The average lifetime of metastable CO molecules in the $a{}_{}{}^3{}_{}{}^{}\Pi$ state excited by electron impact at 7.5 eV at room temperature was found to be about 1 msec. Lifetimes of metastable ${\mathrm{N}}_2$ molecules in the $a{}_{}{}^1{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ and $E{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states were found to be 115 ± 20 and 190 ± 30 μsec, respectively. There was evidence for at least one higher-lying metastable state of CO at about 10eV having a lifetime of about 0.1 msec. The lifetimes were obtained in a time-of-flight experiment and deduced from the measurements without resorting to analytic expressions of the time-of-flight distribution. The observed time-of-flight distributions were essentially Maxwellian. A diffuse-gas source operated at pressures in the ${10}^{-4\mathrm{}}$-Torr range was used. Effects due to metastable recoil, uv photons from metastable decay, and metastable wall collisions were carefully examined and found to be negligible under most conditions. Metastable excitation functions were obtained using a low-energy high-resolution electron gun.

The statistical mechanics of an electron gas in a uniform magnetic field is developed based on a diagram technique. To zero-order exchange graphs, the pair-distribution function is evaluated with electronic spins taken into consideration. The result can be used to obtain the susceptibility to first order in interaction for both high and low temperatures. Under the de Haas-van Alphen (dHvA) condition, the exchange graphs yield not only a nonoscillating susceptibility but also oscillating waves with the same basic frequency as the free-particle waves. These exchange waves, however, have different analytical expressions with different magnetic field dependence from those of free-particle waves. Indeed, higher harmonics play more important roles than the case of free-particle waves. Therefore, the superposed waves can change shape significantly with small change of parameters such as the Fermi energy. The exchange graphs add fine rippling waves to the main dHvA waves due to free electrons. Also the graphs give an account of the Shoenberg-Dingle plot for the magnetic field dependence of the amplitude of dHvA waves. However, the plot may not be a straight line. Explicit numerical evaluations of dHvA waves are performed by using CDC 6400. The ring diagrams are found to yield a contribution similar to the exchange graphs.

It is shown that both the energy and the wave function of the stable Hartree-Fock solution are nonanalytic functions of the coupling constant at the branching point, dividing the symmetry-adapted and the broken-symmetry solutions. The $\pi$-electronic model of benzene is used to illustrate this fact for the case of the Hartree-Fock singlet instability. It is indicated that the same type of nonanalytical behavior is found in other types of instabilities, i.e., nonsinglet (triplet) instabilities for closed shells and doublet instabilities for simple open shells. This nonanalyticity persists even after the projection on the totally symmetric subspace is carried out, and can only be avoided by projecting before the variational principle is applied.

A scheme is proposed in which a multistate ket is variationally computed, subject to certain symmetry constraints. Computational characteristics of the method, including the recovery of single-state kets and energies, and the avoidance of three-center and four-center molecular integrals, are discussed.

Radiationless transition probabilities to the atomic $1s$ shell are calculated for all transitions that contribute measurably to the Auger effect. Screened nonrelativistic hydrogenic wave functions are used. The effective charge for the continuum-electron Coulomb wave function is taken to be the geometric mean of the effective charges appropriate for the state from which the electron originates and the next-higher state. The results are combined with Scofield's radiative transition probabilities to derive theoretical $K$-shell fluorescence yields. Agreement with a selected set of most reliable ${\omega }_K$ measurements is very good in the range from $Z=10\mathrm{} \mathrm{to} 55$, and total $K$-level widths agree very well with measured values.

We report the results of calculations of Sternheimer crystalline electric field shielding and antishielding factors for ${\mathrm{Pr}}^{3+}$, ${\mathrm{Tm}}^{3+}$, ${\mathrm{W}}^{+}$, and ${\mathrm{Au}}^{+}$ ions at all the core electronic sites, in addition to the unfilled valence electron site and the nuclear site of each ion. The calculations take into account the effect of polarization of all the closed shells within the ions, including the exchange interaction terms. Mann's relativistically corrected Hartree-Fock (HF) wave functions were used in the computations. Our calculations thus extend and improve upon the previous calculations by Sternheimer and others who did the computations for rare-earth ions at the location of the $4f$ electron and at the nuclear site only. Our values of shielding and antishielding factors $\lambda \mathrm{s}$ at the location of the $4f$ electron and at the nuclear site for ${\mathrm{Pr}}^{3+}$ and ${\mathrm{Tm}}^{3+}$ ions agree well with previous calculations and measurements. The possibility of experimentally determining the quadrupole splittings of the atomic-core level by the recently developed technique of electron spectroscopy for chemical analysis (ESCA), which underlines the great significance of these calculations, is discussed.

