A recent variational study of the Dirac Coulomb problem using a discrete basis set leads to a conjecture of a type of Hylleraas-Undheim theorem for "positive energy" solutions. Analysis of the matrices involved suggests convergence criteria for the method which may be of use in self-consistent-field calculations.

Frequency shifts of hyperfine splittings of ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ states due to the blackbody radiation field are calculated. It is shown that they can be estimated from the dc hyperfine Stark shifts, which have previously been measured in the ground states of hydrogen and the alkali atoms. The shift at 300 K is large enough to be significant in primary Cs atomic beam frequency standards, and should be measurable. A simple method of calculating the hyperfine Stark shifts is described, which is based on the Bates-Damgaard method for determining radial matrix elements and the Fermi-Segrè formula for determining the contact hyperfine matrix elements. It is applied to ${\mathrm{Ba}}^{+}$ and ${\mathrm{Hg}}^{+}$, for which no experimental data are yet available, and which are currently of interest for frequency standards.

We have demonstrated a new kind of microwave-optical double-resonance experiment monitoring the nonlinear interaction between microwave radiation and a laser beam via changes in light polarization. Compared with conventional microwave-optical double-resonance experiments signals are observed at considerably lower laser power density and with greatly improved resolution.

Temperature versus concentration phase diagrams are obtained for octylcyanobiphenyl (8CB) doped with biphenyl in magnetic fields up to 187 kOe. The data show no observable decrease in the nematic-isotropic latent heat with field. These results seem to be in contrast to the claim by Keyes and Shane that a field-induced critical point may be nearby.

The atomic $L_{2,3}{M}_{4,5}{M}_{4,5}$ Auger electron spectrum of Cu has been measured and analyzed in detail. Besides determination of the kinetic energies and relative intensities of the lines in the Auger spectrum, the free-atom binding energies $E_B\left(2\mathrm{}{p}_{\frac{3}{2}}\right)=939.85\mathrm{}\pm 0.15$ eV and $E_B\left(2\mathrm{}{p}_{\frac{1}{2}}\right)=959.45\mathrm{}\pm 0.15$ eV are also obtained. The comparison with corresponding solid-state results gives 2.5 eV for the solid-state binding-energy shift of $2p$ levels and 13.2 eV for the $L_{2,3}{M}_{4,5}{M}_{4,5}$ Auger shift. $L_{3}M-M_{4,5}{M}_{4,5}M$ satellite Auger lines arising from primary ionization in $L_1$ shell are seen clearly in the measured spectrum. They have been discussed and compared with the corresponding solid-state spectra. After correction for the $L_{2}M-M_{4,5}{M}_{4,5}M$ satellite spectrum, which overlaps the $L_3{M}_{4,5}{M}_{4,5}$ spectrum, the intensity ratio between $L_3$ and $L_2$ Auger groups was found to obey the statistical ratio quite well in contradiction to solid-state measurements, where $L_2{L}_3{M}_{4,5}$ Coster-Kronig transitions are energetically possible and modify this intensity ratio.

Temporal evolution of a depression of plasma edge density was observed near and away from a phased-array antenna launching lower-hybrid waves in a nearly fully ionized plasma. When equilibrium is reached, the magnitude of the depression is in agreement with ponderomotive theory.

A time-dependent quantum theory of multiphoton ionization and dissociation is presented. The novel and crucial feature is the use of Floquet amplitudes from semiclassical radiation theory in an $R$-matrix theory based upon molecular $R$-matrix states dressed by photon number states. A simple numerical example is presented (time dependence of the one-photon dissociation yield from a square well).

