The relaxation of the muon spin in a free radical is complicated by the presence of several molecular degrees of freedom. In particular, for muonated ethylene, ${\mathrm{C}}_2$${\mathrm{H}}_4$Mu, which exemplifies the type of free radical that is being considered, the addition product has an unpaired electron, so the motion of the free radical in an external magnetic field is dominated by the precession of the electron spin. This paper formulates a theory for the muon-spin relaxation of such free radicals. It is based on the Boltzmann equation, so it has a rigorous basis by which both free motion (including all of the angular momentum couplings) and the collisional processes (which cause the decay to equilibrium) can be included. A multipole expansion of the density operator in terms of electron, muon, and rotational angular-momentum operators including terms up to quadratic in the rotational angular momentum is used to represent the state of the system. The multipole coefficients in the Hamiltonian are treated as fitting parameters to give a best interpretation of the experimental data for the longitudinal muon-spin relaxation rate of ${\mathrm{C}}_2$${\mathrm{H}}_4$Mu.

The electromagnetic field operators for a chiral (optically active) molecule are calculated in the Heisenberg picture, using the multipolar Hamiltonian. Interactions involving electric-dipole, magnetic-dipole, and electric-quadrupole moments are taken into account. The operators are expanded in powers of moments, and expressions correct to quadratic powers in the moments are given. Comparable contributions from diamagnetic interactions are also presented. The properties of these operators are discussed. Terms that are linear in the moments are found to act in the electron space alone; those quadratic in the moments act in both the electron and photon spaces. The operators are used to calculate the Poynting vector, from which the spontaneous emission rates for magnetic-dipole and electric-quadrupole transitions are obtained. Attention is drawn to the inverse square dependence of the Poynting vector on the distance of the field point from the source. This behavior is shown to be consistent with the requirement of local conservation of energy. The operators are used in the following paper [J. K. Jenkins, A. Salam, and T. Thirunamachandran, Phys. Rev. A 50, 4767 (1994)] to calculate dispersion energies between two optically active molecules.

The dispersion interaction energy for a pair of chiral molecules in their ground states is calculated using the multipolar form of quantum electrodynamics. The calculations go beyond the electric-dipole approximation, and the interaction Hamiltonian includes the electric-quadrupole, magnetic-dipole, and diamagnetic coupling terms. The energy is calculated using two methods: one with standard fourth-order perturbation theory and another with a response formalism. In the perturbation approach, the intermolecular coupling arises from two-photon exchange whereas in the response method, the energy shift is calculated from the response of one molecule to the Maxwell fields of the other. In both calculations retardation effects are taken into account. It is shown that the dispersion energy contains a contribution that depends on the relative handedness of the two molecules. An expression for this discriminatory energy shift, valid for all intermolecular separations beyond the electron overlap, is presented. In addition to the discriminatory energy shift, results are presented for the interaction energy shift between a molecule with electric-dipole polarizability and another with magnetic-dipole or electric-quadrupole polarizability. The limiting behavior of these shifts in the near and the far zone is examined.

Electron-impact dissociative cross sections for ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ vibrationally excited molecules have been calculated in the frame of the impact-parameter method for dissociative processes involving direct dissociation ${\mathit{M}}_2$(X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$,${\mathit{v}}_{\mathit{i}}$)+e->${\mathit{M}}_2^{\mathrm{*}}$(B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$, ${}_{}{}^1{}_{}{}^{}\mathrm{\Pi }_{\mathrm{u}}^{}{}_{}{}^{}$)+e→2M+e and radiative cascade ${\mathit{M}}_2$(X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$,${\mathit{v}}_{\mathit{i}}$) +e→${\mathit{M}}_2^{\mathrm{*}}$(B ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{u}}^{+}{}_{}{}^{}$,${\mathit{C}}^1$${\mathrm{\Pi }}_{\mathit{u}}$)+e→${\mathit{M}}_2$(X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{+}{}_{}{}^{}$)+e+hν→2M+e+hν (${\mathit{M}}_2$ represents a hydrogen or deuterium molecule). The results show that direct dissociation cross sections strongly depend on the initial vibrational state of the molecule, while an opposite behavior is found in the case of dissociation by radiative cascade. Moreover, for this last process, the fraction of molecules that undergoes dissociation has been evaluated with respect to the total cascade process, yielding in general quite small values in both the ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ cases.

