A theory of electron-impact excitation of atoms in which fine structure is included as a perturbation is presented in detail. Hyperfine structure is included in the target atom but neglected in the electron-atom interaction. Expressions for electron-photon angular-correlation parameters and scattering cross sections are derived in terms of products of complex scattering amplitudes, with emphasis on electron-sodium excitation. Examples are given in which zero-field quantum beats may be observed in electron-photon angular-correlation and differential-cross-section measurements. Some of the interference terms are only observable in angular-correlation experiments. Examples are also given of partial cross sections for electron-impact excitation of state-to-state hyperfine levels in terms of direct- and exchange-scattering amplitudes plus additional terms due to the inclusion of fine-structure effects. The expressions given allow a comparison between the various possible scattering experiments.

Relative elastic-scattering differential cross sections were measured in the 5-100-eV impact energy and 10°-145° angular ranges. Normalization of these cross sections was achieved by utilizing accurate total electron-scattering cross sections. A phase-shift analysis of the angular distributions in terms of real phase shifts has been carried out. From the differential cross sections we obtained momentum-transfer cross sections and established the value of the critical energy and angle (associated with the lowest value of the differential cross section) as 62.5±2.5 eV and 101.7°±1.5°, respectively. The present phase shifts, the critical parameters, and differential, integral, and momentum-transfer cross sections are compared to previous experimental and theoretical results. The error associated with the present data is about 10%.

Absolute differential cross sections (DCS's) for electron-impact excitation of the lowest forty electronic levels in atomic neon have been determined for incident electron energies of 30 and 50 eV, for the four lowest levels at 25 eV, and two levels at 100 eV. The cross sections for these forty electronic levels are grouped into fifteen features, six of which represent excitation to resolved single electronic levels and the remaining nine which contain the unresolved contributions from two or more electronic levels. These DCS's were extrapolated to 0° and 180° and integrated to yield absolute integral cross sections as a function of incident electron energy. The results are compared to other experimental and theoretical results.

First-order many-body theory has been used to calculate the differential and integral cross sections for electron-impact excitation of all the $3s$, ${3s}^{\prime }$ levels, and certain of the $3p$, ${3p}^{\prime }$ levels of neon, for incident electron energies ranging from 20 to 120 eV. The resulting differential cross sections for the excitation of the optically allowed ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ levels show, for the 10° ≤ θ ≤ 80° angular range, a discrepancy no greater than 15% when compared with recent experimental results, except for very few points. Spin-orbit coupling was included in the wave functions and its effect on determining the differential cross sections for the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ level was found to be very important for scattering angles less than 40°. For the differential cross sections of the other $3s$, ${3s}^{\prime }$ levels the discrepancy in the 30° ≤ θ ≤ 80° range is only slightly larger than the experimental errors. For the $3p$, ${3p}^{\prime }$ levels considered here, we have found strong disagreement with experimental data and there is also substantial disagreement among the various theoretical results.

Relative beam-foil populations of the $2p$ term in hydrogen have been measured as a function of the proton energy ($0.015\lesssim E\lesssim 1.10$ MeV). For $E\gtrsim 0.1$ MeV, these populations are found to be proportional to the equilibrium neutral fractions of protons emerging from a carbon foil. At lower energies ($E<\mathrm{}0.1\mathrm{}$ MeV), the behavior of the excitation function of the $2p$ term is compatible with a decrease of the ratio of the $2p$ population to the ground-state population with respect to that ratio at higher energies. The first precise measurements of the dependence on the projectile energy ($0.1<E<\mathrm{}1.8\mathrm{}$ MeV) of the population of the $2p$ term excited by the passage of $\mathrm{H}_2^{}{}_{}{}^{+}$ and $\mathrm{H}_3^{}{}_{}{}^{+}$ ions through carbon foils of various thicknesses (2.5-22 μg/${\mathrm{cm}}^2$) are reported. Only the long-dwell-time region ($t\gtrsim 1.5$ fs) is considered in this work. The variation of $R=\frac{I^{\mathrm{molec}}}{I^{\mathrm{atom}}}$ ($I^{\mathrm{molec}}$ and $I^{\mathrm{atom}}$ are the $\mathrm{L}\mathrm{y}-\alpha$ intensities per incident proton observed with molecular and atomic projectiles of the same velocity, respectively) with the projectile energy per nucleon ($\frac{E}{M}$) and the thickness ($T$) of the foil is well described by the following relation: $R=R_{\infty }[1-C\exp (\frac{-kE}{M}\left)\right]$, where $R_{\infty }$, $C$, and $k$ are parameters depending only on $T$, and on the number of protons in the cluster. A qualitative explanation of the $R\left(\frac{E}{M,T}\right)$ behavior is proposed. Values of $R$ have also been measured for $\mathrm{L}\mathrm{y}-\beta$ radiation and are found to be significantly smaller than those obtained for $\mathrm{L}\mathrm{y}-\alpha$ radiation, for foils of thickness $T\lesssim 6$ μg/${\mathrm{cm}}^2$.

