For a transition in a monatomic gas, it is shown that certain processes in which excitation is transferred from one atom to another lead to different resonance-broadened line shapes in emission and absorption. The absorption line shape is determined by an averaged diagonal matrix element of the resolvent operator (in the representation of the unperturbed states), while in emission some off-diagonal elements contribute. The differences are exhibited formally in terms of resolvent-operator theory, and also worked out explicitly for the case of pure impact broadening with the classical path approximation. In this case, the main effect is a shift of the emission line toward the red, relative to the absorption, by an amount of the same order of magnitude as the width. In the case where the lower level in emission is the one undergoing resonance broadening, the line shapes for emission and absorption (with the same final states) are the same.

This paper deals with the theory of the statistics of photoelectric counting experiments which involve $N$ separate counting intervals. The main new results reported here are: (i) a simple formula for the $N$-fold cumulants of the intensity of Gaussian light; (ii) a detailed study of the relations between the $N$-fold cumulants of the integrated intensity and the cumulants of the $N$-fold photoelectric counts, for light of arbitrary coherence properties. These results are derived and discussed in the context of recent work by other authors.

We have used the atomic-beam magnetic-resonance technique to improve and extend the measurements of Title and Smith on the hyperfine structure of the $\left(6\mathrm{}{p}^3\right) {}_{}{}^4{}_{}{}^{}S_{\frac{3}{2}}^{}{}_{}{}^{}$ ground state of ($I=\frac{9}{2}$). We measured the three zero-field hyperfine intervals and computed the octupole interaction constant. Our experimental results are ${\nu }_1(F=5\mathrm{}\to F=6)=2884.666\mathrm{}\left(2\right)\mathrm{}$, ${\nu }_2(F=4\mathrm{}\to F=5)=2171.419\mathrm{}\left(2\right)\mathrm{}$, and ${\nu }_3(F=3\mathrm{}\to F=4)=1584.502\mathrm{}\left(2\right)\mathrm{}$ MHz. From these values, we obtain for the hyperfine-interaction constants, corrected for the pseudo-octupole interactions due to perturbation by neighboring fine-structure levels $A=-446.937\mathrm{}\left(1\right)\mathrm{}$, $B=-305.067\mathrm{}\left(2\right)\mathrm{}$, and $C=0.0183\mathrm{}\left(1\right)\mathrm{}$ MHz. The assigned errors include only the experimental errors in the measurement of the three hyperfine intervals, and no estimate of the errors in the theoretical corrections has been made. We have also corrected the data of Lurio and Landman for the $\left(6\mathrm{}{p}^3\right){}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ metastable state of bismuth for these octupolelike interactions and have deduced a fairly consistent value for the one-electron octupole-interaction constant. From the average value of the octupole-interaction constant $c_{\frac{3}{2}}=0.0206\mathrm{}$ MHz we find that the nuclear magnetic octupole moment is $0.0086{\mu }_N\mathrm{b}$. This value is compared with the prediction of the shell model.

The change in the wave function of an atom or molecule which interacts with saturating incident radiation is shown to have a time evolution operator $U(t, 0)=\Sigma \mathrm{}\left|n\right)\left(n^{\prime }\right|B\left(n\alpha \right)B^{*}\left(n^{\prime }\alpha \right)\times e^{-i\left[\xi \right(n\alpha )+\frac{E\left(n\right)\mathrm{}}{\hslash }]t}$, where the sum over $n$ and $n^{\prime }$ is over both the ($2J_a+1\mathrm{}$) values of $m_a$ and ($2J_b+1\mathrm{}$) values of $m_b$, and the sum over $\alpha$ is over the $(2\mathrm{}{J}_a+1)+(2\mathrm{}{J}_b+1)$ modes indicated by the index $\alpha$. The eigenvalues $\xi \left(n\alpha \right)$ and their eigenvectors $B\left(n\alpha \right)$ depend on the intensity and polarization of the incident radiation, produce a modulation term in the electric polarization $\overrightarrow{\mathrm{P}}$ of the molecule, and give rise to anomalous polarization in the stimulated radiation. This unitary operator is used to discuss the radiation stimulated by two pulses or photon echoes. Echoes from elliptic pulses are discussed for $J<~2$, and the linear-linear sequence is compared with the theory of Gordon, Wang, Patel, Slusher, and Tomlinson. Echoes from linear-circular and circular-linear pulse sequences are discussed in detail.