We describe a set of experiments that investigate excitation transfer among the barium 6s5d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ metastable levels due to collisions with argon perturber atoms, and quenching of atoms in these levels by nitrogen perturber molecules. The metastable levels were populated through optical pumping of the 6${\mathit{s}}^2$ ${}_{}{}^1{}_{}{}^{}$${\mathit{S}}_0$→6s6p ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}_1^{\mathit{o}}$ intercombination transition with a pulsed laser, followed by stimulated emission or stimulated Raman scattering into the 6s5d ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{1,2}$ levels. Collisional mixing then distributed population throughout the ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ levels. Time-dependent absorption coefficients were obtained by measuring the transmission of a weak cw probe laser beam (after the pulsed laser fired) at several perturber number densities. Argon buffer gas was used to investigate fine-structure mixing, and nitrogen was used to study quenching. The time-dependent absorption coefficients were fitted to appropriate fitting functions, obtained by solving the set of coupled rate equations used to model the time evolution of the metastable level populations. The buildup rates of the initially unpopulated ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_3$ and underpopulated ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_1$ levels were used to determine the collisional mixing rates, while the measured decay rates of the ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ level populations yielded the quenching rates. From plots of buildup rates versus argon number density for the ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{1,3}$ states, we were able to determine four of the six fine-structure mixing rate coefficients ${\mathit{k}}_{\mathit{i}\mathit{j}}$.

The results are ${\mathit{k}}_{12}$=(1.71±0.18), ${\mathit{k}}_{21}$=(1.39±0.13), ${\mathit{k}}_{23}$=(1.42±0.13), and ${\mathit{k}}_{32}$=(1.92±0.16)×${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$. The experiment is not sensitive to the values of ${\mathit{k}}_{13}$ and ${\mathit{k}}_{31}$. Estimated rate coefficients for excitation transfer among the ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}_{\mathit{J}}$ levels due to collisions with barium atoms are ${\mathit{k}}_{21}^{\mathrm{Ba}}$=1.3×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$ and ${\mathit{k}}_{23}^{\mathrm{Ba}}$=5.8×${10}^{\mathrm{-}10}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$. A plot of the population decay rates versus ${\mathrm{N}}_2$ number density for each of the three metastable levels yielded the average nitrogen quenching rate coefficient ${\mathit{k}}_{\mathit{q}}$=(3.14±0.19)×${10}^{\mathrm{-}11}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$.

Using a crossed-beam method, we have measured electron-energy-loss spectra for the excitation of the Schumann-Runge continuum of molecular oxygen. The scattering angle and electron-impact energy ranges covered were 12°–156° and 15–50 eV, respectively. By means of computerized least-squares analysis, we decomposed the spectra into contributions from three superposed Gaussian line shapes. The two lowest in energy are identified as representing excitation of the $1^3$${\mathrm{\Pi }}_{\mathit{g}}$(v) and ${\mathit{B}}^3$${\mathrm{\Sigma }}_{\mathit{u}}^{\mathrm{-}}$(v) states. The other line shape cannot be definitively identified, but we discuss several possibilities for its meaning. Absolute differential and integrated cross sections for all three states are obtained, along with linear electronic potential-energy curves for the Franck-Condon region.

