Combined configuration-interaction-Hylleraas method techniques have been employed in obtaining three-electron ${}_{}{}^2{}_{}{}^{}S$ and ${}_{}{}^2{}_{}{}^{}P$ wave functions. The four lowest $\left(1\mathrm{}{s}^{2}ns\right) {}_{}{}^2{}_{}{}^{}S$ wave functions are obtained in the same 150-term basis. The calculated energies are -7.478 02, -7.354 01, -7.318 40, and -7.303 40 a.u. compared to the respective corrected experimental results -7.478 07, -7.354 10, -7.318 53, and -7.303 55 a.u. In addition, the four lowest $\left(1\mathrm{}{s}^{2}np\right) {}_{}{}^2{}_{}{}^{}P$ wave functions are obtained in the same 120-term basis. The calculated energies are -7.410 05, -7.337 00, -7.311 74, -7.300 14 a.u. compared to the respective corrected experimental results -7.410 16, -7.337 16, -7.311 90, -7.300 30.

Bound-state relativistic contributions to the $g_J$ factor of ground-state atomic lithium are calculated and compared with the experimental value $\frac{g_J\left(\mathrm{Li}\right)}{g_e}=1-(8.9\mathrm{}\pm 0.4)\times {10}^{-6\mathrm{}}$, where $g_e$ is the free-electron $g$ factor. This comparison is taken as the basis for judging the accuracy of several different Li wave functions taken from the literature. Most of these wave functions give agreement with the experimental value within the experimental uncertainty. A more precise experimental measurement would be desirable in order to provide a more stringent test. A wave function of the restricted Hartree-Fock type, however, leads to a value which is in disagreement with the experimental value. This is attributed to the inability of the restricted Hartree-Fock function to account for the exchange polarization of the $1s^2$ core electrons; the latter are found to contribute about -1.2 × ${10}^{-6\mathrm{}}$ to $\frac{g_J\left(\mathrm{Li}\right)}{g_e}$, or about 13% of the total relativistic correction. In addition to the dominant relativistic corrections of order ${\alpha }^2$, radiative corrections (order ${\alpha }^3$), and nuclear-mass corrections (order $\frac{{\alpha }^{2}m}{M}$) are also calculated. An isotopic shift $\frac{g_J\left({}_{}{}^6{}_{}{}^{}\mathrm{Li}\right)}{g_J\left({}_{}{}^7{}_{}{}^{}\mathrm{Li}\right)}=1+3.0\mathrm{}\times {10}^{-11\mathrm{}}$ is predicted. The experimental measurements for Li are not yet precise enough to test these higher-order corrections.

A microwave-optical-pulsing and trapping technique has been employed to observe Lamb-shift ($\mathcal{S}=2\mathrm{}{S}_{\frac{1}{2}}\to 2P_{\frac{1}{2}}$) transitions in ${}_{}{}^6{}_{}{}^{}\mathrm{Li}_{}^{2+}{}_{}{}^{}$. Microwave transitions were induced in trapped metastable ${\mathrm{Li}}^{2+}\left(2\mathrm{}{S}_{\frac{1}{2}}\right)$ ions produced beforehand by a pulsed electron beam incident upon a low-pressure lithium vapor. Resonances were observed in the soft x-ray decay light as an applied magnetic field was swept through the Zeeman transition frequency. Computer fitting of 76 line centers yields $\mathcal{S}=62\mathrm{}765\pm 21$ MHz, in good agreement with theory.

Bounds to the emission probability and lifetime are calculated for the Ar XVII $2 {}_{}{}^3{}_{}{}^{}S$ state using Drake's form of the magnetic dipole transition operator. Variational wave functions of increasing quality lead to theoretical error bounds of about 0.24%, thereby sharpening the discrepancy between theoretically and experimentally determined lifetimes.

