The radial integrals for electron-pair production in a point Coulomb potential have been expressed by Sud, Sharma, and Sud in terms of the matrix generalization of the $\Gamma$ function. Two new partial differential equations in photon energy satisfied by the matrix $\mathit{\Gamma }$ function are obtained. We have obtained, on integrating the partial differential equations, accurate radial integrals as a function of photon energy for the pair production by intermediate-energy photons. The cross section in the tip region of the spectrum are calculated for photons of energy 5.0 to 10.0 MeV for ${}_{}{}^{92}{}_{}{}^{}\mathrm{U}$. The new technique results in extensive saving in computer time as the basic radial integrals in terms of the hyper-geometric function $F_2$ are computed at one photon energy for each pair of partial waves. The results of our calculations are compared with plane-wave Born-approximation results and with the calculations of Dugne and of Deck, Moroi, and Alling.

Recently (e.g., Rich, 1981; Mills, 1983) it has been realized that the effect of the annihilation width on microwave absorption line shape for the Zeeman transitions between the hf levels of the Ps atom in its ground state has to be accounted for at a better level of approximation than it has been in the past. In the traditional Breit-Rabi representation the subtle effects of the annihilation widths show up as an extra off-diagonal coupling between the off-resonant and one of the near-resonant states. In this paper we derive an analytical line-shape formula by solving the rotating-wave amplitude equations within the BR representation, where the off-resonant off-diagonal coupling is treated by the adiabatic-elimination procedure. The resulting line shape is found to be slightly asymmetric in form—a conclusion which has been first reached by Mills (1983). It is seen explicitly that due to the off-diagonal coupling an effective decay constant is dependent on the microwave frequency ($\omega$). It is also shown that only if, as a zeroth approximation, this $\omega$ dependence is neglected, then a formula for the hyperfine interval $\Delta W$, recently given by Rich (1981) on the basis of heuristic arguments, may be obtained. Explicit illustrations of the present slightly asymmetric line-shape function, and the $\omega$ dependence of the said effective decay constant [${\Lambda }_{1,0}\left(\omega \right)$] are also presented. We have taken this opportunity to point out certain apparent discrepancies noted among some of the previous line-shape formulas.

Photoionization in the presence of a probe electromagnetic wave is studied. A continuum wave function is obtained in a weak-field, low-frequency limit for low-energy photoelectrons. When the electron and photon energies are comparable, the absorption and stimulated-emission angular distributions show a significant departure from results based on a much-used on-shell approximation of Kroll and Watson.

Optical four-wave mixing resonances in sodium vapor induced by collisions with inert buffer gases (He, Ar, Xe, ${\mathrm{N}}_2$) are characterized at high resolution (< 5 MHz) using lasers tuned near the $D$ lines of Na. These resonances are interpreted in terms of coherent scattering from a population grating established by collisional absorption of the incident radiation. The roles of homogeneous and inhomogeneous contributions to the resonance line shapes are clarified. The line shapes exhibit structure sharper than the predicted linewidth, that characteristic of the $3P$-to-$3S$ transition rate. We show that this is caused by collision-induced optical pumping which introduces the ground-state lifetime into the grating relaxation physics. These long-lived gratings are exemplified dramatically by experiments in the presence of ${\mathrm{N}}_2$ which collisionally quenches the Na $3P$ states. Similar results are obtained in Xe where it is argued that excimer formation with the $3P$ states plays a role in the population dynamics. Model calculations of the effects of sodium level degeneracy on the grating dynamics are presented to support these conclusions. Finally we present data illustrating interference between the collision-induced population grating resonances detailed here and collision-induced coherent Raman resonances between Zeeman sublevels of the ground state.

