The Coulomb-Born (CB) and a modified Coulomb-Born approximations where distortion has been taken into account in the initial channel have been applied to calculate the electron-capture cross sections by protons passing through some heliumlike ions. Results for the charge-transfer cross sections in CB approximation for different isoelectronic ions have been computed, retaining both the post and prior forms of the interaction potential. The results for the process ${\mathrm{H}}^{+}$+${\mathrm{Li}}^{+}$→H+${\mathrm{Li}}^{2+}$ have been compared with the available theoretical and experimental findings.

An adiabatic approximation in which the eikonal elastic amplitude for fixed molecular orientation is used as input is employed for the calculation of pure elastic scattering ($J=0\mathrm{}\to J^{\prime }=0\mathrm{}$ and $J=1\mathrm{}\to J^{\prime }=1\mathrm{}$) pure rotational excitation ($J=0\mathrm{}\to J^{\prime }=2\mathrm{}$ and $J=1\mathrm{}\to J^{\prime }=3\mathrm{}$), and orientationally averaged elastic cross sections of the nitrogen molecule in its ground electronic and vibrational states using electrons as incident particles. Both differential and integral cross sections are computed at electron energies 20-200 eV. Total momentum-transfer cross sections are also calculated. The effect of target polarization is considered in the effective electron-molecule potential. The effect of electron exchange is not taken into account. Results obtained are compared with those of other theoretical and experimental workers. The qualitative features of the rotational-excitation cross sections are found to resemble those of the hydrogen molecule. Small-angle experimental elastic cross sections are well reproduced.

The effect on the $K$-vacancy-production cross section due to the finite distribution of charge and magnetic moment of the incident proton is examined. Numerical results are given for two target elements, namely, Ni and U. The results show that even at energy as high as ${10}^3$ GeV the incident proton can still be regarded as a point charge. The effect on the stopping power of matter is discussed.

Using a delayed field ionization approach we have observed the radio frequency resonance transitions connecting the Ba $6sng$, $6snh$, $6sni$, and $6snk$ states for $n\sim 20$. The $\Delta l$ intervals may be used to determine the dipole and quadrupole polarizabilities ${\alpha }_d$ and ${\alpha }_q$ of the ${\mathrm{Ba}}^{+}$ core with the use of both the familiar adiabatic core polarization model of Mayer and Mayer and a simple two-electron model of Van Vleck and Whitelaw. While both models give reasonable values for the dipole polarizability, the adiabatic model gives an impossible negative quadrupole polarizability. The two-electron model, however, gives values in reasonable agreement with calculations based on the Coulomb approximation. The values we determine for ${\alpha }_d$ and ${\alpha }_q$ are $125.5\left(10\right)\mathrm{}{a}_0^3$ and $2050\left(100\right)\mathrm{}{a}_0^5$, respectively. Finally, the fine-structure splittings of the levels are roughly one hundred times larger than the analogous He splittings.

Radiative lifetimes of 25 levels in neutral hafnium are reported. Measurements are made on a sputtered atomic beam through the use of time-resolved laser-induced fluorescence. The system is shown to be useful for lifetimes from a few nsec to over 2 μsec.

Multiconfiguration Hartree-Fock calculations have been performed for many doubly excited quartet states of BeII. Total energies and lifetimes are reported as well as wave-lengths and $f$ values for transitions between states. The calculations support many, though not all, recent assignments.

Multiconfiguration Hartree-Fock calculations by Froese Fischer have confirmed nearly all our recent identifications of doubly excited quartet states in Be II and predicted a number of new ones. Experimental data are reported which confirm some of the new theoretical predictions concerning $2p4l$ quartet states.

We have observed that spectral lines obtained in sodium vapor can be strongly distroted when using two-photon spectroscopy with a resonant intermediate state. In some cases, the spectral lines appear to be split into two components. We demonstrate that these effects are due to velocity-selective optical pumping of the atomic ground state; the line shapes reflect the velocity distribution of atoms in the excited intermediate state. We have analyzed the effects using the time-dependent solutions of the rate equations which describe the time evolution of optical pumping for the various atomic velocity groups, and we obtain good agreement with experiment. Optical-pumping problems are often analyzed with the use of steady-state rate equations which incorporate phenomenological relaxation; such approaches are not capable of describing our observations. Velocity-changing collisions are shown to suppress the effects and they explain why these effects were not previously observed; the previous experiments were carried out with slight amounts of a buffer gas in the vapor cell. The effects reported here must be accounted for when carrying out laser-induced line-narrowing experiments in atoms or molecules that can be optically pumped; they can also be used as a new and more sensitive probe of optical pumping in vapors.