Quantum-mechanical examples have been constructed of local potentials with bound eigenstates embedded in the dense continuum of scattering states. The method employed corrects and extends a procedure invented by von Neumann and Wigner. Cases are cited whereby deformation of the local potential causes the continuum bound state to move downward through the bottom of the continuum, and to connect analytically to a nodeless ground state. A doubly excited model atom is also displayed, with interactions between its two "electrons," having an infinite lifetime (in the Schrödinger equation regime). In the light of these examples, attention is focused on quantitative interpretation of real tunneling phenomena, and on the existence of continuum bound states in atoms and molecules.

The hyperfine structures of the $8{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ and $9{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ states of ${}_{}{}^{87}{}_{}{}^{}\mathrm{Rb}$ and of the $12{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state of ${}_{}{}^{133}{}_{}{}^{}\mathrm{Cs}$ have been measured by the method of stepwise excitation spectroscopy using a cw dye laser. We measure the magnetic dipole coupling constants to be $A(8\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}, {}_{}{}^{87}{}_{}{}^{}\mathrm{Rb})=159.2\mathrm{}\pm 1.5$ MHz, $A(9\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}, {}_{}{}^{87}{}_{}{}^{}\mathrm{Rb})=90.9\mathrm{}\pm 0.8$ MHz, and $A(12\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}, {}_{}{}^{133}{}_{}{}^{}\mathrm{Cs})=26.31\mathrm{}\pm 0.10$ MHz.

Beam-foil measurements of the lifetimes of the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state in heliumlike sulphur and chlorine are reported. A Doppler-tuned x-ray spectrometer was used to detect the x rays emitted from the $1{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}\leftarrow 2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ transition. Time-of-flight techniques were used to trace the decay profile of the emitted x rays for 38-55-MeV sulphur and chlorine beams over flight paths of 56-861 cm. For foil-to-detector flight times greater than one half the theoretical lifetimes of 698 nsec (sulphur) and 374 nsec (chlorine), the respective experimental lifetimes of 706 ± 86 and 354 ± 24 nsec are in agreement with theory. For shorter flight times the experimental decay profiles are not single exponentials. This experimental effect is the source of the previously reported discrepancy between experimental and theoretical lifetimes of the $2{}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$ state in heliumlike chlorine.

Delayed x-ray emission has been observed in highly ionized oxygen for both the $1s-np$ H-like (Lyman) and the $1s^2-1\mathrm{snp}$ (${}_{}{}^1{}_{}{}^{}S-{}_{}{}^1{}_{}{}^{}P$) He-like sequence. Within less than 0.5 nsec after formation, the shapes of the decay curves for all the measured transitions were found to be similar, each following a power-law time dependence. This nonexponential shape for the decay curves is attributed to cascade effects from states near the ionization limit.

Lifetimes of the lowest, most metastable, autoionizing quartet state ($1s2s2p$) ${}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}$ of the lithiumlike ions ${\mathrm{Al}}^{10+}$ and ${\mathrm{Si}}^{11+}$ have been measured by the electron spectrometric, time-of-flight technique and are found to be 2.9 ± 0.2 and 2.1 ± 0.1 nsec, respectively. These results can be compared to very recent Dirac-Hartree-Fock lifetime calculations of Cheng, Lin, and Johnson which give 2.58 and 1.84 nsec, respectively. Comparison of our experimental results for the sequence $Z=8, 9, 13, 14, 16, 17, \mathrm{and} 18$ with the new theoretical calculations are now possible with the result that the measured lifetimes tend to be systematically larger than those predicted from theory, after proper allowance for an $M2\mathrm{}$ radiation-decay channel is made. Possible reasons for these systematic differences are mentioned.