The high-energy asymptotic behavior of the oscillator-strength distribution of nonrelativistic $N$-electron atoms and molecules is examined. A derivation is presented which leads to the coefficients of the first two asymptotic terms of the oscillator-strength density in terms of expectation values of the wave function. Furthermore, it is shown that truncating the contribution of these first two terms beyond some cutoff energy leads to a sum rule for the third moment of the resulting modified distribution. Numerical calculations have been performed on atomic hydrogen which illustrate the sum rule for the third moment of the modified distribution.

Quantum-beat and sideband spectra of recoilless $\gamma$ radiation of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ were measured as a function of frequency and the voltage on the quartz crystal on which a ${}_{}{}^{57}{}_{}{}^{}\mathrm{Co}$ source was deposited. The sideband spectra were analyzed using a Rice distribution of the modulation index. The width of this distribution was shown to depend on the frequency; the narrowest distribution was found at 9.795 MHz. The results of the quantum-beat measurements are in agreement with the optical theory of Monahan and Perlow.

We have measured the far-wing collisional redistribution line shape, the redistributed fluorescence polarization, and the collisional alignment decay rates for barium perturbed by argon and xenon. The experiment was performed with a heated gas cell ($T\sim 900$ K) with perturber-gas densities in the 1—30-Torr range and laser light detuned ± 3— 1000 ${\mathrm{cm}}^{-1\mathrm{}}$ from the 5535-Å Ba I $6{}_{}{}^1{}_{}{}^{}S-6\mathrm{}{}_{}{}^1{}_{}{}^{}P$ resonance line. Metal-vapor densities were determined by a Rayleigh scattering technique, which is outlined in detail. By correlating structure in the line shape with that of the polarization, we are able to make definitive statements about the interatomic potentials. The Ba data show strong similarities with previous experimental results for similar two-electron atoms, namely Ca, Sr, and Hg, and so our conclusions are of relevance to these systems as well.

We discuss strong laser-atom interactions that are subjected to jump-type (random telegraph) random-phase noise. Physically, the jumps may arise from laser fluctuations, from collisions of various kinds, or from other external forces. Our discussion is carried out in two stages. First, direct and partially heuristic calculations determine the laser spectrum and also give a third-order differential equation for the average inversion of a two-level atom on resonance. At this stage a number of general features of the interaction are able to be studied easily. The optical analog of motional narrowing, for example, is clearly predicted. Second, we show that the theory of generalized Poisson processes allows laser-atom interactions in the presence of random telegraph noise of all kinds (not only phase noise) to be treated systematically, by means of a master equation first used in the context of quantum optics by Burshtein. We use the Burshtein equation to obtain an exact expression for the two-level atom's steady-state resonance fluorescence spectrum, when the exciting laser exhibits phase telegraph noise. Some comparisons are made with results obtained from other noise models. Detailed treatments of the effects of other than phase noise are given in other papers.

We extend our study of the effects of jump-type noise on laser-atom interactions to frequency-telegraph noise. Such noise can be used as a model of collisional effects, in which the atomic transition frequency randomly jumps, or as a model of finite laser bandwidth effects, in which the laser frequency exhibits random jumps. We show that these two types of frequency noise can be distinguished in light-scattering spectra. We also discuss examples which demonstrate both temporal and spectral motional narrowing, nonexponential correlations, and non-Lorentzian spectra. Its exact solubility in finite terms makes the frequency-telegraph noise model an attractive alternative to the white-noise Ornstein-Uhlenbeck frequency noise model which has been previously applied to laser-atom interactions.

We present detailed measurements of ionization of highly excited triplet helium atoms in a static electric field. The atoms were prepared in states with energy $E$ close to the saddle-point threshold $E=-2\mathrm{}{\left[F\right(\mathrm{a}.\mathrm{u}.\mathrm{}\left)\right]}^{\frac{1}{2}}$. The electric field $F$ was sufficiently strong for the states to be characterized by total spin $S$ and absolute value of the magnetic quantum number $M_L$. For $M_L=0\mathrm{}$ states the experiments measured ionization properties of adiabatic states. In another case, $\left|M_L\right|=2\mathrm{}$, they predominantly measured those of diabatic states. In both cases the ionization rate was found to be a highly nonmonotonic function of the field strength. The observations are analyzed in terms of a theory of the helium density of states in an electric field. A companion paper [D. A. Harmin, Phys. Rev. A 30, 2413 (1984)] develops in detail the general theory, which uses quantum defects to parametrize the effect of the core interaction. The agreement between measured and calculated ionization curves is good, indicating that the field ionization of a nonhydrogenic atom can now be understood in a detailed, quantitative, and predictive sense.