Theoretical photoabsorption cross sections for alkali-metal atoms in a static electric field $F$ are derived for energies near the zero-field ionization threshold ($\epsilon =0\mathrm{}$), extending a previous development for hydrogen. Spectra result from zero-field dipole matrix elements and a density-of-states matrix $D_{l^{\prime }l}^F$. The factors $D_{l^{\prime }l}^F={\left({〈{\Psi }^{\prime }|\Psi 〉}^{-1\mathrm{}}\right)}_{l^{\prime }l}$ represent a renormalization of the photoelectron's wave function ${\Psi }_l$ necessitated by the long-range Coulomb plus Stark potential. The matrix $D^F$ contains all spectral information on quasidiscrete Stark levels and continuum resonances, expressed as an algebraic function of (1) quantum defects ${\mu }_l$ embodying core effects, (2) a frame transformation between spherical and parabolic coordinates in the pure Coulomb field outside the alkali-metal core, and (3) factors $H_{l^{\prime }l}^F$ and $h_{l^{\prime }l}^F$ calculated from asymptotic amplitudes and phases of hydrogen-Stark wave functions of the parabolic dissociation channels. Hydrogenic parameters are calculated semianalytically within the WKB approximation; ${\mu }_l$ and dipole matrix elements are known independently. Predicted cross sections for photoionization of the excited $3{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state of Na agree with experiment. The theory reproduces (a) asymmetric resonances observed at $\epsilon <0\mathrm{}$, parametrized as a Beutler-Fano profile for a simple case, and (b) the oscillations observed at $\epsilon >0\mathrm{}$, attenuated by factors $cos2\pi {\mu }_l$ from their predicted depth in H. Dependences on light polarization are sorted out for two-photon excitation.

The superposition of vibrational states produced in gaseous ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$${\mathrm{H}}_3$F by 9.6-μm infrared laser radiation results in anomalous echo-envelope and free precession-beat effects. The effects arise when pulsed Stark electric fields alter the state mixing among nearly degenerate spin-rotation states. The initial eigenstates are governed by the internal spin-rotation interaction and by applied dc bias Stark electric and Zeeman magnetic fields. Unresolved modulation of the photon echo envelope caused by sudden changes of state mixtures is confirmed by analytic theory. Separate measurement of ground- and excited-state spinrotation interactions is possible for future investigations with increase in apparatus resolution. A new anomalous coherent Raman beat also caused by altering the state mixtures is investigated. The reduction of state mixing by local collisional electric fields which increase with gas pressure is qualitatively confirmed.

New x-ray wavelength (energy) and width measurements are reported for a number of elements from $47\le Z\le 92$. The x rays were produced with the use of an electron Van de Graaff, and the measurements were made with a two-axis flat-crystal transmission spectrometer equipped with angle-measuring interferometers. The new measurements reported here, combined with other high-precision x-ray wavelengths, form a moderately extensive data base for comparison with theoretical calculations. Comparison with recent revisions of a previously available all-$Z$ calculation reveals improved patterns of general agreement with, however, important exceptions. The newly measured linewidths are in agreement with widths calculated via relativistic wave functions used for the term estimates.

The line spectrum between the triplet state $a{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ and the ground state $X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ of ${\mathrm{Na}}_2$ is observed by the laser-induced fluorescence of a ${\mathrm{Na}}_2$ molecular beam. The rotational constants and vibrational frequencies of the $a{}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state are determined.

When a hydrogen atom in a state with principal quantum number $n_i$ is irradiated simultaneously with light of frequency ${\omega }_L$, nearly that required to produce a transition to a higher state with principal quantum number $n_f$ and with microwave radiation of frequency $\omega$, the transition is very probable when the resonance condition ${\omega }_L+k\omega =E_f-E_i$ is satisfied, the emission or absorption of the net number $k$ of microwave photons just compensating for the detuning of the light from the resonance. This process is analyzed with the use of a forward scattering method and the results are used to discuss the experiments of Bayfield et al. on the excitation of hydrogen.

