We report the first measurement of the absolute cross section for the fourth-order quantum electrodynamic process of double atomic-field bremsstrahlung. The experiment observed two photons radiated in coincidence at 90° and 270° with respect to a 75-keV electron beam incident on targets of silver, terbium, gold, and uranium. The measured cross section disagrees with the predictions of the first Born approximation in both magnitude and photon energy dependence. The atomic number dependence, however, is consistent with $Z^2$.

We have measured the three-photon resonant, four-photon ionization profile of atomic hydrogen. The width of the profile is large compared with the laser bandwidth, fine-structure splitting, Doppler width, and radiative and collisional rates. The shape, shift, width, and laser intensity dependence of the measured profiles are in excellent agreement with theoretical predictions.

We present a calculation of the photon energy dependence of the photoelectron spectrum of Ca from 11 to 28 eV, roughly the region between the $4p$ threshold and the lowest resonance due to $3p\to 3d$ excitations. Because of the occurrence of a "Cooper minimum" for $4s\to \epsilon p$ excitation close to threshold, which is not reproduced for the satellites, we predict that at low photon energy the $3d$ and particularly the $4p$ satellite will be stronger than the main $4s$ line.

An analytical solution of the Bloch equations is presented using as a driving function a complex hyperbolic secant pulse. The solution indicates that, under the appropriate conditions, the use of such a pulse creates a highly selective population inversion which, above a critical threshold, is independent of pulse (irradiating $B_1$ field) amplitude and hence $B_1$ field homogeneity. This result is shown to be in excellent agreement with experiment, and as an aid to comprehension, analogies to adiabatic rapid passage and self-induced transparency are drawn.

Convective velocity analysis of the electrohydrodynamic instabilities has been carried out by dynamic light scattering. Evidences of Doppler shift caused by the random motion of disclination lines in the convective flow are proposed. Based on that fact, speed distribution of the flow is analyzed. The validity of the analysis is confirmed measuring the real speed of moving disclination lines by serial photographs.

It is shown that neglecting the temperature dependence of thermal conductivities in the theory of Rayleigh-Bénard instability is inconsistent. A model is presented which takes this dependence into account in the boundary slabs and also, to some extent, in the fluid. As a result, the horizontal scale at the onset of convection even between thick and well conducting slabs can be large as compared to the fluid thickness. A connection is suggested to chaotic behavior at the onset of convection.

The increase in the radial line integral of the electron density in the National Bureau of Standards $\theta$-pinch plasma due to the ionization of the titanium impurity has been measured with the use of a He-Ne laser heterodyne quadrature interferometer. Titanium is injected as an impurity into the base gas of hydrogen with the use of a coaxial gun discharge between titanium electrodes. The Tix ion density at its peak abundance in the plasma is deduced in each discharge from the measured increase in electron density by knowing the temporal charge-state distribution of Ti ions with the use of spectroscopy and assuming charge neutrality.

It is well known that minimum principles for energy eigenvalues can be used not only for calculational purposes but also formally as the basis for studies of the nodal structure of the associated eigenfunctions. This formal feature is shown here to have a natural generalization to the zero-energy scattering problem, the scattering length playing the role of the energy eigenvalue in the formulation of the minimum principle. The number of nodes in the zero-energy wave function in a given partial wave for nonrelativistic potential scattering is shown to be equal to the number of negative-energy bound states of the same angular momentum L. Potentials with Coulomb tails are excluded from the present analysis, but will be treated elsewhere. (The connection with classical Sturm-Liouville theory comes perhaps as less of a surprise if one views the zero-energy state as being at the top of the discrete spectrum as well as at the bottom of the continuum.) The result derived here, when combined with the nodal definition of the phase shift along with some information on its threshold behavior, provides us with an alternative derivation of Levinson’s theorem relating the zero-energy phase shift for orbital angular momentum L, ${\delta }_L$(0), to the number of bound states of the same L. (Very similar results can be derived for potential scattering as described by the Dirac and Klein-Gordon equations.) It may well be possible to extend some of the results obtained here to a number of single-channel multiparticle scattering problems, but this will be discussed elsewhere.

The perturbation series for the ground-state wave function of the anharmonic oscillator has been reexamined. Rigorous analysis enables the factoring of behavior dominant in the true eigenfunction. In particular, the perturbation problem is found to reduce significantly if the asymptotic WKB wave function of zero order is employed as the zero-order wave function.

In this paper the order-α contribution of the inner-vertex graph to the decay rate of orthopositronium is obtained in analytic form.

In this paper the corrections of relative order (Zα${)}^2$ to all multipole polarizabilities of a hydrogenic ion of nuclear charge Z are computed, with use of third-order perturbation theory with nonrelativistic wave functions. To accomplish this, the spin-independent part of the Pauli Hamiltonian of order ${\alpha }^2$ is treated as a perturbation along with the usual Coulomb interaction expanded in a multipole series. The leading (dipole) correction is in agreement with the previous results of Zon et al. In addition, the previously discussed second-order energy shift has now been calculated analytically. Both of these corrections are applied to the high-lying Rydberg states of helium, yielding small but important corrections to the fine-structure splittings.