We have measured the cross section for depolarization of the $5{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ state of silver atoms by collisions with helium atoms using the Hanle-effect technique. We find the nuclear-spin-independent cross section to be $\sigma =1.2\mathrm{}\pm 0.15\times {10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$, significantly smaller than the corresponding cross sections in rubidium and cesium. This is the first measurement of this quantity in any noble-metal atom.

By using the transport theory, we have derived a general expression which connects $\Delta E\left(\theta \right)$, the average energy loss measured at different $\theta$ emergence angles, and $Q\left(\theta \right)$, the average elastic and inelastic energy loss in a single scattering as a function of the scattering angle $\theta$, for ions transmitted through thin films. In this way, the effect of multiple scattering on the angular dependence of the energy loss is properly taken into account. By means of this procedure the average energy-loss function $Q$ is retrieved from experimental $\Delta E\left(\theta \right)$ data, as we show for the cases of 50-200-keV ${\mathrm{H}}^{+}$ on C and A1 foils.

Electronic energy transfer in the ${\mathrm{He}}^{*}\left(2\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)+\mathrm{Ne}$ system was studied in a nozzle-beam—scattering-cell experiment in which the visible emission of product ${\mathrm{Ne}}^{*}$ was measured. Relative populations and cross sections of individual ${\mathrm{Ne}}^{*}$ levels in the $5s$, ${5s}^{\prime }$, and $4d$ manifolds were obtained at collision energies of 0.06 and 0.16 eV. The ${3s}_2$ Paschen level is the major product at both energies. In general, the formation of odd-$J$ levels is favored and a qualitative explanation of this effect is proposed.

The Vainshtein-Presnyakov-Sobel'man approximation (VPSA) has been applied to calculate the $2s$ excitation cross section of projectile ${\mathrm{He}}^{+}$ in the reaction ${\mathrm{He}}^{+}\mathrm{}\left(1s\right)+H\left(1s\right)\mathrm{}\to {\mathrm{He}}^{+}\mathrm{}\left(2s\right)H\left(1s\right)\mathrm{}$. Calculations have been performed for both post and prior forms assuming the peaking approximation. Comparison is made with the existing theoretical calculations and experimental data. It is found that the VPSA (post form) cross sections agree reasonably well with the experimental data. The VPSA (prior form) is in disagreement with other theoretical calculations. At high energies all the theoretical calculations give identical results.

We discuss an adaptation of the Schwinger variational principle which is particularly suitable for dealing with long-range potentials. The method treats the direct interaction potential exactly by numerical integration and assumes a separable representation of the Schwinger type for the exchange potential. The method should be very effective for obtaining the electronic continuum solutions of strongly polar molecular ions. The related photoionization cross sections can be shown to be variationally stable.

The $l$th-partial-wave Coulomb half-off-shell $t$ matrix $t_l^c(k,q,k^2)$ is expressed in terms of hypergeometric functions which are polynomials. The expression is used to compute $t_l^c(k,q,k^2)$ as a function of the off-shell momentum $q$ for two laboratory energies $E_{\mathrm{lab}}(={2k}^2)=10\mathrm{}$ and 20 MeV. Results are presented for $l=0\mathrm{} \mathrm{to} 10$. Our numbers refer to repulsive Coulomb potential encountered in the case of $p-p$ scattering. It is found that in addition to the on-shell discontinuity $t_l^c(k,q,k^2)$ exhibits a singularity as $q\to 0$ for higher partial waves.

Twenty-four quartet states of ${\mathrm{Be}}^{+}$ are calculated using configuration-interaction wave functions. Relativistic and mass polarization corrections are included. The relativistic corrections considered are mass correction to the kinetic energy, Darwin term, and retardation effect. The fine structure is calculated using spin-orbit, spin-other-orbit, and spin-spin operators. The transition wavelengths calculated in this work improve the agreement between theory and experiment in most cases. The lifetimes computed in the present work generally agree with those of the experiment. However, we also point out that the observed line at 3530 Å may have been misidentified in the literature.

The saddle-point complex-rotation method is tested for a three-electron system by calculating the ${\left(1s2s2s\right)}^{2}S$ resonance in ${\mathrm{He}}^{-}$, Li I, Be II, and B III. The energy position and width obtained for this resonance are well converged for a wide range of rotation angles and nonlinear parameters for all atomic systems considered. To obtain higher accuracy, the relativistic and mass polarization corrections are also calculated. The results are compared with those of the most accurate theoretical calculations and experiments. For Be II, the agreement between the theoretical widths is very poor. Experimental data are needed to confirm the correct theoretical value.