A modified Michelson interferometer in which one of the mirrors is driven by a piezoelectric crystal connected to a Gaussian random-noise generator has been used to phase modulate a light beam from a Spectra Physics 119 model laser. The recombination of the modulated and the unmodulated beam reflected by a stationary prism generates a randomly varying interference pattern whose intensity distribution has been analyzed by means of a standard photon-counting technique. The experimental data agree with the theoretical semiclassical predictions in the range of linearity of the piezoelectric crystal. Deviations from the theory have been detected and correlated with the hysteresis of the crystal for large root-mean-square voltages applied to it.

Wave functions and binding energies are calculated for some states of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms in which the electron is in a $1s$ orbit and in which the meson or the antiproton is in a circular or a nearly circular orbit with large principal quantum number $n$. The results which are obtained in the present paper provide a basis for an estimate, described elsewhere, of the probability that atoms in some of these states can exist for an anomalously long time after being formed in liquid helium. Two methods are employed to calculate the wave functions and binding energies. A variational method which employs hydrogenic functions is used for states in which the meson is in a circular orbit. A more elaborate method, which makes use of the Born-Oppenheimer approximation and which is applicable to states with meson orbits which are not necessarily circular, is used for circular and nearly circular orbits of a few levels of the $\alpha {\pi }^{-}{e}^{-}$ and $\alpha K^{-}{e}^{-}$ atoms. It is found, in particular, that an $E4\mathrm{}$ or higher multipole transition is required for an Auger electron to be ejected by a $K^{-}$ meson in a circular orbit of the $\alpha K^{-}{e}^{-}$ atom with $n=27, 28, or 29$. It is found that for levels of the $\alpha K^{-}{e}^{-}$ atom with $n=27, 28, or 29$ the magnitude of the energy difference between two states with the same value of $n$, but with orbital angular momenta ($n-2\mathrm{}$) and ($n-1\mathrm{}$), is roughly 0.5 eV. It is also found that, in some instances, replacing the absolute square of the meson wave function with a $\delta$ function does not significantly affect the accuracy of a calculation.

An investigation is made of the extent to which the binding energies and wave functions for some states of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms are affected by the dipole and higher multipole interactions of the electron with the meson or the antiproton. The meson or antiproton is treated as a classical point charge. Perturbation theory is employed to determine the admixture of discrete excited states of the unperturbed electron Hamiltonian. The unperturbed electron Hamiltonian takes into account only the monopole interaction of the electron with the meson. A variational method is employed to determine approximately the change in the binding energy as well as some of the more important features of the distortion of the electron wave function. It is found, in particular, that the binding energies of those states of the $\alpha K^{-}{e}^{-}$ atom in which the meson is in a circular orbit with principal quantum number $n=27, 28, or 29$ are lowered by slightly less than 1 eV. The maximum relative change in the amplitude of the electron wave function for one of these states is found to be roughly 20%.

Auger rates are estimated for some circular orbits of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms. It is found, as conjectured by Condo several years ago, that the Auger rate for a circular orbit depends sensitively on the multipolarity of the transition. In some instances, the multipolarity may be required by energy conservation to be large enough to permit a ${\pi }^{-}$ or a $K^{-}$ meson to decay rather than to eject an electron. In particular, the estimated Auger rates for those circular orbits of the $\alpha {\pi }^{-}{e}^{-}$, $\alpha K^{-}{e}^{-}$, and $\alpha \overline{p}{e}^{-}$ atoms with binding energies most nearly equal to that of a He atom are, respectively, 2×${10}^{12}$, 4×${10}^5$, and ≲${10}^3$ ${\sec }^{-1\mathrm{}}$. Radiative rates are also computed.

Excitation cross sections for the collisions $\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$,+Ne, Ar, $\mathrm{Kr}\to \mathrm{H}(2s, 2p_0, 2p_{\pm })+\mathrm{N}\mathrm{e},\mathrm{ }\mathrm{A}\mathrm{r},\mathrm{ }\mathrm{Kr}$ are calculated over the velocity range of 0.3-5.0 a.u. in the distorted Born, two-state (for argon only), and four-state impact-parameter approximations that do not allow for electron exchanges between the colliding atoms. The results are compared with earlier first Born and scaled first Born calculations and with experimental data. The four-state cross sections, while greatly reduced from the first Born results, are still between three and ten times greater than experiment. Polarization fractions are also calculated from the four-state cross sections and compared with experimental data and with previous calculations.

Many-electron perturbation theory has been used to investigate the contribution to atomic correlation energies from high-order terms. The treatment analyzes several aspects of the inhomogeneous-electron-gas and the electron-pair approaches. It discusses in detail the coupling of electronic angular momenta with the multipolar components of the Coulomb interaction. The results are expressed in terms of renormalized propagators, which include partial perturbation summations to infinite order. Calculations have been carried out for the neon atom to ascertain the importance of contributions from many-body ring diagrams. Numerical results indicate that the ratio of many-body to two-body correlation energies is about 0.10 for the $2p$ subshell of NeI and that the many-body correlation energy has a positive sign.

