A hydrogen maser operating at fields of up to 16 G has been used as a spin-exchange detector of Zeeman transitions in the hyperfine spectra of hydrogen and tritium. The maser oscillates on the field-dependent $\pi$ transition which is sensitive to the state of colliding atoms. Atomic magnetic moment or $g_J$-factor ratios were obtained from the measured Zeeman frequencies with the aid of the Breit-Rabi formula. Measurements were made at different values of magnetic field and an extrapolation was done to eliminate the effects of spin-exchange frequency shifts. The result is $\frac{g_J\mathrm{}\left(H\right)\mathrm{}}{g_J\mathrm{}\left(T\right)\mathrm{}}=1+(10.7\mathrm{}\pm 1.5)\times {10}^{-9\mathrm{}}$, in agreement with the theoretical predictions.

A theoretical model is described for calculating energy shifts of Auger satellites— Auger transitions that occur in the presence of "spectator" vacancies. The shifts arise through a combination of direct and indirect (or relaxation) interactions between spectator and regular hole states. Both can be expressed in terms of two-electron Coulomb and exchange integrals, and approximate pairwise additivity of the shifts owing to holes or spectator vacancies is demonstrated. An approximate method, based on the "equivalent-cores" approximation, is employed to estimate numerical values of the indirect term using only tabulated two-electron integrals for atomic ground states. Satellite shifts for the $L_3{M}_{45}{M}_{45}\left(M_{45}\right)$ transition are thereby estimated for elements with $70\le Z\le 100$. The predicted value of -38 eV for bismuth is in excellent agreement with the experimental value -36 ± 5 eV reported for ${}_{}{}^{210}{}_{}{}^{}\mathrm{Bi}$ by Haynes, Velinsky, and Velinsky. For americium the predicted value is -61 eV; Freedman and Porter reported an experimental value -56 eV. Other predicted satellite shifts in bismuth also show reasonably good agreement with less accurate experimental values. These results thus strongly support previous interpretations of satellite shifts and appear to provide a fairly accurate and very easy method for predicting these shifts in deep core levels.

Assuming that there exists a correspondence between the methods of the superposition of configurations and linked-cluster perturbation-theory expansions, a method of successive approximations was used to generate the coefficients of the superposition-of-configurations expansion and the correlation energy of a many-electron wave function. The algorithm was applied to the ground state of Be. Using an excited $s$, $p$, $d$ orbital basis set calculated in the $V^N$ potential, and estimating the truncation error of the remaining pair-correlation energies of the partial-wave expansion, a correlation energy of -0.09312 a.u. was obtained.

Measurements are reported on the ratio of forward to back scattering of electrons in the energy range 3-20 eV by He, O, Ar, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$ using the modulated crossed-beam technique. It is found that atomic oxygen has strong forward scattering at the lower energies. Agreement is found between the present results for He, Ar, ${\mathrm{H}}_2$, and ${\mathrm{N}}_2$ and ratios calculated from previously published differential-cross-section measurements except for ${\mathrm{H}}_2$ and ${\mathrm{N}}_2$ at the lower-energy limit.

Equilibrium and pre-equilibrium charge-state distributions have been measured for ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ recoils at a velocity of 11.1 × ${10}^8$ cm/sec from ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}\mathrm{}(d,d)\mathrm{}$ elastic scattering in natural boron targets. A coupled set of linear differential equations describing the capture and loss of electrons has been derived for ions recoiling from nuclear processes in solids. It has been used to obtain electron-capture and -loss cross sections from the ${}_{}{}^{11}{}_{}{}^{}\mathrm{B}$ recoil data. The results are consistent with the existence of very little two-electron capture or loss and, when compared with previous results in gaseous media, do not show any pronounced effects of residual-ion excitation.

Systematic measurements of $\frac{K\beta }{K\alpha }$ intensity ratios have been carried out for a wide range of targets ($19\le Z\le 47$) using 2.35- to 12.5-MeV/amu deuterons, $\alpha$ particles, and carbon ions. Radiative-transition probability ratios were calculated for various $L$- and $M$-shell vacancy configurations using Hartree-Fock-Slater wave functions. Employing information previously obtained on simultaneous $K$- plus $L$-shell ionization, the velocity dependence of the simultaneous $K$- plus $M$-shell ionization probability was characterized and compared with the velocity dependence expected for ionization by direct Coulomb excitation.

The fluorescence yield for a beryllium atom in the vacancy state $1s{\mathrm{}\left(2s\right)\mathrm{}}^2{}_{}{}^2{}_{}{}^{}S$ is calculated. The radiative decay rate is shown to arise from correlation effects. The fluorescence yields for the $1s2s2p{}_{}{}^2{}_{}{}^{}P$ vacancy states are also calculated and found to be very large.

An expansion of the three-body Coulomb potential in generalized angular-momentum eigenfunctions developed earlier by one of the authors is used to compute energy eigenvalues and eigenfunctions of bound $S$ states of three-body Coulomb systems. The results for He, ${\mathrm{H}}^{-}$, $e^{-}{e}^{+}{e}^{-}$, and $p{\mu }^{-}p$ are compared with the results of other computational approaches.