A derivation of resonance projection operators, in the Feshbach sense, is presented in detail, with inclusion of angular momentum and spin variables. The resultant operators, P and Q, are written in a transparent and manifestly symmetric form. The operators depend on eigensolutions of a homogeneous integral equation. The equation is solved and hence the operators are explicitly constructed for the two-electron (i.e., He-like) targets in a nonseparable (the open-shell) approximation; this procedure can readily be extended to any configuration-interaction-type target function. The kernel of the auxiliary integral equation is also explicitly derived for a Hylleraas-type target function; a Rayleigh-Ritz variational principle is written down for its eigenfunctions. It is pointed out that these (Feshbach) P and Q operators are not formally idempotent, but it is shown that their matrix elements between antisymmetric functions are. This makes them completely suitable for calculation of autoionization states via diagonalization of QHQ. A basic problem in using the concomitant optical potential for scattering calculations remains and is briefly discussed. The generalization of these operators to the inelastic domain is also given (in an appendix).

For a classical oscillator subject to a time-dependent perturbation, the average change in the action variable 〈ΔJ〉=〈J-$J_0$〉 is related to its fluctuation 〈(ΔJ${)}^2$〉 by 〈ΔJ〉=(1/2)∂〈(ΔJ${)}^2$〉/∂$J_0$, where $J_0$ is the initial value of J and the average is over the initial value ${\theta }_0$ of the angle variable. In this paper, the quantum-mechanical generalization of this relation is derived, and we discuss the correspondence between our work and the usual treatment of the fluctuation-dissipation theorem for a system which initially is described by a canonical distribution.

The many-body perturbation theory (MBPT) in the coupled-cluster formulation is applied to perform very accurate calculations on the $2^2$S and $2^2$P states of the lithium atom. The computational procedure is based on coupled one- and two-particle equations, which are solved iteratively. In this way it has been possible to evaluate almost all one- and two-particle effects—i.e., the core polarization and the pair correlation—to essentially all orders of perturbation theory. The main reasons for this work are to test the computational procedure and to determine the significance of genuine three-particle effects, which are not included in the calculation. The total energy, the valence electron binding energies, and the hyperfine-interaction parameters are calculated for the two states. The perturbation effect, i.e., the difference between the experimental value and the Hartree-Fock result, is in all cases reproduced within about 1%, except for the small hyperfine parameter of the $2^2$$P_{3/2}$ state, where this discrepancy is about 4%, mainly due to some remaining error in the induced contact interaction. The quadrupole parameter of the $2^2$$P_{3/2}$ state is expected to be accurate to a few tenths of a percent. No improved value of the quadrupole moment can be given, however, due to experimental uncertainty.

A general method for constructing bases for operator manifolds for any propagator, which satisfy ‘‘vacuum annihilation conditions’’ (VAC’s) is developed. This approach is based on the observation that if the transformation of the unperturbed ground state to the correlated ground state is represented as a rotation in the Fock space, the corresponding rotation induced in the basis of the concerned operator space would generate a basis which satisfies VAC’s on the correlated ground state. The associated requirements for the Hermiticity of superoperator Hamiltonian would also be met in this new basis. The proposed method is noniterative in that, once the form of the ground-state function is specified, the expansion of the operator manifold satisfying VAC’s on the ground state does not require any iterative readjustment. The resultant propagators in this approach are fully linked. It is shown that this theory is equivalent to a propagator formalism in terms of hole- and particle-creation and/or annihilation operators with a modified effective Hamiltonian. The self-consistent electron and polarization propagators are considered as examples, and their underlying perturbative structures are analyzed. The role of density shift operators and higher-rank operators are discussed.

The well-known magnetic or optical Bloch equations are extended to the case of unstable systems such as, e.g., spontaneously decaying particles and molecules undergoing chemical reactions or decaying from excited states back to states other than those involved in resonance. The modified equations are derived from a general theory of irreversible processes where quantum Markovian master equations and the corresponding completely positive dynamical semigroups dictate the time evolution of density operators. The results are of particular importance in those situations where decay occurs level-selectively and all relaxation and decay constants are of comparable order of magnitude. The obtained generalized Bloch equations are of direct applicability to problems of time-resolved magnetic or optical resonance spectroscopy.

