The angular distribution of electrons elastically scattered from C${\mathrm{O}}_2$ has been measured utilizing a crossed-beam method. The energy and angular ranges are 3.0 to 90,0 eV and -105° to + 156°, respectively. The total elastic cross section and momentum-transfer cross sections have been determined. The total elastic cross section of C${\mathrm{O}}_2$ at 10.0 eV has been calibrated with respect to that of He at 10.0 eV, and the C${\mathrm{O}}_2$ cross section has been placed on an absolute scale by using the theoretical value of LaBahn and Calloway for He at 10.0 eV. The results are compared with theory and other experimental results with generally good agreement but with some noteworthy differences.

The inelastic collisional cross sections of the $\mathrm{nD}$ states of Cs are measured by the technique of selective laser excitation and observation of collision-induced fluorescence. The cross sections (in units of ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$) for the fine-structure-changing collisions [i.e., $\mathrm{Cs}\left(n{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}\right)+\mathrm{Cs}\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)\to \mathrm{Cs}\left(n{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)+\mathrm{Cs}\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)$] for $n$ being 6-10 are 2.7±0.5, 3.7±0.7, 8.6±1.7, 18.4±3.7, and 29.8±6.0, respectively. The cross sections (in ${10}^{-14\mathrm{}}$ ${\mathrm{cm}}^2$) for excitation transfer out of the $\mathrm{nD}$ doublet [i.e., $\mathrm{Cs}\left(n{}_{}{}^2{}_{}{}^{}D_{\frac{5}{2}}^{}{}_{}{}^{}\right)+\mathrm{Cs}\left(6\mathrm{}{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}\right)\to \mathrm{states}\mathrm{other}\mathrm{than} \mathrm{Cs}\mathrm{}\left(\mathrm{nD}\right)\mathrm{}$] for $n$ being 6-10 are 1.1±0.6, 5.3±1.5, 3.6±1.5, 6.3±2.3, and 15.5±4.0, respectively. The fine-structure-changing cross sections are found to be nearly equal to the geometrical cross section $\pi n^{*4\mathrm{}}{a}_0^2$ for all the $\mathrm{nD}$ states studied, except $6D$, whose fine-structure-changing cross section is unusually large.

Minima and maxima of the generalized oscillator strength for the $2s\to 3p$ transition of atomic hydrogen are found using the Glauber approximation. In contrast to the first-Born approximation, the number of extrema and their positions are found to vary with the energy of the incident particle, and the values at the minima do not vanish. There is qualitative agreement in the behavior of the first minimum with known experimental data on the resonance transitions of rare gases and mercury. For large incident energy, the transition amplitude in the Glauber approximation falls off with large momentum transfer more rapidly than predicted by a previous calculation based on the second-Born approximation.

The close-coupling method has been applied to the electron-${\mathrm{H}}_2$ collision to obtain excitation cross sections of the $b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $a{}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, $e{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$, $c{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$, and $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states. Cross sections of the triplet states are presented at several incident-electron energies between threshold and 40 eV, and those of the $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ state at 25, 50, 75, and 100 eV. Vibrational levels are treated by the Franck-Condon-factor approximation, and the cross sections are rotationally averaged. Cross sections by the Born-type calculations are markedly different from those of the present calculation. Furthermore, the manner and degree to which they differ also vary from state to state. Comparison with experiment is limited to a set of experimental data of total dissociation cross sections.

By taking as an example ionization collisions between atoms with simultaneous excitation of one of the atoms, a mutual relation between the impulse and the semi-quantum-mechanical approximation is made clear in the case in which the electron-atom scattering amplitude is a function only of the momentum transfer. An improved impulse approximation is proposed, which employs the smallest number of assumptions among the various formulas and has an advantage of practical usefulness. It is shown that the formula can be simplified to a single integral if an average of the cross section is taken with respect to the initial azimuthal quantum number of an atom to be ionized.

Expressions for the scattering amplitude of multiphoton processes occurring during the collision of electrons with a hydrogen atom in the presence of an electromagnetic field have been obtained in several approximations: the momentum translation, the space translation, and the Keldysh approximation for the bound-electron wave function. We also propose a perturbation approach based on the space-translation approximation to treat the hydrogen-atom bound states. Our results show that it is of fundamental importance to consider the modifications of bound states due to the presence of the field.

The total photoionization cross section of the $1s$ level of nitrogen in ${\mathrm{N}}_2$ and ${\mathrm{N}}_2$O molecules has been measured using monochromatized synchrotron radiation. High-resolution spectra in the range $390<\mathrm{}\hslash \omega <450\mathrm{}$ eV were recorded. A broadband in the continuum at 9.4 eV above the ionization threshold, due to the $f$-type shape resonance, has been measured with high resolution. The data are compared with theoretical calculations of photoionization cross section. Recent Hartree-Fock calculations in the static-exchange approximation agree better than earlier results, which employed the multiple-scattering method.