Resonances in the $e-{\mathrm{O}}_2$ total cross section in the energy range 50-300 meV were studied with a high-resolution ($\Delta E<\mathrm{}10\mathrm{}$ meV) electron time-of-flight spectrometer. Each vibrational resonance was found to have a well-resolved doublet structure, which has not previously been observed, and which is due to spin-orbit coupling in the ${}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ ground state of ${\mathrm{O}}_2^{-}$. The spin-orbit coupling constant of ${\mathrm{O}}_2^{-}$ was measured to be $\mathrm{}\left|A\right|=20\mathrm{}\pm 2 \mathrm{meV}=161\mathrm{}\pm 16 {\mathrm{cm}}^{-1\mathrm{}}$, in agreement with theoretical estimates. On an energy scale established from the measured electron flight times, the energy of the center of the $v^{\prime }=4\mathrm{}$ resonance was measured to be 91 ± 5 meV. This value is in agreement with a recent photodetachment measurement of the electron affinity of ${\mathrm{O}}_2$, and with a previously observed accidental coincidence between the $v=3\mathrm{}$ level of ${\mathrm{O}}_2$ and the $v^{\prime }=8\mathrm{}$ level of ${\mathrm{O}}_2^{-}$. The electron time-of-flight spectrometer is described in detail.

The photoelectron spectra as the result of photoionization in the various subshells of Ar, Kr, and Xe have been studied using $\mathrm{Al}K\alpha$ (1487 eV), $\mathrm{Mg}K\alpha$ (1254 eV), and in some cases $\mathrm{Zr}{M}_{\zeta }$ (151 eV) x rays. In addition to the main photoelectron peaks there appears satellite structure at slightly lower kinetic energy. When photoionization occurs in the core levels, this structure can be explained as an electron shakeup in terms of the sudden approximation, and the experimental results are compared with Hartree-Fock calculations of the expected excited states. When photoionization occurs in the valence shell, two-electron excitations leading to the configuration-interaction states $n{s}^{2}n{p}^{4}n{d}^1{}_{}{}^2{}_{}{}^{}S$ are found to be the dominant processes. Photoelectron spectra were also taken of the valence shell of solid alkali-metal halides, and the satellite structure compared with that of the rare gases. From our results similar phenomena seem to occur with the alkali-metal ions, although the intensities are greater than in the case of the rare gases.

The effect of ${\mathrm{Hg}}_2$-Hg collisions on the formation and decay of excited ${\mathrm{Hg}}_2\left({}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}\right)$ and ${\mathrm{Hg}}_2\left({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\right)$ molecules in Hg-${\mathrm{N}}_2$ mixtures was investigated in a series of delayed-coincidence experiments. $\mathrm{Hg}\left({}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}\right)$ atoms, formed by irradiating the vapor-gas mixture with pulses of Hg (2537 Å) resonance radiation, were transferred collisionally to the ${}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}$ state. The ${\mathrm{Hg}}_2\left({}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}\right)$ molecules, formed in subsequent $\mathrm{Hg}\left({}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\right)+\mathrm{Hg}\left({}_{}{}^3{}_{}{}^{}P_0^{}{}_{}{}^{}\right)+{\mathrm{N}}_2$ collisions, underwent collisional ${}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}$ mixing. The time-decay spectra of the 3350 and 4850-Å fluorescent bands, associated with the ${}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}$ states, respectively, were studied in relation to ${\mathrm{N}}_2$ and Hg densities and the resulting decay constants were extrapolated to zero ${\mathrm{N}}_2$ and Hg pressures, yielding the following total cross sections $Q(A\to B)$ for collisional transfer between states $A$ and $B$. For ${\mathrm{Hg}}_2$-${\mathrm{N}}_2$ collisions: $Q({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})=2.3\mathrm{}\times {10}^{-21\mathrm{}}$ ${\mathrm{cm}}^2$; $Q({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\leftarrow {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})=6.9\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$; for ${\mathrm{Hg}}_2$-Hg collisions: $Q({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\to {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})=2.2\mathrm{}\times {10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$; $Q({}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}\leftarrow {}_{}{}^3{}_{}{}^{}1_u^{}{}_{}{}^{})=6.8\mathrm{}\times {10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$. The radiative lifetime ${\tau }_4^0$ of the ${}_{}{}^3{}_{}{}^{}0_u^{-}{}_{}{}^{}$ state was found to be 21.4 msec ± 7%.

Absolute cross sections and excitation functions have been measured for Zn $K$-x-ray production by proton impact and for Pb $L$-x-ray production by proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-ion impact over the bombarding energy range from 1.4 to 4.4 MeV using a Si(Li) detector. The total ionization cross sections for the Zn $K$ shell and x-ray production cross sections for the Pb $L$ shell obtained are compared with the binary-encounter approximation (BEA) and the plane-wave Born approximation calculations and the agreement is found to be good. X-ray production ratios, such as $\frac{L\alpha }{L\beta }$ and $\frac{L\alpha }{L\gamma }$, for Pb are also compared with the BEA calculations. The cross-over behavior of the $Z_1$ (projectile nuclear charge) dependence of the x-ray production cross sections was studied for the Pb $L$ lines.