Recent experimental determinations of energy separations within the $1snl$ term system ($n=2-6\mathrm{}$) have been used to reevaluate 35 levels. Most of the levels have estimated errors less than 0.001 ${\mathrm{cm}}^{-1\mathrm{}}$ relative to the $2 {}_{}{}^3{}_{}{}^{}P$ levels. Addition of accurate theoretical term values (ionization energies) available for several $1snl$ levels to the corresponding experimental level values gives generally consistent values for the principal ionization energy ($E_I$). The theoretical energies are further confirmed by the agreement of the weighted average of seven of these $E_I$ values with a value obtained by fitting Ritz formulas to three accurately determined $1snl$ series; the suggested new $E_I$ is 198 310.7745(40) ${\mathrm{cm}}^{-1\mathrm{}}$ on an energy scale fixed by the value 171 135.0000 ${\mathrm{cm}}^{-1\mathrm{}}$ for $2 {}_{}{}^1{}_{}{}^{}P$. Lamb shifts are derived for the $2$, $3$, $4 {}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}$, $2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$, $2 {}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, and $2 {}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ levels as differences between experimental term values obtained with the new $E_I$ and corresponding calculated term values not including Lamb shifts. The experimental and calculated values for the ${1s}^2 {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ ground level relative to the present $1snl$ excited-level system are 0.00±0.15 and 0.073±0.009 ${\mathrm{cm}}^{-1\mathrm{}}$, respectively, so that a ∼20-fold increase in the experimental accuracy would be required to test the calculated ground-level Lamb shift.

The hyperfine structure in the $J=3\mathrm{}\leftarrow J=2\mathrm{}$ rotational transition of the diatomic AgI molecule in its vibrational states $v=0,1,2,3, \mathrm{and} 4$ of the electronic ground state has been studied in the frequency region of 8 GHz. The variation of the nuclear quadrupole coupling of the iodine nucleus with vibrational state in ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ and ${}_{}{}^{109}{}_{}{}^{}\mathrm{Ag}$${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ has been investigated and the nuclear quadrupole coupling constant $e{q}_{v}Q$ can be expressed as $e{q}_{v}Q\left({}_{}{}^{127}{}_{}{}^{}I\right)=-1061.37\mathrm{}\left(11\right)-[2.13(5\left)\right](v+\frac{1}{2})$ MHz. Stark-effect measurements have been carried out on ${}_{}{}^{107}{}_{}{}^{}\mathrm{Ag}$${}_{}{}^{127}{}_{}{}^{}\mathrm{I}$ in its electronic and vibrational ground state. A least-squares fit of the Stark shifts at various electric fields gives the electric dipole moment of AgI as $\left|{\mu }_0\mathrm{}\right|=4.550\left(50\mathrm{}\right)\mathrm{}$ D.

The line-shape parameter ($q$) for the three lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization states of He and ${\mathrm{Li}}^{+}$ below the first excited target (${\mathrm{He}}^{+}$, ${\mathrm{Li}}^{2+}$) level are accurately calculated. In order to do this we rederive a rigorous expression for $q$ in terms of the Feshbach formalism; the formula contains additional terms representing the effect of other resonances on the resonance being calculated. Hylleraas functions are used to calculate $Q\Phi$, and the exchange approximation is used for the nonresonant continuum. Results agree well with the experiment where available. Our previous calculations of positions and widths are not affected; however, it is noted that the energy of the newest experiment of Morgan and Ederer for the lowest ${}_{}{}^1{}_{}{}^{}P$ autoionization state of He (60.151 ± 0.01 eV) is such that when it is combined with the older experimental value of Madden and Codling (60.133 ± 0.015 eV), the weighted mean of the two measurements (60.145 ± 0.008 eV) is in exceptional agreement with our previous value (60.145 eV).

The central position of the $2s2p {}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ two-electron resonance of He at 206.21 Å has been remeasured using the background continuum of the National Bureau of Standards storage ring facility. In addition, the line-shape parameter $q$ and width $\Gamma$ of the resonance have also been obtained. We obtained a value of 60.151 ± 0.010 eV for the resonance position, -2.6 ± 0.3 for the line-shape parameter, and 0.038 ± 0.002 eV for the width of the resonance. Our value for the resonance position is in good agreement with the theoretical calculation of 60.145 eV of Bhatia and Temkin and lies within the error budget of the previous experimental measurements of Madden and Codling. Parameter values for the other resonances have also been obtained and are in good agreement with the earlier measurements of Madden and Codling.

Our analysis shows that if an electromagnetic field excites a coherent superposition of states of two different types of atoms, then the results of a collision of those two atoms can be quite different from the usual dephasing that a coherently excited atom suffers upon collision with another atom. We present the concept of "two-atom" coherence as one feature of this interaction where the field of a given wavelength may interact with the system coherently over a wide range of internuclear distances.

A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.

A quantum-mechanical formulation for the generation of third-harmonic radiation in an atomic medium undergoing three-photon resonant multiphoton ionization is given. The generation of the third harmonic is treated as a cooperative emission and its pressure dependence is shown to be in agreement with experiments. The formulation is general enough to include both transient and steady-state phenomena and includes both traveling-wave and standing-wave cases. A comparison of the results of the present theory with those of Jackson and Wynne is given.