon, and molecular nitrogen as a function of temperature. In the range 70-500°C, the change in pressure shift was linear with temperature, and the values were for helium, -(0.1±0.1) ×${10}^{-4\mathrm{}}$; for neon, (0.6±0.1) ×${10}^{-4\mathrm{}}$; and for molecular nitrogen (1.4±0.3)×${10}^{-4\mathrm{}}$ in units of Hz/Torr°C. The measurements also give $A=10\mathrm{}450929.4\pm 1.8$ Hz for the free atom. The quadrupole interaction constant was also measured and found to be independent of temperature and pressure. The value was $B=1.3\mathrm{}\pm 0.5$ Hz.

The matrix element for the elastic scattering of photons by atomic hydrogen is evaluated analytically in closed form in the nonrelativistic case including retardation. The method of integration is similar to the one used previously by one of the authors for the dipole approximation. It is based on the possibility of expressing the matrix element in terms of the Green's function for the Coulomb field, for which the momentum-space integral representation derived by Schwinger and others is then used. Some integrations yield the matrix element in terms of essentially two hypergeometric functions of Appell's type $F_1$, with variables and parameters depending on the photon energy. A discussion of the result is given.

The polarization of Lyman-$\alpha$ radiation resulting from the direct excitation of hydrogen atoms by proton impact has been measured in the energy range 2-21 keV. A Brewster's angle polarization analyzer was used to measure the polarization of the observed Lyman-$\alpha$ radiation. The results are compared with the four-state Sturmian calculation of Gallaher and Wilets.

The polarization of Lyman-$\alpha$ radiation arising from charge-transfer collisions between protons and helium, argon, and neon has been measured for incident proton energies from 0.6 to 24 keV. A lithium fluoride crystal set at the Brewster's angle was used to measure the polarization of the radiation. Structure has been observed in the energy dependence of the polarization fraction for ${\mathrm{H}}^{+}$-Ne and ${\mathrm{H}}^{+}$-Ar collisions which reflects the structure in the total cross sections for electron capture into the $2P$ state of atomic hydrogen for these collisions. The present results are in poor agreement with those of Gaily et al.

A convenient and accurate numerical method is given whereby inelastic scattering information can be obtained by construction of the Fredholm determinant $\det [1-\mathit{G}(E+i\epsilon \left)\mathit{V}\right]$ for the coupled Lippmann-Schwinger equations. The method is noniterative and is easily applied when the potential matrix is nonlocal or energy dependent. It is shown that the determinant $\det [1-\mathit{G}(E+i\epsilon \left)\mathit{V}\right]$ may be factored as $\det [1-\mathcal{P}\mathit{G}\mathrm{}(E\left)\mathrm{}\mathit{V}\right]\det (1-i\mathit{R})$ when $\mathcal{P}\mathit{G}\mathrm{}\left(E\right)\mathrm{}$ is the principal-value Green's function and $R$ is the usual $R$ matrix of principal-value Lippmann-Schwinger theory; the $R$ matrix may be obtained from $\det [1-\mathit{G}(E+i\epsilon \left)\mathit{V}\right]$ by a single partial triangularization. As a simple example of the extraction of the $R$ matrix from the Fredholm determinant, the problem of electron scattering from hydrogen atoms is considered in the $1s$, $1s-2s$, $1s-2s-3s$, and $1s-2s-3s-4s$ close-coupling approximations. The use of optical potentials in the Fredholm theory is discussed: The two-channel problem originally suggested by Huck is solved numerically by construction of an optical potential.