The use of a hydrogen maser oscillating on a magnetic-field-dependent transition for the measurement of atomic magnetic-moment ratios is discussed. Unlike the well-known field-independent transition of the hydrogen maser, the field-dependent ones operate on a population difference that is directly dependent on the electron-spin polarization of the hydrogen atoms. It is possible, therefore, to introduce other atoms into the storage volume of the maser, and observe transitions in their hyperfine Zeeman spectra by spin-exchange coupling to the hydrogen-maser oscillation level. The hydrogen maser was operated under conditions of self-excited oscillation at 7.6 G on a magnetic-field-dependent transition. By spin exchange, the atomic magnetic moment of ${\mathrm{Rb}}^{87}$ was measured relative to the magnetic moment of hydrogen. The value of this ratio was found to be 1.000 023 590 (110). The largest part of the uncertainty is a systematic effect attributed to an "inhomogeneity shift" and is an order of magnitude larger than statistical error.

The "vibrational" structure is shown to consist of electric dipole transitions of the protons from their ground state characterized by a principal quantum number $n$, to an excited state with $n^{\prime }=n+1\mathrm{}$. In hydrogen fluoride, the transition from the ground state $108s$ to the state $109p$ is calculated to be 4277.4 ${\mathrm{cm}}^{-1\mathrm{}}$ which compares well with the experimental transition of 3961.57 ${\mathrm{cm}}^{-1\mathrm{}}$. For lithium hydride in its first excited electronic state, an energy of 1562.3 ${\mathrm{cm}}^{-1\mathrm{}}$ is calculated for the first protonic transition. The experimental value is 1359.2 ${\mathrm{cm}}^{-1\mathrm{}}$. Water, ammonia, and methane are also discussed, as are the electric quadrupole, magnetic dipole, the two-proton, and the electron-proton transitions. It is postulated that the "rotational" structure arises from electric dipole transitions from the ground state to states of higher angular momentum with the same principal quantum number as the ground state.

The separable-expansion method for solving the Faddeev equations is applied to the positron-hydrogen system at energies below the positronium-formation threshold. The results for the scattering length and phase shift are compared with those obtained by other methods. The three-body bound state and resonance obtained using only the first few terms in the separable expansion are shown to disappear when more terms are included in the expansion. The problem of convergence of the separable-expansion method in the Sturmian-function representation is discussed.

Auto-ionization accompanying $\beta$ decay was studied in an equilibrium mixture of ${\mathrm{Sr}}^{90}$-${\mathrm{Y}}^{90}$ by a comparison of the intensities of $K$ x rays accompanying these decays. Since both nucleides undergo $\beta$ decay of the unique first forbidden type, the main difference between the two decays is a factor of ∼ 4 in endpoint energy. The ratio of the amount of x rays accompanying the ${\mathrm{Y}}^{90}$ decay to the amount accompanying ${\mathrm{Sr}}^{90}$ decay was found to be 1.3. This is interpreted to mean that the direct collision process plays an unimportant role in auto-ionization in these two isotopes and that it is most likely that the probability of auto-ionization in $\beta$ decay is independent of the energy of the $\beta$ particle in decays with endpoint energies high compared with the $K$-shell ionization energy.

Many-body perturbation theory is used to calculate a value of -0.156 ± 0.005 a.u. for the correlation energy of the ${}_{}{}^3{}_{}{}^{}P$ ground state of the carbon atom. This value was obtained with a basis set of bound and continuum orbitals of angular momentum $s$, $p$, $d$, and $f$, and the contribution from excitations into states of higher angular momentum is estimated to be less than 2% of this result. A detailed study of three-body correlations is presented; their contribution to the correlation energy is 0.0041 a.u. Special attention is also given to diagrams which produce coupling between the correlation energies of different electron pairs.

Two autodetaching states of ${\mathrm{O}}^{-}$ have been found by observing the electron energy spectrum of ${\mathrm{O}}^{-}$ ions excited in collisions with a He target at keV beam energies. The energies of the states have been measured as 10. 112 and 12. 115 ± 0. 010 eV. The ${\mathrm{H}}^{-}$ ${}_{}{}^1{}_{}{}^{}S$, ${}_{}{}^3{}_{}{}^{}P$, and ${}_{}{}^1{}_{}{}^{}D$ autodetaching states below the $n=2\mathrm{}$ hydrogen level are excited in ${\mathrm{O}}^{-}$ on ${\mathrm{H}}_2$ collisions, and the ${\mathrm{Ar}}^{-}$ autodetaching states below the first excited argon level are formed in ${\mathrm{O}}^{-}$ on Ar collisions. No structure in the electron energy spectrum was seen for collisions of ${\mathrm{O}}^{-}$ on ${\mathrm{O}}_2$ or Ne.

Calculated Auger, Coster-Kronig, and radiative transition rates are used to compute atomic L-shell Coster-Kronig and fluorescence yields. The results are compared with other calculations, experimental yield determinations, and radiative half-width measurements.

