The third-harmonic coefficient of an atom is obtained in terms of zeroth-, first-, and second-order wave functions. The results of an accurate variations calculation of the third-harmonic coefficient of helium is presented. The zero-frequency third-harmonic coefficient is 42. 8 a. u. which is identical to the static hyperpolarizability obtained by Grasso, Chung, and Hurst. The $1s^2\to 1s2p$ transition wavelength is determined to be 582 Å compared with the experimental result of 584 Å.

The linked-cluster many-body perturbation theory has been applied to small heteronuclear diatomic molecules using a variational Hartree—Fock molecular-orbital basis set. This procedure has been applied to study the isotropic hyperfine interaction in the ${}_{}{}^2{}_{}{}^{}\Pi$ ground state of the free radical ${\mathrm{O}}^{17}$H and to the magnetic shielding of ${\mathrm{H}}^1$ and ${\mathrm{F}}^{19}$ in the HF molecule. These investigations have led to a number of physical conclusions about the influence of correlation and exchange polarization effects on the isotropic hyperfine interactions in OH. The calculated shielding parameters and hyperfine constants were found to be in better than 15% agreement with experimental data wherever available.

The hyperfine pressure shift of the metastable helium ($1s2s:{}_{}{}^3{}_{}{}^{}S$) in a buffer gas consisting of ground-state helium atoms is studied by the linked-cluster many-body perturbation approach. Owing to the existence of the repulsive barrier in the intermolecular potential of this system at sizable intermolecular separation, the main contribution to the hyperfine pressure shift comes from the long-range attractive region of the van der Waals potential and the contribution from the short- and intermediate-range region may be neglected. We calculate a shift of -15.0 × ${10}^{-9\mathrm{}}$/torr, in essential agreement with the experimental value of (-7.4 ± 3.0) × ${10}^{-9\mathrm{}}$/torr.

Screening corrections to the muon binding energies are computed for Pb, Tl, Ba, and O. Available methods of calculation are compared. It is shown that in a broad range of atomic charges and muon states the screening of nuclear charge by the muon is almost complete, and therefore the electron density of the $Z-1\mathrm{}$ element can be used in most applications. The effect of the muon on the electron cloud and the effect of the vacancies in electron shells on the screening corrections are calculated and discussed. The degree of ionization of the electron $1s_{\frac{1}{2}}$ orbit is determined by a cascade calculation including repopulation from the $2p$ shell.

Excited electronic states of the $\mathrm{O}_2^{}{}_{}{}^{-}$ molecule have been calculated with configuration-interaction (CI) variational trial functions that assure formally correct asymptotic behavior as well as the single-configuration self-consistent-field (SCF) approximation. CI results were obtained by both multiconfiguration self-consistent-field (MC-SCF) and pseudonatural orbital (PNO) techniques. The MC-SCF results are most accurate and are used to analyze the energy curves and wave functions of these states for internuclear separations larger than 3 a. u. All the excited states are found to have equilibrium-internuclear separations at least 1 a. u. larger than the ground state. The two lowest energy states, the ${}_{}{}^4{}_{}{}^{}\Sigma _u^{-}{}_{}{}^{}$ and ${}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, are characterized, respectively, as shape and valence Feshbach resonances. They are sufficiently bound to make it likely they play a role in low-energy-electron scattering by oxygen.

This paper constitutes a continuation of previous work on magnetic interactions of one-electron atoms. In earlier papers the magnetic moment of a hydrogenic atom in its ground state was calculated, including radiative and nuclear-mass corrections. In this work the $g_J$ and $g_I$ factors are calculated for arbitrary hydrogenic states, including radiative and nuclear-mass corrections. The magnetic moment of a hydrogenic atom is obtained for any state. An extensive analysis of the Zeeman levels of positronium is carried out for the $n=1\mathrm{}$ and $n=2\mathrm{}$ states, including higher-order corrections. For the $n=1\mathrm{}$ state, the results confirm the validity of the Breit—Rabi formula with $g$ factors in agreement with those given in an earlier paper by Grotch and Hegstrom. The annihilation diagram is included in the analysis but does not lead to any additional correction terms (to the accuracy we are working with). The Zeeman corrections in the $n=1\mathrm{}$ state are relevant to the precise experimental determination of the positronium hyperfine structure. The analysis of the $n=2\mathrm{}$ state Zeeman structure of positronium is similar to that carried out by Brodsky and Parsons for the $n=2\mathrm{}$ states of hydrogenic atoms. Although the results in the hydrogenic case were immediately applicable to Lamb-shift measurements, the present results are not yet applicable since at present there is no experimental data on the excited states of positronium.

