The influence of molecular structure on the nuclear capture probability of stopped negative pions has been observed by comparing the ${\pi }^0$ gamma-ray spectrum from ${\pi }^{-}$ mesons stopped in HD gas to that from a mixture of equal amounts of ${\mathrm{H}}_2$ plus ${\mathrm{D}}_2$. The fraction of stopped pions that are captured by a proton in the ${\mathrm{H}}_2$+${\mathrm{D}}_2$ mixture is $f_{{\mathrm{H}}_2{\mathrm{D}}_2}=0.417\mathrm{}\pm 0.004$, while for HD it is $f_{\mathrm{HD}}=0.338\mathrm{}\pm 0.008$, independent of the gas pressure between 6 and 90 atm. The ratio, $\frac{f_{{\mathrm{H}}_2{\mathrm{D}}_2}}{f_{\mathrm{HD}}}$, of the fractions is 1.23±0.03.

A complete account is given of a new method for the solution of the problem of electron scattering by a one-electron atom or ion. The method treats all relevant effects explicitly. Reaction channels under consideration are treated by the coupled-channels method in momentum space. Other channels, including the continuum, are treated by adding complex-polarization potentials computed from experimentally tested approximate amplitudes for the relevant reactions. Computational methods are discussed in detail since this is the first successful application of the momentum-space solution to the atomic multichannel problem. The effect of the inclusion of channels outside the coupled space is demonstrated by comparison with three-state close coupling for hydrogen at 54.42 eV.

A new straightforward technique for the evaluation of the rearrangement-scattering amplitude for the process ${\mathrm{H}}^{+}+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to \mathrm{H}\mathrm{}\left(\mathrm{nlm}\right)+{\mathrm{H}}^{+}$ has been presented in the continuum—intermediate-state approximation. We reduce the scattering amplitude to a closed analytical form. The asymptotic behavior of the capture cross sections with respect to $n$ has also been derived. It has been shown conclusively that the charge-exchange cross sections asymptotically obey the $n^{-3\mathrm{}}$ power law throughout the entire energy range of the projectile. It is found that the cross sections for capture into different angular momentum states can be calculated from the respective asymptotic cross-section values with the help of a simple scaling law. The present calculated results have been compared with the available experimental findings.

Collision-induced scattering is studied in a gas mixture of two kinds of optically isotropic particles. Rayleigh and vibrational Raman collisional depolarization ratios are obtained in the first-order dipole—induced-dipole (DID) approximation, in terms of two-, three-, and four-body correlation contributions. At the low-density limit, Rayleigh and vibrational Raman depolarization ratios due to the unlike-particle pairs are found to be equal and given as a function of the intermolecular pair potential. Experimental data are obtained for Rayleigh and Raman depolarization ratios of the gas mixture argon-tetrafluoromethane at 296 K. The experimental Rayleigh depolarization ratio induced by unlike-particle pair argon-tetrafluoromethane are deduced for the case of binary-collision conditions. It is in good agreement with the value calculated from the DID model using a Lennard-Jones intermolecular potential. However, a comparison between Rayleigh and Raman data shows that all collision-induced integrated intensities for the unlike-particle pair Ar-${\mathrm{CF}}_4$ may not be described only in terms of DID interactions.

Measurements of $M$-shell x-ray production cross sections are reported for thin solid targets of ${}_{79}{}^{}{}_{}{}^{}\mathrm{Au}$, ${}_{83}{}^{}{}_{}{}^{}\mathrm{Bi}$, and ${}_{92}{}^{}{}_{}{}^{}\mathrm{U}$. Fluorine ions of energies 25, 27, and 35 MeV and charge states of 4, 5, 6, 8, and 9 were used. The microscopic cross sections were determined from measurements made with targets ranging in thickness from ∼1 to ∼300 μg/${\mathrm{cm}}^2$. An enhancement in the target $M$-shell x-ray production cross section was observed for fluorine ions with one or two $K$-shell vacancies over those without a $K$-shell vacancy. The sums of cross sections for direct ionization to the target continuum and electron capture to the projectile's $L,M,N,\dots$ shells are inferred from charge state $q=4,5,6\mathrm{}$ data. The first Born calculations overpredict the cross-section data at all energies. Cross sections for electron capture from the target $M$ shell to the projectile $K$ shell for one ($q=8\mathrm{}$) and two ($q=9\mathrm{}$) $K$-shell vacancies in the projectile are also overpredicted by the first Born approximation for electron capture, i.e., the Oppenheimer-Brinkman-Kramers approximation of Nikolaev. The data are in good agreement with the ECPSSR theory of Brandt and Lapicki, which accounts for the energy-loss, Coulomb-deflection, and relativistic effects in the perturbed-stationary-state theory.