A simple modification of the Thomas-Fermi statistical model for electrons in atoms and ions is presented, which corrects one of the model's major deficiencies, namely, its overestimation of the electron density near the nucleus. Exploiting the fact that near the nucleus the potential is nearly Coulombic, boundary conditions are derived from wave mechanics and incorporated into the model equations. The resulting equations are expressed in integral form and solved by a straightforward iterative technique. Results for total atomic energies show marked improvement over the corresponding results obtained from the Thomas-Fermi model, with only a slight increase in the required computational effort. The procedure is extended to obtain a relativistic statistical model of the atom. Numerical results show good agreement with wave mechanics in total energy calculations and in the form of the density near the nucleus. The relativistic effects are of greater magnitude than exchange or inhomogeneity corrections to the Thomas-Fermi model for large $Z$ atoms.

Differential scattering cross sections for excitation of helium by electron impact from its ground state to its $2{}_{}{}^1{}_{}{}^{}P$ excited state have been measured at four incident electron energies in the range 26-55.5 eV for scattering angles between 10° and 70°, and at 81.6 eV for scattering angles between 10° and 80°. These differential cross sections have been placed on an absolute scale by normalizing them to the experimental absolute integral cross sections of Jobe and St. John. These experimental differential and integral cross sections have been compared with the results predicted by the Born approximation, and by several other first-order approximations in which direct excitation is calculated in the Born approximation and exchange scattering by various Ochkurlike approximations. The calculations provide reliable tests of these scattering theories since they are made using the accurate generalized oscillator strengths of Kim and Inokuti. As expected, these first-order theories are poor near threshold and exchange is important at high scattering angles for all energies. Further, the absolute magnitude of the calculated integral and small-angle differential cross sections is too large and is within 50% of experiment only at energies greater than 80 eV. These first-order models are in qualitative agreement with the experimental angular dependence at 34-81.6 eV for scattering angles between 10° and 40°. At higher scattering angles (corresponding to momentum transfers greater than about 1.6 a.u.), the calculated differential cross sections fall well below the experimental ones. The phase between the direct and exchange scattering amplitudes was found to be important at all energies, and is apparently not predicted correctly by any of the first-order models examined here. Some approximations for the exchange (e.g., Ochkur approximation and the post interaction form of the Ochkur-Rudge approximation) were found to be better for integral cross sections and some (e.g., prior Ochkur-Rudge approximation) were better for differential cross sections. The use of good analytic self-consistent-field (SCF) wave functions for both the ground and excited states was tested by computing generalized oscillator strengths from them and comparing these results with the calculations using the accurate generalized oscillator strengths. The SCF functions yield differential cross sections in quantitative disagreement (20%) with the accurate results, although the energy and angle dependence of the cross sections is predicted qualitatively correctly.

A general approximation method is developed for the treatment of bound quantum systems in the presence of an intense external electromagnetic field of long wavelength. The method is based upon a unitary transformation which approximately removes the electromagnetic field from the problem. The accuracy of the technique increases with the number of photons involved in any given process; and in the case of large photon number, the results have a simple, concise form resembling first-order perturbation theory. It is possible to handle intense-field problems with small numbers of photons also, but then the formalism takes on a complexity analogous to the corresponding perturbation expressions for the same number of photons. The theory is extended to the case where two electromagnetic field modes are present, one or both of which may be intense. Bound-bound transitions in a hydrogenlike atom are calculated as an illustration of the application of the method. One of the explicit nonlinear effects to appear is an intensity-dependent deviation of the transition probability behavior from $I^n$ for $n$-photon transitions, where $I$ is the field intensity. It is demonstrated that intensity effects are much more probable with bound electrons than with free electrons.

Cross sections have been measured for production of ${\mathrm{He}}^{+}$ ions by the collision of 10- to 30-keV ${\mathrm{He}}^0$ atoms in the triplet metastable state with target atoms of Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, and He. Fast ${\mathrm{He}}^0$ atoms are produced in the first of two gas targets in which various neutralizer gases may be present at low density. The fractions of ${\mathrm{He}}^0$ produced in the triplet metastable state in these various neutralizer gases are known. The fraction of fast ${\mathrm{He}}^{+}$ emerging from a second target containing Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, or He is analyzed as a function of the density of the second gas target, and the cross sections for ionization of ${\mathrm{He}}^0$ atoms from the metastable triplet state are determined. Typical values of the cross sections at 30 keV are 110±40, 37±17, 122±58, 86±42, 18±12, and 65±31 in units of ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$ for gas targets of Xe, Kr, ${\mathrm{H}}_2$, ${\mathrm{N}}_2$, Ar, Ne, and He, respectively.