Some time ago, an accurate upper limit on a possible permanent electric dipole moment of the thallium atom in the $6 {}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ ground state was obtained by Gould. The result was $D_{\mathrm{Tl}}=\left[\right(1.3\mathrm{}\pm 2.4)\times {10}^{-21\mathrm{}} \mathrm{cm}]e$. In connection with this value, we have carried out a calculation of the electric dipole enhancement factor $R_{\mathrm{Tl}}$, which is defined as the ratio $\frac{D_{\mathrm{Tl}}}{D_e}$, where $D_e$ is the corresponding upper limit on a possible electric dipole moment of the (valence) electron. A value $R_{\mathrm{Tl}}=700\mathrm{}$ was obtained, which leads to an upper limit $D_e=\left[\right(1.9\mathrm{}\pm 3.4)\times {10}^{-24\mathrm{}} \mathrm{cm}]e$. This result is comparable with the value $D_e<(3\mathrm{}\times {10}^{-24\mathrm{}} \mathrm{cm})e$ previously obtained by Weisskopf et al. from measurements on the cesium atom, and with the result of Player and Sandars of $\left[\right(0.7\mathrm{}\pm 2.2)\times {10}^{-24\mathrm{}} \mathrm{cm}]e$ obtained from the search for an electric dipole moment in the ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$ metastable state of xenon. All three results set a stringent upper limit on the amount of a possible violation of $T$ and $P$ invariance in electromagnetic interactions.

Using an electromagnetically driven shock tube and rapid scanning Fabry-Perot spectrometer, the Lorentzian half-width of the 4663-Å line of singly ionized aluminum was measured and found to be 0.45 Å ± 20% for an environment corresponding to $N_e={10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and $T_e=18\mathrm{}500$ °K. Semiclassical and semiempirical calculations yielded values of 0.56 Å and 0.41 Å, respectively, while the distorted-wave approximation gave 0.51 Å. Our measurement and the calculated values fall a factor of 5 below the results of a previous experiment.

At incident electron energies of 0.5-1.5 MeV, bremsstrahlung linear polarization was measured for thin targets of beryllium, aluminum, silver, and gold at emission angles of 10°-122° as a function of photon energy. Data were corrected for electron scattering in the target and for multiple scattering of photons in the Compton polarimeter used. For low-atomic-number targets the experimental results are perfectly in agreement with Born-approximation theory and with computations using Sommerfeld-Maue eigen-functions, whereas the high-atomic-number results are described satisfactorily only by partial-wave calculations.

Electron-spin-resonance (ESR) spectra, detected 90° out of phase with respect to the Zeeman modulation and using a saturating microwave field, are sensitive to molecular motion several orders of magnitude slower than are ordinary ESR spectra observed in phase with the modulation. A comprehensive theory of electron magnetic resonance based on an extension of the stochastic Liouville equation, explicitly including the effects of electromagnetic radiation and Zeeman modulation fields, of Markoffian motion modulating the magnetic anisotropy, and of relaxation and Heisenberg spin exchange, is presented. The theory is quite general and capable of explaining a large body of "modulation effects" in both single- and double-resonance experiments. Application to ${}_{}{}^{15}{}_{}{}^{}\mathrm{N}$-labeled nitroxides is studied in detail, and a number of experimental spectra for the model system 2,2,6,6-tetramethyl-4-piperidone-1-oxyl (TANONE) in supercooled sec -butylbenzene are presented for comparison with theoretical results. When the eigenfunctions of the time-independent Hamiltonian are used as a basis set for computing spin matrix elements, pseudosecular transitions (simultaneous electron and nuclear spin flips) are found to make an important contribution to the computed spectrum in the slow tumbling region. While the out-of-phase dispersion at the first harmonic of the Zeeman modulation and the out-of-phase absorption at the second harmonic are both sensitive to slow motion, arguments based on saturation and modulation behavior favor the former as the more sensitive; greater signal-to-noise sensitivity should in fact be possible than for the ordinary ESR signal for the study of very slowly tumbling molecules.