A general theorem is derived which applies to any quantum-mechanical system subject to two perturbations $H$ and $G$. It is shown that the eigenvalues of the system can be found by first solving exactly the secular equation in $H$. Then the first-order perturbation of the energy by $G$ can be written explicitlv without solving for the eigenfunctions. This leads to a simple method for finding the exact Landé $g$ factors for the Zeeman effect of any quantum-mechanical system. These results are applied to the Zeeman effect of the hydrogen molecule in the metastable $c{}_{}{}^3{}_{}{}^{}\pi _u^{}{}_{}{}^{}$ state. Jette and Cahill's theory of the Zeeman effect is extended to cover all magnetic fields. Excellent agreement is found between experimental $g$ factors and theory. At higher magnetic fields, "anti-crossings" are found between pairs of states for which $\Delta J=\pm 1, \pm 2$, $\Delta F=0, \pm 1, \pm 2$, and $\Delta M_F=0\mathrm{}$. The repulsion between these levels is very small, of the order of a few Mc/sec. This causes the noncrossing rule of von Neumann and Wigner to be violated experimentally. The Landau-Zener theory of level crossings is applied. It is shown that the observed loss of quantization in the molecular-beam experiments is consistent with theory.

A general asymptotic expression for the energy separation $\Delta \mathrm{}\left(R\right)\mathrm{}$ of the symmetrical and antisymmetrical states in the ($A^{-},A$) system is derived. A great influence of the atomic short-range forces on $\Delta \mathrm{}\left(R\right)\mathrm{}$ has been found. At large values of the atomic effective range $r_0$, the present expression for $\Delta \mathrm{}\left(R\right)\mathrm{}$ leads to the previous result of the authors, and for small $r_0$, a Smirnov-like behavior of the molecular term splitting is obtained. As an application of the result obtained for $\Delta \mathrm{}\left(R\right)\mathrm{}$, the resonant charge transfer in ${\mathrm{O}}^{-}$-O collisions is calculated and a comparison with the experimental data is made.

A variational principle possessing a minimum, i.e., $I=\int ({\mathfrak{L}G-X)}^2\mathrm{dr}\ge 0$, is examined for the case of an electron scattered off the static field of hydrogen with and without exchange effects. $\mathfrak{L}=H-E$, where $H$ may be either an effective one-electron Hamiltonian or the total Hamiltonian operator, and $X$ contains the exchange interactions. The positive definite character of $I$ eliminates the occurence of false resonances which appear in the Kohn and Hulthén procedures. Bounds on the phase shift based on Kato's identity and related to $\int |\mathfrak{L}G-X| \mathrm{dr}$ are derived which are useful in estimating the error in the phase shifts not only for the Kohn and Hulthén variational principles, but also in the one proposed. Through Schwartz's inequality, these bounds are also related to $\sqrt{I}$.

Measurement of the total cross section for electron transfer between a ground-state singly ionized helium atom and a ground-state helium atom has been made in the energy range 2-22 keV. The method used was that of collection of the slow ions produced by the charge transfer process. The collection was made via parallel plates with an electric field imposed perpendicular to the ion beam. The results are estimated to be accurate to 5%. The data are compared with the theories of Rapp and Francis; Sural, Mukherjee, and Sil; and Moiseiwitsch.

In this article we analyze the quenching of metastable hydrogen atoms by helium in the energy range below roughly 250 eV. Two methods are discussed. In one, a perturbation-theory approach is used; in the other, a pseudopotential is employed which attempts to relate the quenching matrix elements to low-energy-electron elastic scattering data. At thermal energies, both methods predict very large quenching cross sections. The pseudopotential approach gives a result of about $80\pi a_0^2$ while the perturbation analysis yields $40\pi a_0^2$. As one goes to higher energies, the cross sections decrease, with the pseudopotential result falling off much less rapidly than the perturbation-theory result. Reasonable agreement between experiment and the pseudopotential method is found at about 300 eV, which is the lowest energy experimentally available at present.

The scattering of ${\mathrm{Be}}^{++}$ ions of energy 100-800 eV by He has been measured by observing the energy-loss spectrum of the ions on traversing various path lengths of the scattering gas. The scattering data have been analyzed to determine an interaction energy for ${\mathrm{Be}}^{++}$ and He for the internuclear separations from 0.15 to 1.0 Å. While not strictly logarithmic, the results can be approximately fitted by an expression for the interaction which is $V\left(r\right)=6.0\mathrm{}\times {10}^2\times e^{-5.70r}$ eV, with $r$ in Å. A Thomas-Fermi-Dirac calculation of the interaction energy fits the experimental result well for $r>\mathrm{}0.3\mathrm{}$ Å.

The various possible ground-state structure factors are defined for a multispecies quantum fluid. These structure factors are then used to construct the Born approximation to the scattering cross sections for the multispecies fluid. The cross sections are used in conjuction with the results of an earlier paper to discuss the scatering of (i) charged particles, (ii) neutrons, and (iii) x rays from a two-species system composed of electrons and nuclei at high densities.