The theory of resonant reactions, in the projection-operator formulation of Feshbach, is generalized to account for the presence of an external electromagnetic field. The theory is used as the basis for the construction of low-frequency approximations for the transition amplitude. Results obtained here for scattering in a laser field confirm earlier versions of the low-frequency approximation when the resonances are isolated. However, if there are several closely spaced resonances additional terms must be included (their importance magnified by the appearance of near singularities) which account for the effect of radiative transitions between pairs of nearly degenerate resonant states. The weak-field limit of this result yields a low-frequency approximation for single-photon spontaneous bremsstrahlung which, through the inclusion of correction terms associated with closely spaced resonances, provides an improvement over the Feshbach-Yennie version derived some time ago. A separate treatment is required to deal with the limiting case of a static external field and this is worked out here in the context of a time-dependent formulation of the scattering problem. Linear and quadratic Stark splitting of the resonance positions, and resonance broadening due to the tunneling mechanism, are expected to play a significant role in the static limit and these effects are included in the approximation derived here for the transition amplitude.

A relatively simple nonempirical formula for the imaginary part of the optical potential for electron scattering is derived from a quasifree-scattering model with Pauli blocking in which the target is treated as a free-electron gas. The resulting absorption potential is local and energy dependent and is a function of the electron density of the target. This model is tested for electron-helium and electron-neon scattering at 30-3000 eV. For these tests the real part of the potential is also approximated by a local expression, which is partitioned into static, exchange, and polarization terms. Reasonably good agreement with experimental data is obtained for the elastic integral, absorption, and elastic differential cross sections.

The relative photoionization cross sections of atomic and molecular cesium and rubidium have been measured between 2300 and 3400 Å. The variations of the atomic cross sections with wave-length are in excellent agreement with published semiempirical calculations.

$L$—x-ray production cross sections were measured for thin targets of Ag, In, Sn, and I in the proton energy range 0.300-5.000 MeV. Subshell ionization cross sections were extracted and compared with existing data and with the predictions of plane-wave Born approximation (PWBA), perturbed—stationary-state theory including energy loss, Coulomb deflection and relativistic corrections (ECPSSR), binary-encounter approximation with corrections accounting for binding effect and Coulomb retardation (BEABC), and semiclassical approximation taking into account binding, energy loss, Coulomb deflection, and relativistic effects (SCABCR). Large disagreement was found with PWBA, but the other theories reproduced the experimental data rather well. Owing to the nodal structure of the $2s$ wave function, deeper insight was achieved by considering the ratios of the sub-shell ionization cross sections. These results were found to be in good agreement with analogous measurements on high-$Z$ elements and favor the ECPSSR over the other theories. A realistic value for the ${\omega }_1$ fluorescence yield was suggested for indium near the discontinuity at $Z\sim 50$.

The photodetachment cross section of the ${\mathrm{H}}^{-}$ ion has been obtained with the use of two variants of the polarized-orbital method. Calculation takes into account the matrix elements involving a distorted-target wave function that has been neglected by Bell and Kingston. The results have been compared with other theoretical results.