A new accelerator concept is proposed which has the potential to reach particle energies comparable to the largest particle energies in cosmic rays and far in excess of what can be reached with conventional accelerator technology. In the proposed new concept, a large cylindrical cloud of charged particles is produced by radial injection into a long solenoid where it is radially compressed by a rising magnetic field. The magnetic field confines the cloud radially, but not axially, and the cloud is therefore permitted to expand axially. During this axial-expansion process, the few particles positioned near the head of this cloud, albeit not the particles in the rest of the cloud, attain very large energies. The head of the axially expanding cloud thereby becomes a very powerful pulsed beam. If the compressing magnetic field rises to ∼ ${10}^5$ G in about ∼ ${10}^{-5\mathrm{}}$ sec, and if the solenoid is ∼ 10 km long, the attainable particle energies are ∼ ${10}^{13}$ eV. If, as in the single-pass collider concept, two accelerators are used projecting their beams head on, the equivalent stationary-target energies for electrons are as large as ∼ ${10}^{20}$ eV and for protons ∼ ${10}^{17}$ eV. The power of the pulsed beam reaches ∼ ${10}^{18}$ W, lasting for 3 × ${10}^{-11\mathrm{}}$ sec with an energy of ∼ ${10}^7$ joule. The particle number density in the beam is ∼ ${10}^{13}$ ${\mathrm{cm}}^{-3\mathrm{}}$. With the use of magnetic-flux-compression techniques the attainable particle energies can conceivably be raised to ∼ ${10}^{14}$ eV, with equivalent colliding-beam energies of ∼ ${10}^{22}$ eV for electrons and ${10}^{19}$ eV for protons.

The solution of the time-dependent Hamiltonian for the semiclassical dipole interaction of a multilevel atom with monochromatic electromagnetic fields is presented. Characteristics of the eigenvalue equation are investigated. Results are presented for the interaction of unequally spaced multilevel atoms with multiple monochromatic electromagnetic fields. The connection with the quantized-field method is discussed. Complications due to atomic decay are included only in the final discussion.

The relativistic random-phase approximation is generalized to describe excitations of an atomic system having a multiconfiguration ground state. The response of such an atom to an imposed harmonic perturbation is determined by applying the time-dependent variational principle to a multiconfiguration wave function constructed from Dirac orbitals. Terms in the wave function independent of the external field lead to the multiconfiguration Dirac-Fock description of the ground state. Terms proportional to the external field lead to a multiconfiguration generalization of the relativistic random-phase approximation. For the special case of an atom having a ground state with two electrons coupled to $J=0\mathrm{}$ outside of closed shells, we write out in detail equations for the configuration weights and for the electronic orbitals. These equations are expanded in a suitable basis to give expressions for the excitation probabilities. An angular momentum analysis is carried out leading to a set of coupled algebraic equations for the configuration weights and a set of radial differential equations for the electronic orbitals.

Self-consistent polarization-propagator approximations (i.e., those based on a proper vacuum) are compared to conventional time-dependent Hartree-Fock — random-phaseapproximation ones, with special attention to the fulfillment of the $f$-sum rule. The effect on the properties of the consistent propagator, based on a general-antisymmetrizedgeminal-power vacuum, when degeneracies occurring in the first-order reduced-density matrix of this vacuum are examined. The foregoing analysis shows that low-lying electronic states can be expected to become degenerate with the vacuum in conjunction with superphenomena in extended systems and oscillator-strength anomalies in finite ones.

Nonrelativistic and relativistic self-consistent-field wave functions of the Hartree-Fock type and with statistical exchange have been used for the calculation of radial hyperfine integrals for the $3d$-shell atoms within the $3d^{N+1\mathrm{}}4s$ and $3d^{N+2\mathrm{}}$ configurations. The mean value of $r^{-3\mathrm{}}$ for the $3d$ electron and the electron density at the nucleus for the $4s$ electron have been evaluated with the nonrelativistic wave functions. The relativistic wave functions have been used for the calculation of radial integrals appearing in an effective hyperfine Hamiltonian for the magnetic dipole and electric quadrupole interaction. For the magnetic dipole interaction the relativistic wave functions calculated with a statistical exchange potential are found to describe the hyperfine interaction for the $4s$ electron in a better way than what is achieved with the HF potential. The experimental orbital, spin-dipole, and contact radial parameters for the $3d$ electrons of some of the elements seem to be strongly influenced by configuration-interaction effects, which are not included in our theoretical values. The magnitude of configuration-interaction effects has been estimated for the orbital and spin-dipole parts by comparing existing experimental radial integrals with the corresponding relativistic ones. The pure relativistic parameters in the effective Hamiltonian for the quadrupole interaction are found to be in good agreement with the experimental values for manganese and cobalt, while the experimental uncertainty for the parameters of the other elements is still too large for a critical comparison to be done. Quadrupole moments have been evaluated with the use of published experimental hyperfine parameters and theoretical radial integrals calculated in this work. A comparison between ratios of experimental quadrupole parameters and relativistic ones gave an estimate of the quadrupole shielding, known as the Sternheimer effect.