The foil-excitation technique has been used to study atomic lifetimes in multiply charged ions at moderate ion energies (i. e., below 1 MeV). The emission spectra of foil-excited ion beams of gallium, germanium, arsenic, and selenium at 450-keV initial ion energy showed low-lying transitions in Ga II, Ga III, Ge III, Ge IV, As IV, As V, Se V, and Se VI with sufficient spectral intensity for lifetime determinations. In the Cu I sequence, seven lifetimes of transitions in Ga III through Se VI have been measured, while for the Zn I sequence, eight lifetimes of singlet and triplet levels in Ga II through Se V have been reported. Systematic trends in $f$ values for $4s{}_{}{}^2{}_{}{}^{}S-4p{}_{}{}^2{}_{}{}^{}P$ and $4p{}_{}{}^2{}_{}{}^{}P-4d{}_{}{}^2{}_{}{}^{}D$ transitions in the Cu I sequence and for $4s^2{}_{}{}^1{}_{}{}^{}S-4s4p{}_{}{}^1{}_{}{}^{}P$ and $4s4p{}_{}{}^3{}_{}{}^{}P-4s4d{}_{}{}^3{}_{}{}^{}D$ transitions in the Zn I sequence have been studied and compared with similar trends in the Na I and Mg I sequences. Based upon the experimental results, $f$ values for transitions in Br VII through Sr X and Br VI through Sr IX have been found by extrapolation and compared with theoretical and experimental results for homologous atoms with lower masses.

This work reports multiphoton ionization and dissociation of molecular hydrogen under the influence of laser radiation at 0.53 $\mu$. The six-photon ionization probability of hydrogen atoms is derived for laser radiation acting upon atomic hydrogen from a molecular hydrogen beam which is up to 80% dissociated by radio-frequency power. The experimental six-photon ionization probability of atomic hydrogen has been found to be in good agreement with the corresponding probability calculated using time-dependent perturbation theory if the statistical properties of the incident light are taken into account.

Absolute total cross sections for D-He scattering were measured with an accuracy of 1% at 0.3, 0.5, and 0.6 eV. These new data were combined with published relative measurements of the velocity dependence of the H-He cross section in a ${\chi }^2$ minimalization procedure. The resulting potential $V\left(R\right)\mathrm{}$ as function of internuclear separation $R$ is precisely determined in the repulsive range $1.7\mathrm{\AA }<R<\mathrm{}{R}_0$ with $V\left(R_0\right)=0\mathrm{}$. Several multiparameter potential models were tried. Of these the four-parameter ansatz $V\left(R\right)=A(e^{-\alpha R}-e^{-\alpha R_0})$ $(\mathrm{for} R<\mathrm{}{R}_0)=4\mathrm{}\epsilon [{\left(\frac{R_0}{R}\right)}^{12}-{\left(\frac{R_0}{R}\right)}^6]$ (for $R>\mathrm{}{R}_0$) was found to describe the data best. Parameters obtained are $A=70.00\mathrm{}$ eV, $\alpha =3.383\mathrm{}$ ${\mathrm{\AA }}^{-1\mathrm{}}$, $R_0=3.20\mathrm{}$ Å, and $\epsilon =0.39\mathrm{}$ meV. The well depth $\epsilon$, to which the measurements are insensitive, is chosen to match the theoretical van der Waals constant $C_6=2.83\mathrm{}$ a. u. The potential is compared with results of $\mathrm{ab}$ initio calculations, and a probable $\epsilon$ range is discussed. For $0.35\lesssim \epsilon \lesssim 0.70$ meV the calculated low-energy cross section shows a pronounced Ramsauer-Townsend minimum. The possibility of its observation is pointed out.

A simple application of the Stark-pulse technique, developed by Brewer and Shoemaker, demonstrates optical free induction decay-the optical analog of free induction decay in NMR. A molecular sample which is coherently prepared by a cw laser beam exhibits such a decay when it is suddenly switched out of resonance by a Stark field. Observations are presented for a nondegenerate Doppler-broadened infrared transition of N${\mathrm{H}}_2$D, where the sample is optically thin, and the decay behavior can be compared quantitatively with a solution of the Bloch equations. When the molecular sample is prepared under steady-state conditions, the solutions are analytic; for pulse excitation, a numerical solution is required. The treatment invokes a hard-collision relaxation model. Such characteristics as the abrupt termination of the decay and the related edge echo, which result from Doppler dephasing, can be examined for Stark pulses of finite extent.

The spectral moments of ir and Raman bands of diatomic molecules in inert solutions are calculated by the help of recent stochastic theories of ir- and Raman-band profiles. Both vibrational and rotational motions are considered. It is found that for ir and rotational Raman bands, the stochastic theories produce expressions for the band moments which closely parallel the corresponding thermodynamic expressions. New expressions are proposed for the moments of isotropic and of vibrational-rotational anisotropic Raman bands.