When focusing a 4-GW, fast-rise-time, nsec-range laser onto a solid deuterium target, neutron production is observed. We give evidence for nuclear fusion reactions, measure the electronic temperature, and estimate the number of neutrons for each laser shot.

Inelastic energy ($Q$) profiles and ionization probabilities are measured for ${\mathrm{N}}^{+}$-Ar and ${\mathrm{O}}^{+}$-Kr collisions using the coincidence techniques of Kessel and Everhart. Incident-ion energies from 10 to 150 keV and scattering angles from 9° to 40° for ${\mathrm{N}}^{+}$-Ar collisions, and from 25 to 230 keV and 10° to 40° for ${\mathrm{O}}^{+}$-Kr collisions, are studied. The range of average $Q$ values ($\overline{Q}$) is from about 100 eV to about 1 keV for both cases. The average number of electrons lost in the collision varies from about 0.6 to 1.3 for nitrogen and from 3.3 to 4.6 for argon in the ${\mathrm{N}}^{+}$-Ar collisions. For the ${\mathrm{O}}^{+}$-Kr collisions, the ranges are zero to 1.7 and 2.6 to 6.6 for oxygen and Kr, respectively. For ${\mathrm{N}}^{+}$-Ar collisions, a plot of $\overline{Q}$ versus the distance of closest approach shows an abrupt increase of about 115 eV at about 0.15 Å. A study of the natural linewidths of the coincidence profiles indicates the presence of unresolved structure in this vicinity. For the ${\mathrm{O}}^{+}$-Kr collisions, $\overline{Q}$ was found to depend on both the distance of closest approach and the collision velocity, but not strongly on the scattering angle at higher energies.

The cross section for the excitation of the (0, 0) first negative band of ${\mathrm{N}}_2^{+}$ by electron impact has been measured, using photon-counting techniques, in the energy range from threshold to 3 keV and extrapolated to 10 keV by means of a Bethe-Oppenheimer relation. In order to avoid polarization effects, the primary measurements were made at the "magic angle" of 54° 44′; complementary measurements at 90° were also obtained for comparison purposes. The excitation cross section for the (0, 0) band reached its maximum value at an energy of about 100 eV where it was (1.74 ± 0.17) × ${10}^{-17\mathrm{}}$ ${\mathrm{cm}}^2$. The ratio of the total ionization cross section to the excitation cross section was nearly constant over the energy range from 30 eV to 10 keV, and had a value of 14.1.

Using a proportional counter as an x-ray detector, thin-target yields, as well as $K$ x-ray production and ionization cross sections, were determined for Ca, Ti, and Ni when bombarded with 2-28-MeV protons. Broad maxima in the cross sections were found at approximately 8.5, 10.4, and 16.6 MeV for Ca, Ti, and Ni, respectively, in agreement with theoretical calculations based on the Bethe-Born approximation. The shape of the cross-section-versus-bombarding-energy curve agrees well with theory. However, the absolute values of the cross sections were observed to be higher than predicted by theory when the generally accepted value for the effective charge ($Z-0.3\mathrm{}$) was chosen.

Inelastic energy-loss spectra induced by impact of ${\mathrm{H}}^{+}$, ${\mathrm{H}}_2^{+}$, and ${\mathrm{Ar}}^{+}$ on ${\mathrm{N}}_2$ have been measured at incident ion energies of 20-120 keV, with an energy resolution of about 2 eV. Prominent peaks are observed at energy losses of 9.5 and 13.8 eV. The first of these is well resolved and is attributed to excitation of the Lyman-Birge-Hopfield (LBH) system of ${\mathrm{N}}_2$. The peak at 13.8 eV is believed due primarily to excitation of the $b{}_{}{}^1{}_{}{}^{}\pi _u^{}{}_{}{}^{}$ band of the Worley-Jenkins series. The locations of these features on the energy-loss scale do not agree with results of the electron impact work of others and, in general, show trends with projectile velocity that are consistent with an assumed enhancement of excitation to higher vibrational states with the heavier particles. Collision cross sections for excitation of the two peaks are presented, as well as the total ionization cross section and the cross section for total inelastic processes in the case of proton impact.

We present a method for calculating the elastic scattering of electrons from atoms and molecules using the many-body Green's-function techniques of Martin and Schwinger. The procedure involves the self-consistent solution of a pair of equations; one for the one-particle Green's function and the other for the response function of the target in the time-dependent Hartree-Fock approximation (random-phase approximation). That both equations are one-dimensional provides a great computational advantage over more conventional techniques. We discuss the physical nature of our approximation and a numerical scheme to implement our theoretical discussion.