A theory of nonhydrogenic Stark spectra based on the hydrogen atom is specialized to quasidiscrete levels. Algebraic expressions for level positions ${\epsilon }_r$, widths ${\Gamma }_r$, and oscillator strengths $f_r^F$ are derived in terms of matrices ${\mathit{H}}^F$ and ${\mathit{h}}^F$, which represent the hydrogenic density of states in a Stark field $F$. Core effects appear through zero-field quantum defects ${\mu }_l$ and dipole matrix elements $d_l^0$. Normalized oscillator strengths ${\overline{f}}_r^F$ are defined which are independent of all $d_l^0$ for $s\to p$ transitions. Isolated and interacting Stark manifolds with $m=0\mathrm{} \mathrm{and} 1$ are examined for systems with two nonnegligible ${\mu }_l$. Extensive comparisons are made with experimental Li spectra and matrix-diagonalization calculations of Zimmerman, Littman, Kash, and Kleppner [Phys. Rev. A 20, 2251 (1979); ZLKK]. For small fields $F<\mathrm{}\frac{1}{3n^5}$ level positions are given analytically with respect to H levels of fixed $n$; $m=0\mathrm{}$ intensity distributions do not appear hydrogenic in Li since ${\mu }_0\sim \frac{1}{2}$. At $F>\mathrm{}\frac{1}{3n^5}$, degenerate parabolic eigenstates from different manifolds are coupled by the spherical core and avoid crossing. The upper levels disappear at $m=1\mathrm{}$ anticrossings in Li, as observed in ZLKK. For $m=0\mathrm{}$ the lower levels usually vanish instead. A full Stark map of calculated intensities ${\overline{f}}_r^F$ is presented for Li ($m=0\mathrm{}$) and agrees with experiment. Pseudocrossings occur at near triple degeneracies of hydrogen Stark states. Extensions to include $\mathrm{ls}$ coupling are indicated. Experimental ionization rates in He are analyzed in a companion paper by van de Water, Mariani, and Koch [Phys. Rev. A 30, 2399 (1984)].

Natural radiative lifetimes have been determined in the determined in the $3\mathrm{sns} {}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{} \mathrm{}(n=4-15\mathrm{})\mathrm{}$ and the $3\mathrm{snd} {}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{} \mathrm{}(n=3-15\mathrm{})\mathrm{}$ sequences of Mg I employing a pulsed-laser system. The radiative lifetimes in the ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ sequence and of the higher members in the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ sequence are unperturbed and scale as ${\left(n^{*}\right)}^{2.6}$ (where $n^{*}$ is the effective principal quantum number), while the lifetimes of the lower members in the ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$ sequence are perturbed by the doubly excited $3p^2$ configuration. The measured lifetimes are compared with available theoretical calculations, and a very good agreement is obtained.

The problem of stimulated recombination at a resonance is investigated by a time-dependent, non-perturbative approach. The number of pairs recombined by a laser pulse is computed as a function of the intensity, of the pulse duration, and of the initial electron-energy distribution (as well as of the parameters which characterize the atomic resonance and its field-induced coupling to the final bound state). The role of spontaneous emission (or other paths) from the recombined state (if it is excited) is also discussed. Numerical results are given including an example of recombination to the ground state in the Sr atom.