The atomic-beam magnetic-resonance method has been used to study atoms of the isotopes ${}_{}{}^{253}{}_{}{}^{}\mathrm{Es}$ and ${}_{}{}^{254m}{}_{}{}^{}\mathrm{Es}$. The parameters of the Hamiltonian which fit the experimental data for ${}_{}{}^{253}{}_{}{}^{}\mathrm{Es}$ are $I=\frac{7}{2}$, $J=\frac{15}{2}$, $A=817.153\mathrm{}\left(7\right)\mathrm{}$ MHz, $B=-4316.254\mathrm{}\left(76\right)\mathrm{}$ MHz, ${\mu }_I=4.10\mathrm{}\left(7\right)\mathrm{}{\mu }_N$, and $g_J=1.1851\mathrm{}38\left(5\right)\mathrm{}$. The spectroscopic nuclear electric quadrupole moment calculated from the $B$ factor is $Q_s=6.9\mathrm{}\left(8\right)\mathrm{}$ b. For ${}_{}{}^{254m}{}_{}{}^{}\mathrm{Es}$ the parameters $I=2\mathrm{}$, $A=1020\mathrm{}\left(12\right)\mathrm{}$ MHz, and $B=-2387\mathrm{}\left(160\right)\mathrm{}$ MHz fit the data. The magnetic dipole moment and electric quadrupole moment inferred from these values are ${\mu }_I=2.90\mathrm{}\left(7\right)\mathrm{}{\mu }_N$ and $Q_s=3.8\mathrm{}\left(5\right)\mathrm{}$ b. The high precision of the Landé $g$-value determination was used to calculate an atomic ground-state eigenvector. For ${}_{}{}^{253}{}_{}{}^{}\mathrm{Es}$ the ratio of the measured $A$ factor to the nuclear magnetic moment agrees well with the calculations of Lewis et al.

A curved crystal spectrometer has been used to resolve structure in $K\alpha$ x rays from thick targets of Al, Sc, and Ti following bromine-ion bombardment. We find that this structure is due to states with different numbers of $L$-shell vacancies. From this we can deduce the relative intensities for single $K$-, and multiple $L$-shell vacancy production as well as the number of $M$-shell vacancies of each $K{L}^n$ configuration undergoing $K\alpha$ x-ray emission. These results are compared to previous measurements with Br beams in which $K{L}^n$ configurations could not be resolved.

A detailed study is made of the nature of rotational Feshbach resonances in the elastic scattering of extremely-low-energy electrons by diatomic polar molecules. The bound-state properties of an electron in the field of a dipole rotator, determined previously, are used in establishing the resonance behavior of elastic-scattering phase shifts in the energy region below the first rotational excitation threshold. Feshbach resonances of very narrow widths are found in partial-wave scattering channels with total angular momenta greater than zero when the strength of the interaction potentials is somewhat less than that necessary to yield bound states of the same symmetry type, and very much less than those necessary to yield a "bound state" of the projected Hamiltonian $\mathrm{QHQ}$. The latter implies a non-negligible value of the resonance energy shift for polar molecules.

The metastable fraction of He atoms produced by electron detachment from ${\mathrm{He}}^{-}$ ions in single collisions with ${\mathrm{H}}_2$, He, ${\mathrm{N}}_2$, Ne, and Ar has been measured in the energy range 25-400 keV by the beam-attenuation technique, using ${\mathrm{H}}_2$ as attenuation gas. These data support earlier results, pointing to the existence of a bound, long-lived doublet state of ${\mathrm{He}}^{-}$. Further, the electron loss and deexcitation cross sections for metastable He atoms in He, ${\mathrm{N}}_2$, Ne, and Ar have been measured individually at 50 keV, and it is shown that the deexcitation cross section is comparable to the electron-loss cross section.

Phase shifts and their weighted sum over angular momentum are reconsidered for the static screened Coulomb potential (SSCP). Results are given for both an attractive and a repulsive SSCP. The numerical results are derived in the present work from two independent and simple techniques based upon the Numerov method and the variable-phase approach, respectively, applied to the Sturm-Liouville form of the Schrödinger equation. Special emphasis is given to the high-density low-temperature domain (${\lambda }_D<10\mathrm{}$ a.u.). Excellent agreement is found with results obtained previously by Rogers using the WKB approximation.