The 29-state R-matrix calculations in which physical target states of helium with n=1, 2, 3, 4, and 5 are included in the total scattering wave functions have been employed by Fon, Lim, and Sawey [J. Phys. B 26, 305 (1993)] to obtain the cross sections for the electron-impact excitations of the 2 ${}_{}{}^{3,1}{}_{}{}^{}$S states of helium. The same R-matrix calculations are now extended to obtain integral and differential cross sections of 1 ${}_{}{}^1{}_{}{}^{}$S–3 ${}_{}{}^{3,1}{}_{}{}^{}$S and 1 ${}_{}{}^1{}_{}{}^{}$S–4 ${}_{}{}^{3,1}{}_{}{}^{}$S transitions. The calculations are performed at 400 energies ranging from the thresholds to 24.1 eV. The results, together with those of Fon, Lim, and Sawey for n=2 excitation, are used to analyze the experiments of Allan [J. Phys. B 25, 1559 (1992)]; his interpretation of the decay of the doubly excited Wannier-ridge resonances is reexamined.

The formation and decay of the ‘‘2p’’ electronic excited states of the rare gases neon, argon, krypton, and xenon in a buffer gas of either helium or neon has been studied by pulse radiolysis techniques. The formation rate constants for these states are all greater than ∼2×${10}^{\mathrm{-}9}$ ${\mathrm{cm}}^3$ ${\mathrm{s}}^{\mathrm{-}1}$, precluding atom-atom collisional processes and supporting a subexcitation electron mechanism. The rate constants generally show a trend ${\mathit{k}}_{\mathrm{Xe}}$>${\mathit{k}}_{\mathrm{Kr}}$>${\mathit{k}}_{\mathrm{Ar}}$>${\mathit{k}}_{\mathrm{Ne}}$. Quenching rate constants for the deactivation of some of the 2p levels are also reported.

The elastic scattering of positrons from the heaviest noble gases has been formulated by using a parameter-free semiclassical model for the polarization forces in the short- and intermediate-range distances. The exact Coulomb repulsive interaction has been obtained from self-consistent-field wave functions of near-Hartree-Fock quality and the scattering equations have been solved over a broad range of collision energies. The elastic integral cross sections agree well with experiments in spite of the great simplicity of the employed computational model. Angular distributions also compare favorably with available experiments and the relative importance of various second-order corrections is discussed in relation to their bearing on the final results.

Interaction potentials for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ and a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ states of ${\mathrm{Na}}_2$ are constructed and used in calculations of the elastic scattering of two Na atoms at ultralow temperatures. The sensitivity to retardation effects (or Casimir corrections) is explored. The calculated elastic and spin-change cross sections are very large, of the order of ${10}^{\mathrm{-}12}$–${10}^{\mathrm{-}13}$ ${\mathrm{cm}}^2$ at zero temperature. The predicted scattering lengths are both positive, 34.9 ${\mathit{a}}_0$ for the X ${}_{}{}^1{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{g}}^{+}{}_{}{}^{}$ state and 77.3 ${\mathit{a}}_0$ for the a ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$ state. Pronounced shape resonances appear for the l=3 and 7 partial waves for the singlet and l=6 for the triplet states.

Total and partial photoionization cross sections, branching ratios, and angular-distribution asymmetry parameters for the 4d, 4p, 4s, and 3d subshells of palladium have been calculated using the relativistic random-phase approximation and the relativistic random-phase approximation modified to include relaxation effects. Comparisons are made between results that include relaxation effects and those that do not. Minor relaxation effects are noted for the 4d and 3d photoionization parameters. However, substantial relaxation effects are noted for both the 4p and 4s subshells. Large relaxation effects are observed in the 4p partial cross section and branching ratio. Also observed is the appearance of a Cooper minimum in the 4s photoionization cross section and a corresponding change in the 4s angular-distribution asymmetry parameter.

Large-basis coupled-channel Dirac-equation calculations of bound-electron–positron pair production in relativistic heavy-ion collisions are presented. The relative importance of the enhancement of the coupled-channel calculations over corresponding calculations performed in perturbation theory is shown to decrease with increasing basis size, indicating a systematic reduction of this effect of nonperturbative enhancement with improving convergence of the calculations. The total nonperturbative enhancement of the cross section is shown to be about 7 b for ${\mathrm{Pb}}^{82+}$ on ${\mathrm{Pb}}^{82+}$ at the Brookhaven Relativistic Heavy-Ion Collider, only some 6% over perturbation theory.