$M$-subshell ionization cross sections of Au, Pb, Bi, and U by proton bombardment were obtained over the projectile range 0.3-4.0 MeV. X rays were detected by Si(Li) spectroscopy. At least one characteristic radiative transition line for each $M$ subshell was isolated and measured. Radiative and nonradiative branching ratios were taken from theoretical calculations of Bhalla and McGuire. Our total x-ray-production cross sections are compared with the measurements of other authors. Comparison of our scaled subshell ionization cross sections with calculations in the plane-wave Born approximation shows, in general, good agreement. Uncertainties in fluorescence yields and in super—Coster-Kronig coefficients can introduce great imprecision in some experimentally determined subshell ionization cross sections.

The projection-operator approach of Feshbach is applied to potential scattering. The aim is to describe single-particle or shape resonances in a mathematically rigorous manner as discrete states interacting with a continuum, in analogy to the well-known description of closed-channel resonances in scattering from targets with internal degrees of freedom. A projection operator $Q$ is defined as $Q=\Sigma {\nu =1\mathrm{}}^N\left|{\chi }_{\nu }〉〈{\chi }_{\nu }\right|$, where $\left\{〈\overrightarrow{\mathrm{r}}\right|{\chi }_{\nu }〉\}$ is an arbitrary orthonormal set of $L^2$ functions. The complementary $P$ space is spanned by a set of scattering states obtained in explicit form by orthogonalizing the free continuum to the set $\left\{〈\overrightarrow{\mathrm{r}}\right|{\chi }_{\nu }〉\}$. The free Green's function in $P$ space is constructed explicitly and the $P$-space scattering problem is solved with the use of separable expansions of the potential. Two standard model problems—$s$-wave scattering from the square-well potential and the $\delta$-shell potential—are solved exactly, with the use of an arbitrary number of eigenstates of a particle in a spherical box to define the $Q$ space. It is shown that the formalism leads to a decomposition of the exact $T$ matrix and scattering phase shift into an orthogonality scattering, a direct scattering, and a resonant scattering contribution. The pole structure of the corresponding $S$ matrices in the complex momentum plane is analyzed. Finally, the question of how to construct the appropriate discrete state, which projects out a given resonance, is briefly discussed.

The electron capture to continuum (ECC) from atoms by a fast bare ion is investigated assuming that the electron-projectile interaction in the final state is a screened Coulomb potential. The cut-off Coulomb and Hulthén potentials are used to show that the ECC cross section is either finite or diverges as $\frac{1}{v^2}$ for small final relative electron-projectile velocities ($\overrightarrow{\mathrm{v}}$). Theoretically this represents a considerable deviation from the usual premise of the $\frac{1}{v}$ behavior given by the Coulomb factor. However, for gaseous targets we get the usual ECC peak shape as an average over the screening range of the interaction. We discuss some experimental conditions where anomalies due to screening are expected to be observable.

We measured all the collisional dissociation channels of $\mathrm{D}_2^{}{}_{}{}^{+}$ in the energy range 200-600 keV in the gas targets ${\mathrm{H}}_2$ and Ar. The various channels were resolved with the use of an electrostatic deflector into a set of detectors. Rate equations were developed and used in the analyses of the data to extract ratios of cross sections. These ratios of ${\mathrm{D}}^{+}$ and ${\mathrm{D}}^0$ charge-exchange cross sections and $\mathrm{D}_2^{}{}_{}{}^{+}$ dissociation cross section were found to be consistent with those of $\mathrm{H}_2^{}{}_{}{}^{+}$ dissociation at the same velocities. The measurement of the negative fragments shows that there is hardly any direct population of the dissociation channels containing ${\mathrm{D}}^{-}$ fragments. The negative fragments are formed via a secondary collision of the non-negative fragments formed in the dissociation process.

External bremsstrahlung spectra produced in thick targets of copper, molybdenum, cadmium, iodine, and lead by $\beta$ particles of ${}_{}{}^{90}{}_{}{}^{}\mathrm{Sr}$-${}_{}{}^{90}{}_{}{}^{}\mathrm{Y}$ were measured using a 4.55-cm × 5.08-cm NaI(T1) crystal. The conventional $\beta$-stopper method was followed. The measured spectra were unfolded according to the Liden and Starfelt procedure. The exponents of $Z$ for energy yield and photon yield were found to be 1.20±0.02 and 1.26±0.02, respectively.