Two rigorous lower bounds to $T_2$, the Weizsäcker correction, have been derived: $T_2\ge \left(\frac{{\pi }^{\frac{4}{3}}{2}^{\frac{2}{3}}}{24}\right)\times {\left(\int {\rho }^3\left(\overrightarrow{\mathrm{r}}\right)d\overrightarrow{\mathrm{r}}\right)}^{\frac{1}{3}}=T_2^{B1\mathrm{}}\left[\rho \right]$ and $T_2>\left(\frac{1}{72}\right)<\mathrm{}{r}^{-2\mathrm{}}>=T_2^{B2\mathrm{}}\left[\rho \right]$. The first bound is universal, while the second holds only for spherically symmetric bound systems. Numerical comparisons employing the Hartree-Fock atomic densities reveal that the bounds are not very tight; however, the ratios $\frac{T_2}{T_2^{B1\mathrm{}}}$ and $\frac{T_2}{T_2^{B2\mathrm{}}}$, though decreasing slowly with increasing $Z$, remain fairly constant for $Z=2\mathrm{}$ through 24. The implications of these bounds in the variational context are discussed.

The different approximate versions of a coupled-cluster approach (CCA) are discussed and applied for the correlation-energy calculations of small closed-shell molecular systems. The CCA results reproduce the corresponding configuration-interaction correlation energies with very high accuracy. The CCA construction of Nesbet's hierarchy of Bethe-Goldstone equations and the Newton-Raphson method to accelerate the iterative solution of CCA systems of coupled nonlinear equations are presented.

Absolute emission cross sections for electron-impact excitation of the $3d^{10}4p {}_{}{}^2{}_{}{}^{}P$ and $3d^{10}5s {}_{}{}^2{}_{}{}^{}S$ terms of ${\mathrm{Zn}}^{+}$ have been measured from below threshold to about 790 eV (${}_{}{}^2{}_{}{}^{}P$) and 388 eV (${}_{}{}^2{}_{}{}^{}S$) using the crossed-charged-beams technique. Both transitions have the abrupt onset at threshold characteristic of positive-ion excitation. The ${}_{}{}^2{}_{}{}^{}P$ cross section shows considerable structure in the interval from threshold to near 20 eV, above which it falls off smoothly. Agreement with five-state close-coupling theory is excellent below 100 eV when cascading is included in the theory. Above 100 eV, the data lie above the theory. The peak value of the ${}_{}{}^2{}_{}{}^{}P$ cross section is 9.4×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ essentially at threshold, while the peak value of the ${}_{}{}^2{}_{}{}^{}S$ cross section is about 0.47×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$. The net linear polarization of the $3d^{10}4p {}_{}{}^2{}_{}{}^{}P$ emission was measured (unresolved from the $3d^{10}4d {}_{}{}^2{}_{}{}^{}D\to 3d^{10}4p {}_{}{}^2{}_{}{}^{}P$ cascading transition), and these data were used to correct the cross-section data for anisotropy of the emitted light. The effective lifetime of the $3d^{9}4s^2{}_{}{}^2{}_{}{}^{}D_{\frac{3}{2}}^{}{}_{}{}^{}$ level was measured by observing exponential decay of the 589.6-nm photons resulting from its decay.