Electron capture and excitation in ${\mathrm{O}}^{+}$${(}^4$S${,}^2$D${,}^2$P)+He collisions above 100 eV are studied theoretically by using a semiclassical molecular representation and electron capture in ${\mathrm{He}}^{+}$+O${(}^3$P) collisions; excitation and deexcitation in ${\mathrm{O}}^{+}$${(}^4$S)+He⇆${\mathrm{O}}^{+}$${(}^2$D)+He collisions at lower energies are studied by using a fully-quantum-mechanical molecular representation. At higher energies, nonadiabatic couplings are the driving forces that cause transitions. At collision energies below 10 eV, transitions are driven by spin-orbit couplings. At kilo-electron-volt energies, the contribution from metastable ${\mathrm{O}}^{+}$${(}^2$D${,}^2$P) ions to electron capture is much larger than that from the ground ${\mathrm{O}}^{+}$${(}^4$S) ions. At energies below 1 eV, the cross section for electron capture in ${\mathrm{He}}^{+}$+O collisions is very small, with a magnitude of less than ${10}^{\mathrm{-}20}$ ${\mathrm{cm}}^2$. The cross sections for the excitation-deexcitation of metastable ${\mathrm{O}}^{+}$ ions are larger, with values near ${10}^{\mathrm{-}18}$ ${\mathrm{cm}}^2$.

Calculations of cross sections for electron (${\mathit{e}}^{\mathrm{-}}$) and positron (${\mathit{e}}^{+}$) scattering from ground-state He, Ne, Ar, Kr, and Xe at projectile energies below the lowest inelastic thresholds are presented. The main focus in the present work is on the differential cross sections, since angular distributions depend sensitively on the choice of interaction potentials used in the calculations. A part of the interaction potential used in the calculations includes a parameter-free correlation-polarization potential which is (a) based on physical ideas of what a correlation-polarization potential should be, (b) different for various target gases, and (c) distinct for electron and positron scattering. The present calculations of differential cross sections predict the locations of the principal maxima and minima with good accuracy and the shapes of the calculated differential cross-section curves compare quite well with available experimental cross sections.

Double photoionization of atomic Na has been investigated by combining the results of photoelectron and photoion spectroscopies from synchrotron radiation measurements in the photon energy range between 50 and 135 eV. Distinction with regard to the double-photoionization mechanism (one-step or two-step processes) and to final-state configuration allowed an accurate determination of the relative cross section for one-step direct double photoionization. Above 71 eV photon energy double photoionization is dominated by 2s photoionization followed by Auger decay (two-step process) whereas direct double photoionization accounts for only ≃20% of double photoionization.

The method of complex-coordinate rotation is used to calculate shape resonances lying above the N=5 hydrogen threshold in ${\mathit{e}}^{\mathrm{-}\mathrm{-}}$H scattering. We report resonance parameters for ${}_{}{}^3{}_{}{}^{}$${\mathit{P}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{F}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{F}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}^{\mathit{e}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{G}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{G}}^{\mathit{o}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{G}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{H}}^{\mathit{o}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{H}}^{\mathit{e}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{I}}^{\mathit{e}}$, ${}_{}{}^3{}_{}{}^{}$${\mathit{I}}^{\mathit{o}}$, ${}_{}{}^1{}_{}{}^{}$${\mathit{K}}^{\mathit{o}}$, and ${}_{}{}^3{}_{}{}^{}$${\mathit{K}}^{\mathit{e}}$ states for a total of 19 shape resonances. Resonance energies and widths are obtained by employing up to 1642 terms of wave functions constructed by the products of Slater-type orbitals. The shape resonances are the top portions of the supermultiplet structures for doubly excited intrashell states of ${\mathrm{H}}^{\mathrm{-}}$ associated with the N=5 hydrogen threshold. For completeness, we also list the doubly excited Feshbach resonances obtained in previous complex-rotation calculations. Together with the present results for shape resonances, all the doubly excited intrashell states associated with the N=5 hydrogen threshold are now accounted for.