We have presented a method for the evaluation of the Coulomb-Born matrix element between arbitrary initial and final Slater orbitals. Since for the two- or more-electron ionic target the wave functions may be constructed by the combination of the Slater orbitals of various angular momenta, one can easily apply this method to calculate the cross sections for the electron-impact excitation of a complex ion from an arbitrary initial state to an arbitrary final state. As an example we have calculated the excitation cross sections of the ${\mathrm{He}}^{+}$ ion from the ground state to the $4f$ state at several energies.

The effect of $4f$ orbital collapse on the spectra of Xe-like ions in the region of $4d\to nf,\epsilon f$ excitations is studied with the use of a term-dependent Hartree-Fock technique. We find that the collapse of the $4f$ orbital is strongly term dependent, and that the appearance of intense absorption lines in the observed ${\mathrm{Ba}}^{2+}$ spectrum is due to the partial collapse of the $4f$ orbital in the $4d\to f{}_{}{}^1{}_{}{}^{}P$ channel. We also show that after the $4f$ orbital is completely collapsed for high degrees of ionization along the isoelectronic sequence, the bulk of absorption oscillator strengths is concentrated at the $4d^{9}4f{}_{}{}^1{}_{}{}^{}P$ level so that the only strong line in the spectrum is again the $4d\to 4f{}_{}{}^1{}_{}{}^{}P$ transition.

Photoionization of the inner $4d$ shells for Xe, ${\mathrm{Cs}}^{+}$, ${\mathrm{Ba}}^{2+}$, and ${\mathrm{La}}^{3+}$ are studied with the use of the relativistic random-phase approximation. Total cross sections, partial cross-section branching ratios, and angular-distribution asymmetry parameters are calculated, and their systematic trends along the isoelectronic sequence are studied. Important dynamic effects of electron correlations are obtained from an eigenchannel analysis involving the eigenquantum defects, the eigendipole amplitudes, and the transformation $U$ matrices. We find that there are shape resonances in the effective potential for $f$ electrons, and that the collapse of the $4f$ orbital along the isoelectronic sequence is closely related to changes in $f$ orbitals in passing through these resonances.

Relativistic radiative and radiationless atomic inner-shell transition rates have been calculated with Dirac-Fock wave functions with the use of matrix elements that correspond to different gauges. Radiative rates computed in the length gauge are found to be larger than Coulomb-gauge results; for $K$-shell radiative widths, the difference is ∼20% at $Z=10\mathrm{}$ and falls to ∼4% at $Z=30\mathrm{}$; the difference for $L_2$ radiative widths is a factor of 2 at $Z=18\mathrm{}$ and ∼7% at $Z=48\mathrm{}$. Especially large discrepancies between length- and Coulomb-gauge results are found for $\Delta n=0\mathrm{}$ radiative transition rates. Auger transition rates calculated in the Lorentz and Coulomb gauges agree to better than 1% in all cases tested here; it is inferred that in first-order perturbation theory the Auger rate is practically gauge invariant. Certain general features of the effects of relativity on radiationless transitions are also discussed. These effects can arise from relativistic changes in the transition energies, relativistic orbital effects, and relativistic aspects of the pertinent operators. The relative importance of these factors is evaluated.

We present a comprehensive investigation of the ${\mathrm{He}}^{+}$-CO, ${\mathrm{He}}^{+}$-NO, He-CO, and He-NO collisions in the $0.5<\mathrm{}{E}_{\mathrm{lab}}<3\mathrm{}$-keV energy range. The comparison of ionic and neutral systems allows a determination of the excitation mechanisms that are common or specific to each case. In the course of this study new states of the ${\mathrm{CO}}^{+}$ and ${\mathrm{NO}}^{+}$ molecular ions were discovered. The previously proposed excitation mechanisms—(i) direct Demkov-type transitions populating the exothermic charge-exchange channels, (ii) molecular-orbital (MO) promotion giving rise to MO crossings and subsequent electron transitions, and (iii) two-electron transitions leading to direct-excitation and charge-exchange processes in the ionic systems—are also found to apply to the present case, thus confirming their generality.