A semiclassical method of approach to the origin of radiation in a simple quantum transition is reinterpreted and extended. The resulting concepts are applied to an analysis of the Compton effect, yielding the Klein-Nishina formula as usual. More significant is the natural appearance in this case of photonlike behavior of the purely classical electromagnetic fields. The same phenomenon can be hypothesized to occur in any transition in which a quantized-photon nature of radiation appears evident. A similar classical viewpoint taken toward the Lamb shift leads to a straightforward explanation which seems to give very good agreement with experiment. The calculated frequency for the $2P_{\frac{1}{2}}\to 2S_{\frac{1}{2}}$ transition in H is 1064.57 MHz = 0.0355102 ${\mathrm{cm}}^{-1\mathrm{}}$. The argument also has some important implications for ideas about the physical nature of quantum states.

The lifetime of the ${}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}$ metastable state of oxygen was measured by monitoring 1356-Å photons from inflight radiative decay of the metastables in a beam. Metastables were produced by electron-impact dissociation of ${\mathrm{O}}_2$ and velocity selected using a time-of-flight (TOF) technique. The ${}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}$ state was identified by passing photons from its radiative decay through a ${\mathrm{N}}_2$O gas filter, which had a high transmission for 1356-Å radiation and good discrimination against other uv photons of shorter wavelength. The use of ${\mathrm{O}}_2$ as another filter gas served as a consistency check for the absence of shorter-wavelength radiation. The metastable detector assembly also contained a surface detector that responded to metastable particles in the usual manner by Auger emission of secondary electrons. TOF spectra of the metastable dissociation fragments were measured with both these detectors at various distances from the source. The $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}\right)$ lifetime obtained from a series of photon and particle measurements was found to be 180±5 μsec. This value represents a substantial improvement in accuracy over previous lifetime determinations and the only TOF study in which the $\mathrm{O}\left({}_{}{}^5{}_{}{}^{}S_{}^o{}_{}{}^{}\right)$ state was identified through radiative decay.

Time-dependent Hartree-Fock theory is used in conjunction with the Stieltjes imaging method to calculated the inner-shell photoionization cross sections of the beryllium isoelectronic sequence.

Difficulties in the straightfoward application of the complex-coordinate method to the calculation of resonance states in many-electron systems are examined. For the case of shape resonances, it is shown that many of these difficulties can be avoided by using complex coordinates only after reduction of the system to an effective one-electron problem. Further simplifications are achieved by the use of an inner-projection technique to facilitate the computation of the complex Hamiltonian matrix elements. The method is first illustrated by application to a model-potential problem. Its suitability for studying many-electron problems is demonstrated by calculation of the position and width of a low-energy ${}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$ shape resonance in ${\mathrm{Be}}^{-}$. We discuss the modifications necessary to study core-excited (Feshbach) resonances.

A unitary transformation on the total Hamiltonian of quantum electrodynamics is shown to relate the length and velocity forms of both nonrelativistic and relativistic oscillator strengths. For the gauge-violating self-consistant Hamiltonian of the Hartree-Fock approximation, the conventional relation between length and velocity forms is an approximation to a general relation between interaction Hamiltonians connected by the unitary transformation. From the point of view of the unitary transformation, the velocity form is as reliable as the length form, and the forms of length formulas of relativistic and nonrelativistic oscillator strengths are identical.

A systematic study of the influence of cascades on heavy-ion beam-foil decay curves has been made. Using theoretical data for the lifetimes and initial populations of excited states, decay curves simulating beam-foil excitation conditions have been constructed for the resonance transition of three ions in the copper isoelectronic sequence. Various models for the initial population distribution were tested by comparison with a detailed beam-foil decay curve available for Krviii. We found that customary exponential-fitting methods were not able to extract the primary lifetimes from the simulated curves used in constructing them, although the replenishment ratios were close to zero. General implications of this subtle masking of the primary lifetime by numerous cascades for the accuracy of experimental beam-foil data are discussed, especially for $\Delta n=0\mathrm{}$ transitions in heavy ions.

Nonrelativistic $\mathrm{gf}$ values for the $4s^2{}_{}{}^1{}_{}{}^{}S-4s4p{}_{}{}^1{}_{}{}^{}P$ transition based on multiconfiguration Hartree-Fock wave functions are reported for a number of ions from Zni to Wxlv. In addition to the correlation among the outer electrons, the effects of core polarization associated with the $3d^{10}$ subshell are taken into account to first order. Relativistic effects are estimated by using observed energies and allowing for spin-orbit interactions. When only the correlation among the outer electrons is taken into account, these approximate relativistic $\mathrm{gf}$ values agree well with relativistic calculations published recently, which also include only outershell correlation. The final values are compared with experimental observations. It is found that the discrepancy between theory and experiment is reduced by taking core polarization into account, and that there is good agreement for Zni. However, for the heavier ions a discrepancy remains which increases with increasing ionization to a factor of 2 in Krvii. Possible reasons for this discrepancy are discussed.