We present a complex-coordinate rotation calculation for doubly excited ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ resonance states in ${\mathrm{H}}^{\mathrm{-}}$ associated with the N=3 threshold of hydrogen atoms. Elaborate Hylleraas-type wave functions with up to M=1330 terms for ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ states and M=1430 terms for ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ states are used. In addition to ${}_{}{}^{1,3}{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ and ${}_{}{}^1{}_{}{}^{}$${\mathit{D}}^{\mathit{e}}$ Feshbach resonances, we have identified a ${}_{}{}^3{}_{}{}^{}$${\mathit{D}}^{\mathit{o}}$ shape resonance lying above the H(N=3) threshold. With the present results for the D-wave resonances, together with the other angular-momentum states determined in earlier complex-rotation calculations, all the doubly excited intrashell states of ${\mathrm{H}}^{\mathrm{-}}$ associated with the hydrogen N=3 threshold are now accounted for.

The population distributions of the rotational quantum states of the nascent MgH(v’’=0 and 1) produced in the reaction of Mg(3s3p ${}_{}{}^1{}_{}{}^{}$${\mathit{P}}_1$) with ${\mathrm{H}}_2$ are bimodal. With the use of the surprisal method, the two components are separated. The minor low-N component of the distribution in the v’’=0 state is found to be larger than that in the v’’=1 state, whereas, the major high-N component of the distribution in the v’’=0 state becomes roughly equivalent to that in the v’’=1 state. The two parallel low-N and high-N processes are expected to correspond to two distinct types of reaction dynamics. One (minor) type produces MgH in lower rotational levels and preferentially v’’=0, and the other (major) type produces MgH in higher rotational levels with comparable v’’=0 and v’’=1 populations. Possible dynamical models are discussed.

The laboratory energy distribution of protons in coincidence with ${\mathrm{L}}_{\mathrm{\alpha }}$ photons produced in collision-induced dissociation of 4.0-keV ${\mathrm{H}}_2^{+}$ on He targets has been measured for protons that are collected along the incident-beam direction. An approximate energy distribution of proton–${\mathrm{L}}_{\mathrm{\alpha }}$-photon pairs in the projectile frame is obtained by transforming the measured laboratory distribution. The transformed results reveal that the dominant processes for production of near-zero energy projectile frame protons are the 1s${\mathrm{\sigma }}_{\mathit{g}}$ to 2p${\mathrm{\pi }}_{\mathit{u}}$ and 3d${\mathrm{\sigma }}_{\mathit{g}}$ transition at 2.5–3 times the equilibrium separation of ${\mathrm{H}}_2^{+}$. This transformation technique provides a simple method of identifying inelastic processes from the convoluted laboratory energy distributions of the fragments produced in the dissociative excitation of the ${\mathrm{H}}_2^{+}$ molecule.

The cross sections for ejecting electrons into a cone of half-angle ∼2° centered on the backward direction have been measured as a function of electron energy for 1-MeV/u ${\mathrm{O}}^{\mathit{q}+}$ (q=3–8) projectiles colliding with Ar. For ${\mathrm{O}}^{3+}$ and ${\mathrm{O}}^{4+}$ projectiles, the cross sections have also been measured in coincidence with exit charge states (q+1) and (q+2) of the projectile. A prominent feature in all spectra is a target LMM Auger peak. The cross sections for producing Ar LMM Auger electrons are nearly independent of projectile incident charge states. A projectile electron-loss peak is produced when the projectile brings loosely bound L-shell electrons into the collision. The shape of this peak is independent of the projectile exit charge state within experimental error. The measured electron-loss production cross sections at 180° are compared with the predictions of various on-shell approximations to the impulse approximation. Peak height and position are sensitive functions of the on-shell approximation used. The predictions of the elastic scattering model agree well with the data.