We examine the electric and magnetic form factors in the nonrelativistic on-shell photon-atom scattering amplitude both with and without retardation and with and without spin. We show that to the extent that we neglect hyperfine splitting compared to ordinary atomic-level separations, the Pauli spin interaction with the photon field leads only to a magnetic form factor even with the inclusion of retardation. On the other hand, the radiation Hamiltonian in the minimal-coupling scheme leads to both electric and magnetic form factors when retardation is included. However, if the scattering atom is in a rotationally invariant S state, we can show that the electric and magnetic form factors are not independent when spin is neglected. This observation is then discussed along with the higher-multipole contributions to the retarded long-range potential between a pair of spinless neutral atoms and in Rydberg states between the core and the outer electron. When the atoms and the core ions in the Rydberg atoms involved are hydrogenic, another relation occurs because of $O_4$ symmetry in hydrogen when spin is neglected. In this case it becomes possible to express all derivatives with respect to the 4-momentum transfer square t of the electric and magnetic spectral functions in terms of the electric spectral function at zero t, which is in turn expressible in terms of hydrogen dipole oscillator strengths. It is thus possible to express all nonrelativistic higher multipole contributions to the retarded long-range interaction due to two-photon exchange between a pair of hydrogenic atoms or in heliumlike Rydberg atoms in terms of hydrogenic dipole oscillator strength sum rules.

A distorted-wave method is applied to electron-impact excitations of He-like (Li ii and O vii) and Be-like (C iii) ions. In the method, the same distortion potential is assumed for both the initial and the final states, and electron exchange is taken into account only between interacting electrons. The collision strengths are calculated for the excitations of 2 ${}^1$P, 2 ${}^1$S, 2 ${}^3$P, and 2 ${}^3$S states of the He-like ions and 2s2p ${}^1$P and 2s2p ${}^3$P states of the Be-like ion, and compared with the results of more elaborate calculations (e.g., the close-coupling-type ones). Good agreement is found in most cases if use is made of the target wave functions of the same or comparable accuracy. Also examined is the Coulomb-wave approximation, in which the distorted wave is replaced by the corresponding Coulomb wave.

The elastic and inelastic differential cross sections of 35-keV electrons incident on Ne were measured in the momentum-transfer range of 1–10 a.u. (20–200 mrad). The accuracies maintained throughout the experiment were 0.2% for the elastic scattering intensities and 2’’ for the scattering angles. The diffraction unit is discussed. The elastic data are compared with partial-wave cross sections based on several atomic wave functions (Hartree-Fock, configuration-interaction, and independent-electron-pair approximation). None of the theoretical results coincides with the data within the error limits over the whole measured angular range. The large-angle results show very small deviations from the calculated cross sections and so this range is used to bring the measured cross sections to an absolute scale. The elastic, inelastic, and total cross sections were integrated and several potential energies were evaluated. The differences between the measured potential energies and the Hartree-Fock results reveal the importance of correlation for the electron-nuclear potential $V_{\mathrm{ne}}$ and the electron-electron potential $V_{\mathrm{ee}}$ which in turn can be decomposed into $V_{\mathrm{ee}}$(Coulomb) and $V_{\mathrm{ee}}$(exchange) parts.

A comprehensive theoretical treatment is presented for the electron detachment cross section, differential in both electron momentum and direction, for collisions of 0.5-MeV ${\mathrm{H}}^{\mathrm{-}}$ projectiles on He targets. Our calculation, which assumes that the residual H atom is left in the 1s state, employs the usual first Born approximation as well as the closure approximation (in order to sum over all He target final states). Electron correlations within the ${\mathrm{H}}^{\mathrm{-}}$ system are treated in detail within the framework of the adiabatic hyperspherical coordinate approximation. In particular, for the first time for this collision process, angular correlations are included. The s, p, and d partial-wave components of the detached electron hyperspherical coordinate wave function are also included. The helium target is described by the atomic form factor and the incoherent scattering function tabulated by Hubbell et al. as well as by an average He excitation energy, I${¯}_{\mathrm{He}}$. The prescription of Lee and Chen for I${¯}_{\mathrm{He}}$, which for small scattering angles gives the value 35 eV is found to result in the best agreement of our calculated doubly differential cross sections with experiment, both in shape and in predicted peak energies. The unique feature of the experimental doubly differential detachment cross section of Menendez and Duncan, that for electron-scattering angles less than 4° there is a double peak, is reproduced in our calculations. However, the predicted higher-energy peak is smaller in magnitude and higher in energy than that observed experimentally. This difference is attributed to the influence of excited H-atom states, which are measured in the experiments. Fictitious calculations are carried out for the doubly differential cross sections in which the s-wave electron phase shift is fixed at zero radians instead of its true monotonically decreasing value with increasing electron energy from the value π at threshold. These fictitious calculations demonstrate the disappearance of the double-peak structure of the cross section and confirm the origin of the double peak in the s- and p-wave interference and in the initial π phase shift of the s partial wave. Though our single differential cross sections differ quantitatively from previous calculations of Maleki and Macek, the approximate factor of 2 discrepancy between the theoretical predictions and the absolute experimental measurements remains unexplained.