Using a previously developed semiclassical theory of electronic excitations, the cross sections that result from potential-curve crossings are calculated for a model system. The phenomena appearing in the differential cross sections are displayed and discussed.

A theory, which exhibits the characteristic features of scatterings initiated by two coherent beams, is discussed in the present paper. We show that the imaginary part of the scattering amplitude is an experimentally measurable quantity. To know the imaginary part of the amplitude is quite important for certain aspects of quantum mechanics, for example, the dispersion relation for a fixed momentum transfer. This relation has not yet been experimentally verified.

The modified effective-range theory, which has enjoyed great success in its application to electron-atom scattering, is hereby extended to electron scattering from molecules. An analytic expression for the diffusion cross section for molecules in any rotational state is obtained. It is utilized to analyze the detailed results of recent swarm experiments on ${\mathrm{H}}_2$, and to comment on the less-detailed experimental results on ${\mathrm{D}}_2$, ${\mathrm{N}}_2$, and ${\mathrm{O}}_2$.

We report neutron-scattering measurements of the coherent scattering function $S(Q,\omega )$ of liquid rubidium at 315 K, in the range of wave vectors $1.25\le Q\le 5.5$ ${\mathrm{\AA }}^{-1\mathrm{}}$. In this range there is no evidence of peaks at finite $\omega$ in $S(Q,\omega )$ plotted at constant $Q$. On the other hand the Fourier transform $F(Q,t)\mathrm{}$ exhibits structure, notably for $Q=2.0\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, which indicates at least two characteristic (wavelength-dependent) relaxation times in the liquid. For wave vectors >3.0 ${\mathrm{\AA }}^{-1\mathrm{}}$, $F(Q,t)\mathrm{}$ may be characterized by a single relaxation time. These results, in conjunction with our results for $Q<\mathrm{}1.0\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, offer the possibility of detailed comparisons with models of the liquid state and with molecular-dynamics calculations.

Molecular-dynamics (MD) calculations on liquid rubidium at 46 °C and 1.502 g ${\mathrm{cm}}^{-3\mathrm{}}$ have been made using a suitable pair potential. Whereas for wave number $\kappa <1.2\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$ propagating density fluctuations were obtained, only overdamped nonpropagating fluctuations are found for larger $\kappa$. For all $\kappa$ there is good agreement with recent neutron inelastic-scattering experiments. The mean-square acceleration given by MD is found to be much larger than the value derived from another neutron experiment extending over $\kappa =4\mathrm{} \mathrm{to} 8$ ${\mathrm{\AA }}^{-1\mathrm{}}$; the reason for the discrepancy is analyzed to show that the neutron-scattering data cannot be interpreted in terms of the mean-square acceleration alone.

The effect of fluctuations on a Landau-Ginzburg model of a first-order phase transition in one dimension is studied. Extremely sharp pseudotransitions can be obtained. The critical region or width of the transition is found to vanish exponentially with the effective number of interacting units across a cross section of the system. The results are physically interpreted in the context of the Landau-Lifschitz proof that phase equilibrium is impossible in one dimension.

Several aspects of the mode-coupling description of the long-time behavior of the autocorrelation function corresponding to the mutual- and self-diffusion coefficients are investigated. Our calculations of the generalized diffusion coefficient are carried out by employing a set of linear, bilinear, and trilinear variables in the generalized Langevin equation. The diffusion coefficient is expressed in terms of a bare diffusion coefficient and a frequency- and wave-number-dependent nonlinear transport coefficient, which in turn can be written as a bare nonlinear transport coefficient plus a frequency- and wave-number-dependent term. We discuss the validity of calculations that take into account only bilinear coupling. For the case of test-particle diffusion, we examine the structure of the transport coefficients that enter in the mode-coupling calculation by making use of the techniques in the density expansions of transport coefficients. By summing a certain class of collisions to all orders in the density, we show how that part of the bare diffusion coefficient which corresponds to a cross correlation between the test-particle momentum and that of the bath exactly cancels that part of the velocity-autocorrelation function that gives rise to the long-time tail. The bare nonlinear transport coefficient is also examined.

The optimized cluster theory is applied to the Lennard-Jones fluid. The coexistence curve obtained from the theory is presented. It represents the most accurate microscopic calculation of the liquid-gas phase diagram for a fluid with a realistic Hamiltonian. The theory is shown to be quantitatively accurate for all fluid states except those very close to the critical point. Phenomenological procedures are devised which extrapolate towards the critical point from regions in which the optimized cluster theory is accurate. The extrapolation calculations predict nonclassical values for the critical exponents which are in fairly good agreement with experiment. In addition to investigating the liquid-gas phase transition, the equilibrium pair correlation functions are calculated at several states. Further, the internal consistency of the optimized cluster theory is discussed.