The results of an exact analytic calculation of the Kramers-Heisenberg matrix elements for the two-photon transitions $3s-1s$ and $3d-1s$ in hydrogenic atoms are presented. The formulas obtained are used for the study of two-photon emission in the $n=3\mathrm{}\to n=1\mathrm{}$ transition. The numerical results are compared with the experimental data of Bannett and Freund concerning the $K$-shell vacancy filling by two-photon emission in Mo. Our hydrogenic calculation supports the experimental conclusion that in the Mo case the $K^{-1\mathrm{}}\to M^{-1\mathrm{}}$ transition is more probable than the $K^{-1\mathrm{}}\to L^{-1\mathrm{}}$ transition.

We obtain and discuss a closed-form expression for the time-dependent density matrix associated with spontaneous radiative decay from a continuum or a set of discrete states to a lower discrete state.

Energy shifts in the $M-NN$ Auger spectrum of krypton caused by strong electron correlation in $4s^{0}4p^6$ and $4s^{1}4p^5$ configurations are studied by comparing the experimental results with the theoretical estimates based on Dirac-Fock multiconfiguration computations.

The problem of nonlinear coherence in three-level systems exposed to two monochromatic radiation fields is treated using the unitary symmetries of SU(3). The Hamiltonian and the initial density operator are brought by a series of unitary transformations into a form in which the problem is reduced to a nutation between the two levels connected by the two-photon transition, i.e., to a time-dependent unitary rotation within the proper SU(2) subgroup. The net effect of the two modes in which the photons can combine in the nonlinear transition is shown to vanish gradually as the three levels approach an equidistant pattern. This certifies that two-photon processes can occur in systems which obey SU(3) symmetry, but not in those which obey the symmetry of SU(2). Four independent constants of motion are identified for the process of two-photon nutation in three-level systems.

Differential incoherent-scattering cross sections of 661.6-keV $\gamma$ rays in Si, C, and SiC and Ag, I, and AgI have been measured to establish the validity of the mixture rule. Differential incoherent-scattering cross sections for the same energy in solid compounds CaO, ${\mathrm{CaCl}}_2$, ${\mathrm{MgF}}_2$, NaCl, ${\mathrm{NaNO}}_2$, ${\mathrm{KNO}}_3$, ${\mathrm{LiSO}}_4$, ${\mathrm{ZrO}}_2$, ${\mathrm{SrF}}_2$, ${\mathrm{NaBrO}}_3$, ${\mathrm{ZrNO}}_3$, KI, ${\mathrm{AgNO}}_3$, ${\mathrm{V}}_2$${\mathrm{O}}_5$, ${\mathrm{MgSO}}_3$${.6\mathrm{H}}_2$O, ${\mathrm{MgSO}}_4$${.7\mathrm{H}}_2$O, and ${\mathrm{CoSO}}_3$${.6\mathrm{H}}_2$O and in elements Ca and Mg have been measured by an improved conical geometry method. Using these cross sections and the mixture rule, the cross sections of gaseous elements N, O, F, and Cl, liquid element Br, and solid elements Li, Na, S, K, V, Co, Sr, and Zr have been derived. Measured cross sections are in good agreement with the theoretically calculated cross sections.

The coupling between betatron and synchrotron oscillations in a tapered wiggler free-electron laser (FEL) is investigated analytically and numerically. The resonance between the oscillations, first investigated by Rosenbluth, is shown to be important only for a very limited range of parameters. In general, the resonance is not a serious detrapping mechanism for high-power FEL amplifiers.

We examine from first principles the effects of a stochastic pump on the output fluctuations of a laser. The Hamiltonian for a four-level molecule interacting with a stochastic semiclassical pump field and quantized laser field is used to obtain density-matrix equations of motion. Noise from the pump field and from spontaneous emission is introduced systematically, as opposed to the ad hoc inclusion of random forces in the semiclassical equations. The relationship of this theory with previous quantum and semiclassical equations is described. New equations are derived on which computer simulations are performed to compare our theoretical results to experimental data for a single-mode dye laser.