The hyperfine structure (hfs) of the $J=6\mathrm{}$ member of the $4f^{6}6s^2{}_{}{}^7{}_{}{}^{}F$ ground multiplet of ${}_{}{}^{147,149}{}_{}{}^{}\mathrm{Sm}$ has been measured by the atomic-beam magnetic-resonance technique, and that of the $J=1-5\mathrm{}$ states has been remeasured. The magnetic-dipole and electric-quadrupole hyperfine-interaction constants obtained, after correction for second-order hfs, are found to be consistent to a very high order with the three-parameter formulation of the Sandars-Beck effective-operator theory of hfs and with the Conway-Wybourne eigenvectors for the $J=1-6\mathrm{}{}_{}{}^7{}_{}{}^{}F$ states of Sm. The earlier apparent failure of these eigenvectors to be consistent with the magnetic dipole hfs of the ${}_{}{}^7{}_{}{}^{}F$ states with $J=1-5\mathrm{}$ is now resolved.

The calculations were based on fitting radial parameters to the observed energy levels, but with a requirement of regularity in the behavior of each parameter value along the isoelectronic sequence. Some parameters or ratios of parameters were fixed at values based on isoelectronic comparisons or adjusted Hartree-Fock values. The calculated levels, $g$ values, and $\mathrm{LS}$ percentage compositions are given for each atom, and comparisons with experimental data are made. The results support new $5d^{9}6s^{2}6p$ levels recently found in Hgi, Tlii, and Biiv, and one experimental $5d^{9}6s^{2}6p$ level in Pb iii is rejected as unreal. The calculated ratio of the lifetimes of the Hgi $5d^{10}6s6p{}_{}{}^3{}_{}{}^{}P_1^0{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}P_1^0{}_{}{}^{}$ levels is compared with the experimental value. Some comparisons of calculated and observed isotope shifts are made for Hgi, Tlii, and Pbiii. The leading percentages in the $\mathrm{jj}$ coupling scheme are listed for levels having assigned $\mathrm{jj}$ names ($5d^{9}6s^{2}6p$ levels in all four atoms and $5d^{10}6s7p$ levels in three atoms).

Estimated values for the fluorescence yields for various atomic configurations of the carbon atom and the calculated energy shifts of the x rays resulting from these initial configurations are presented. These results are used in conjunction with recent results concerning the probability of multiple ionization as a function of the incident proton energy to give a more detailed analysis of the variable fluorescence yield observed and presented in an earlier publication.

The Harris-Nesbet algebraic close-coupling method is used to calculate the $S$-wave phase shift and positronium-formation cross section for various types of close-coupling expansions of the total wave function. The positronium channels are included explicitly, and polarization effects, in both the hydrogen and positronium atoms, are incorporated by pseudostates that give the correct static polarizabilities.

Quantitative predictions for atomic-electron screening effects in low-energy pair production follow from the knowledge that the small-distance shape of screened-electron and positron continuum wave functions is close to that of point-Coulomb wave functions of shifted energy. These predictions are verified by making exact numerical calculations in representative cases. The energy-shift normalization theory is then used in conjunction with the point-Coulomb results of Øverbø to obtain predictions for atomic-pair-production energy distributions and total cross sections for photon energies from threshold to 5 MeV. Atomic-electron screening effects cause appreciable modifications of the total cross sections for photon energies below 1.5 MeV and continue to have a major effect on some portions of the energy distribution at higher photon energies. Results are also compared with Bethe-Heitler predictions and with experiments.

It is shown, for a model in which the nuclear-charge distribution is that of a uniformly charged sphere of radius $R$, that the isotope or isomer shift is proportional to $R^k$ where $k=1+{(1-{\alpha }^2{Z}^2)}^{\frac{1}{2}}$.

The problem of the Fourier transform of the response to a $\frac{\pi }{2}$ pulse of a single nucleus of spin ½ interacting with a strong rf field is examined theoretically using the density-matrix master equation. In this experiment the nuclear spins are polarized in the rotating frame along a direction different from the laboratory $z$ axis. It is shown that the resulting Fourier-transform spectrum differs in intensities from the steady-state double-resonance spectrum—in contrast with the usual single-resonance case. This phenomenon is understood physically in terms of a rotating-frame model.

Analytic Hartree-Fock-Roothaan calculations have been carried out for the states arising from the $3d^{n}4s^2$ configurations for neutral transition-metal atoms and from the $3d^n$ configurations for the doubly ionized ions. The atomic orbitals have been expanded in terms of linear combinations of Slater-type functions, 21 of them for the neutral atoms and 18 for the doubly ionized ions.

For a nonrelativistic quantal particle moving with the angular momentum $l=0\mathrm{}$ in a spherically symmetric, smooth potential well, which in the neighborhood of the center of force gives rise to an attractive Coulomb force, a formula for the probability density of the particle at the center of force is derived by means of certain phase-integral approximations of an arbitrary order. From this formula, which is expected to be very accurate, the non-relativistic approximation of the Fermi-Segrè formula for the probability density of finding an $s$ electron at the nucleus of an atom or ion is obtained. The limits of validity of the Fermi-Segrè formula in the nonrelativistic approximation are clarified by this derivation.