Collision strengths are calculated for excitation of Zn II from the $4s$ ground state to excited states $4p,3d^{9}4s^2,5s, \mathrm{and} 4d$ in a five-state close-coupling approximation for the electron-impact energy range $15<E<\mathrm{}400\mathrm{}$ eV, and from $4s \mathrm{to} 4p,5s, \mathrm{and} 3p^{5}3d^{10}4s^2$ in a two-state close-coupling approximation for the same energy range. Accurate target functions are used in the expansion. Very good agreement with measurements of absolute emission cross sections of Rogers et al. is obtained for energy region $15<E<\mathrm{}100\mathrm{}$ eV, when cascade contributions are included. Poorer agreement is obtained with experiment for excitation of the $5s$ state, owing to sensitivities in the close-coupling approximation.

Total cross sections are reported for electron transfer into all bound states in collisions of protons with ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{+}{}_{}{}^{}$ ions and ${}_{}{}^4{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions with H atoms at center-of-mass energies from 4 to 120 keV and 4 to 40 keV, respectively. The coupled-state calculations employ 19-24 Sturmian basis functions. Convergence of cross sections with respect to the size of this basis has been studied, and total cross sections are estimated to be converged to a few percent. A comparison is made with molecular-state, atomic-state, classical, and experimental results. In the energy region of overlap, Sturmian-state results and plane-wave-factor, molecular-state results agree to within 9% except for the $p-{\mathrm{He}}^{+}$ process at 14 keV, where the Sturmian results are 37% larger, probably reflecting the need to include the continuum which was omitted in the molecular calculations. There is also a similar discrepancy with the experimental results of Peart, Grey, and Dolder; these Sturmian results, however, do tie in with the experimental results of Angel, Sewell, Dunn, and Gilbody at higher energies.

The spectra of secondary electrons emitted from carbon foils have been measured for excitation by 1-MeV-proton impact. $K$-Auger electron spectra observed in these measurements are compared to similar spectra from gas targets and to calculations based on Monte Carlo track-structure techniques. The calculations are shown to accurately reproduce the Auger spectral shapes observed with foil targets. These calculations illustrate the significance of inelastic-scattering processes on the spectra of Auger electrons emerging from foil targets. The potential influence of multiply scattered Auger electrons on the interpretation of Auger spectra observed in beam-foil spectroscopy is illustrated.

Unitarized-distorted-wave-approximation calculations based on a complete set of channels are performed to obtain ionization, excitation, and charge-transfer cross sections for impacts of ${\mathrm{H}}^{+}$, ${\mathrm{Li}}^{3+}$, ${\mathrm{B}}^{5+}$, ${\mathrm{C}}^{6+}$, and ${\mathrm{Si}}^{14+}$ ions on atomic hydrogen. The ionization channels are represented by Coulomb wave functions centered on the projectiles to account for "charge transfer to the continuum". The ionization cross sections depend less than in a quadratic relationship on projectile charge. The inclusion of ionization and excitation channels makes charge-transfer cross sections considerably smaller for higher values of the projectile charge at impact energies above 10 keV/amu. A new scaling rule to charge-transfer cross sections is discussed in comparison with experiments and other theories for the energy range 0.01-5000 keV/amu.

Absolute cross sections for electron-impact ionization of ${\mathrm{Zn}}^{+}$ and ${\mathrm{Ga}}^{+}$ have been measured from below threshold to 2 keV with the use of the crossed-charged-beams technique. Excitation autoionization was shown to be of major importance in both ions for the region between 1 and 2 times threshold, leading to enhancement of the cross sections by factors of up to ∼2.5. Discrepancies between experiment and the well-known semi-empirical formula of Lotz were up to 70%, but reduction of Lotz's $a_{3d}$ coefficient by a factor of 2 leads to satisfactory agreement at high energies. Comparison is also made with scaled-Born-approximation calculations.