Crossed beams of electrons and ${\mathrm{D}}_2^{+}$ ions were used to measure absolute cross sections for the dissociative recombination process, $e+{{\mathrm{D}}_2}^{+}\left(X {}_{}{}^2{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\right)\to \mathrm{D}+{\mathrm{D}}^{*}\mathrm{}(n=4\mathrm{})\mathrm{}$ over a range of electron energies extending from 0.6 to 7 eV. The process was monitored by detecting a known portion of the 485.9-nm emission resulting from radiative decay of the product ${\mathrm{D}}^{*}\mathrm{}(n=4\mathrm{})\mathrm{}$ atoms. The cross sections, which correspond to a known vibrational-state distribution of the target ions, exhibit the same dependence on electron energy as recent measurements of the total dissociative recombination cross section reported by Peart and Dolder, and have a magnitude of about 10% of the total cross section, suggesting that the product D atoms are formed in excited states with a variety of principal quantum numbers. Systematic measurement uncertainties at high confidence are about 14%, and random uncertainties are at the 25% (standard deviation) level. The calculation of cross sections from the observed light intensities depends on the mean lifetimes and branch ratios for 485.9-nm emission, whose evaluation in turn requires assumptions concerning the recombination process. The situation is complicated by the presence of an electron-beam-confining magnetic field in the collision volume, which causes the incident ions and product atoms to experience a transverse motional electric field. A time-independent perturbation calculation of the weak-field Stark and Zeeman effects was performed and mean lifetimes and branch ratios were estimated under different assumptions concerning the recombination process. Assuming that all perturbed product $n=4\mathrm{}$ states are equally populated by dissociative recombination yields an experimental cross section of 1 × ${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ at 0.7 eV, decreasing to 3.3 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 3 eV, and to 1 × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ at 7 eV. Assuming that only the perturbed $4s$ states are initially populated results in cross sections larger by some 50%.

We measured the polarization of the photon echo which was stimulated in a gas of S${\mathrm{F}}_6$ molecules by either linear-linear, circular-linear, or linear-circular pulse sequences from the $P\left(14\right)\mathrm{}$, $P\left(16\right)\mathrm{}$, $P\left(18\right)\mathrm{}$, $P\left(20\right)\mathrm{}$, $P\left(22\right)\mathrm{}$, and $P\left(24\right)\mathrm{}$ C${\mathrm{O}}_2$ laser lines near 10.4 μm. For $P\left(16\right)\mathrm{}$ a linear-linear pulse sequence with angle $\beta$ between the linearly polarized pulses produced a linearly polarized echo at angle $\varphi$ with the second pulse, and $\varphi$ rotated in the same sense as $\beta$; a left-circular-linear sequence produced an echo with right elliptic polarization, and a linear-left-circular sequence produced an echo with left-circular polarization. For all other lines a linear-linear sequence produced an echo polarized along the second pulse, and results were similar to the measurement of Gordon et al. on $P\left(20\right)\mathrm{}$. For $P\left(14\right)\mathrm{}$, $P\left(18\right)\mathrm{}$, and $P\left(20\right)\mathrm{}$ a circular-linear sequence produced an echo linearly polarized along the second pulse. For $P\left(14\right)\mathrm{}$ through $P\left(20\right)\mathrm{}$ a linear-left-circular sequence produced a left-circular echo. A theory is developed for these pulse sequences for arbitrary values of angular momentum $J_a$, and a simplification found for large $J_a$. For laser radiation in direction $Y$ and the linear polarization of the second pulse along $Z$, the polarization vector for a linear-linear sequence is approximately $\mp \left(\frac{1}{2}\right)\hat{X}sin\beta +\hat{Z}cos\beta$, and for a left-circular-linear sequence $\pm \left(\frac{i}{2}\right)\hat{X}+\hat{Z}$, where the upper sign refers to $J_a=J_b\pm 1$ or the $P$ and $R$ branches and the lower sign to $J_a=J_b$ or $Q$ branch. For a linear-left-circular sequence the echo is left circular for $J_a=J_b$, $J_b\pm 1$ or the $P$, $Q$, and $R$ branches. The general features of the linear-linear sequence are similar to those suggested by Gordon et al. when a sign ambiguity is considered. Only $P\left(16\right)\mathrm{}$ was in good agreement with theory. The $-\left(\frac{1}{2}\right)\hat{X}sin\beta$ or the $+\left(\frac{i}{2}\right)\hat{X}$ terms were not observed for the other lines.