A theoretical study is presented which permits the analysis of multiphoton processes in the presence of homogeneous, inhomogeneous, and power-broadening mechanisms. A method derived from the Markov model microfield theory is used. This is based on the statistics of the fluctuations of the interaction between the radiator and a perturbing environment. Application is made to velocity-changing collisions in Doppler-free spectroscopy and to homogeneous and inhomogeneous pressure broadening in two-photon absorption or resonance fluorescence.

A systematic quantitative estimation of the photoionization cross section from the excited $p$ states of the rare-gas atoms is carried out in a single-configuration calculation. Our calculation has shown that the photoionization from these excited states is quasihydrogenic in nature. At a fixed photoelectron energy, the cross section is found to decrease as the effective quantum number $n^{*}$ increases from state to state and to scale approximately as ${\left(n^{*}\right)}^{-3\mathrm{}}$. As the photon energy $\epsilon$ increases, the cross section decreases approximately as ${\epsilon }^{-3\mathrm{}}$. Our result is also found to compare favorably with the available experimental and theoretical data.

High-resolution double-resonance spectroscopy experiments in the millimeter-wave domain have yielded precise values of quantum defects in the $S$, $P$, $D$, and $F$ Rydberg levels of cesium (principal quantum number $n$ ranging from 23 to 45). In addition, fine and hyperfine structures have been measured in these levels. These experiments provide a precise mapping of the cesium Rydberg levels, allowing us to predict with an accuracy of about a MHz any transition frequency between two states with $n\ge 20$ and $l\le 3$.

In this work the lowest eleven ${}_{}{}^1{}_{}{}^{}P_{}^o{}_{}{}^{}$ resonances of helium below the $n=4\mathrm{}$ threshold of ${\mathrm{He}}^{+}$ have been investigated. The $\mathrm{QHQ}$ eigenvalues of these states have been calculated and found to be lower than the $\mathrm{QHQ}$ results of Oberoi and of Herrick and Sinano$\stackrel{\mathrm{̌}}{\mathrm{g}}$lu. The saddle-point energies of these resonances are found to be generally in good agreement with the experimental results of Madden and Codling and of Woodruff and Samson. The oscillator strengths from both the $1{}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ and $2{}_{}{}^1{}_{}{}^{}S_{}^e{}_{}{}^{}$ states to these autoionizing levels are also calculated together with various pertinent expectation values which allow us to arrange the eleven states into six Rydberg series, one of which we identify as the resonant series seen in the experiments.

The probabilities $P_{\mathrm{KK}}$ of double-$K$-shell-vacancy production per $K$-electron-capture decay of ${}_{}{}^{181}{}_{}{}^{}\mathrm{W}$ and ${}_{}{}^{165}{}_{}{}^{}\mathrm{Er}$ have been determined by means of $K\alpha$ x-ray—$K$ x-ray coincidence experiments: $P_{\mathrm{KK}}=(2.4\mathrm{}\pm 0.6)\times {10}^{-6\mathrm{}}$ and $P_{\mathrm{KK}}=(8.2\mathrm{}\pm 2.8)\times {10}^{-6\mathrm{}}$, respectively. The observed energy shifts of the hypersatellite $\mathrm{Ta}K{\alpha }_1^H$ x-ray and $\mathrm{Ho}K{\alpha }_1^H$ x-ray lines are 1026±62 eV and 930±70 eV, respectively. In the case of ${}_{}{}^{181}{}_{}{}^{}\mathrm{W}$, the theoretical $P_{\mathrm{KK}}$ value deviates significantly from the above-mentioned experimental value. In combination with results from other experiments, this strongly suggests that, contrary to what the present theory predicts, $P_{\mathrm{KK}}$ shows a considerable dependence on the ratio of transition energy to threshold energy.

Recently, the author put forward a theory of the motion of photons in physical space, which provides a new approach to problems of photon-counting statistics. Here that theory is briefly reviewed, and a proof of its Lorentz covariance is given.

The possibility of formulating a treatment of pressure-induced extra resonances (PIER) in four-wave mixing, in terms of effective two-level equations, is examined. With the use of the method of adiabatic elimination of fast variables, effective two-level equations, which are valid for arbitrary slowly varying field envelopes, are obtained. Such equations are found to have a structure that is very different from that of the Bloch equations. In the new structure important inhomogeneous terms appear that are crucial for PIER. The present description is then used to study the effect of laser fluctuations on PIER.