The fine structure of the $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}-1s2\mathrm{}{p}^2{}_{}{}^4{}_{}{}^{}P$ multiplet in the doubly excited quartet system of three-electron Civ, Nv, and Ovi has been measured using the method of beam-foil spectroscopy. The fine-structure splittings have been determined to within ∼ 5 ${\mathrm{cm}}^{-1\mathrm{}}$ in both the upper and lower states of each ion, and the absolute transition wavelengths have been measured to within ∼ 0.1 Å (∼ ${10}^{-3\mathrm{}}$ eV). The wavelength results show that existing relativistic and nonrelativistic energy separations calculated for these ${}_{}{}^4{}_{}{}^{}P$ states are inaccurate by ∼ 1% for $Z=6-8\mathrm{}$, and that calculations of the fine-structure splittings are inaccurate by (10-20)% for $1s2s2p{}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}$ and by ≳ 20% for $1s2p^2{}_{}{}^4{}_{}{}^{}P$. Lifetimes have also been measured for the $J=\frac{5}{2}, \frac{3}{2}, \mathrm{and} \frac{1}{2}$ levels of $1s2p^2{}_{}{}^4{}_{}{}^{}P$. Differential metastability is found to be a characteristic feature of these core-excited fine-structure states in all three ions. Comparison with calculated autoionization and $K$ x-ray transition rates for $Z=7\mathrm{} \mathrm{and} 8$ indicates that the $1s2p^2{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^{}{}_{}{}^{}$ lifetime is determined essentially by its autoionization rate to the doublet continuum through magnetic interactions, whereas the $J=\frac{3}{2} \mathrm{and} \frac{1}{2}$ states decay at a slower rate that is more characteristic of the ${}_{}{}^4{}_{}{}^{}P_{}^o{}_{}{}^{}-{}_{}{}^4{}_{}{}^{}P$ radiative transition rate.

The theoretical results are presented here in detail for the atomic device proposed earlier by the author. This device absorbs energy from a continuous radiation source and stores some of it with atoms in metastable states for a long time without any loss. At a later time, when the energy is required, the system can be "triggered" by an external perturbing field to release the energy in the form of a strong pulse of radiation.

We have previously presented a semiclassical treatment of highly excited atoms in a magnetic field (for application to an analysis of the observed Zeeman effect in the BaI absorption spectrum) and a similar treatment of a one-dimensional Coulomb field with an electric field in the same direction (of interest for the study of far-infrared emission from Si inversion layers, and also for the discussion of electrons outside a free surface of liquid helium). Since the latter experiment has also been carried out in the presence of a magnetic field, an analysis is now presented, based on the simultaneous presence of both electric and magnetic fields, which is applicable to low-lying as well as highly excited states.

We derive reduced equations of motion for simple quantum systems which are strongly driven by an external field and are modulated stochastically by a coupling to a bath. In the derivation we make use of the cumulant-expansion method of Kubo using two different time-ordering prescriptions. We demonstrate how the choice of the ordering prescription is related to the statistical properties of the bath, once the cumulant expansion is truncated. Our equations of motion are valid for arbitrary time scale for the motions of the bath relative to those of the system, and they change smoothly from the static to the Markov (motional narrowing) limit. As examples, we consider the problems of a randomly modulated and driven harmonic oscillator and a modulated and damped two-level system. In the Markovian limit both ordering prescriptions yield Bloch-type equations of motion; in general, however, the driving and modulation interfere and the different statistical properties of the bath, as determined by the two truncated ordering prescriptions, lead to different results.

By an optical double-resonance experiment on ${}_{}{}^{199}{}_{}{}^{}\mathrm{Hg}_{}^{+}{}_{}{}^{}$, suspended in a rf quadrupole trap, we determined the ground-state hyperfine separation. Linewidths as small as 4 Hz have been observed. The final result of $\Delta {\nu }_{\mathrm{hfs}}=40\mathrm{}507347997.8\pm 1.0$ Hz includes corrections to zero magnetic field and zero kinetic energy. The accuracy of the result and possible improvements lead to the feasibility of a new frequency standard in the microwave region.

The photodissociation (photoabsorption) cross sections of ${\mathrm{Ar}}_2^{+}$, ${\mathrm{Kr}}_2^{+}$, and ${\mathrm{Xe}}_2^{+}$ have been measured from 6200 to 8600 Å. The rare-gas dimer ions were produced in a drift-tube mass spectrometer and irradiated by a dye laser. The wavelength dependence of the photodissociation cross sections, which is similar for all three dimer ions, reflects a direct dissociation process. The broad maxima of ${\mathrm{Ar}}_2^{+}$, ${\mathrm{Kr}}_2^{+}$, and ${\mathrm{Xe}}_2^{+}$ occur at 7200, 6850, and 7000 Å, respectively, with cross sections of 0.19, 2.9, and 12×${10}^{-18\mathrm{}}$ ${\mathrm{cm}}^2$. The processes for formation of dimer ions in the drift tube are discussed. It is concluded that the ions are essentially in thermal equilibrium near 300°K at the time of photon interaction. The present photodissociation cross sections of ${\mathrm{Ar}}_2^{+}$ and ${\mathrm{Kr}}_2^{+}$ are in reasonable agreement with theoretical calculations based on recently determined potential curves.