Radially correlated wave functions for the ground state of the lithium atom are constructed using a variant of the integral-transform or generator-coordinate method. The best of these is estimated to be close to the radial limit.

We propose in this article that the non-Hermitian equations typical of some many-body scattering theories be used to help solve many-body bound-state problems. The basic idea is to exploit the channel nature of manybody bound states that must exist because bound states are obvious negative-energy extensions of scattering states. Since atomic, molecular, and nuclear systems all display multichannel effects for $E>\mathrm{}0\mathrm{}$, at least through Pauli-principle effects if not through mass-transfer reactions, this use of positive-energy methods for solving bound-state problems could have wide applicability. The development used here is based on the channel-component-state method of the channel-coupling-array theory, recently described in detail for the $E>\mathrm{}0\mathrm{}$ case, and various aspects of the formalism are discussed. Detailed calculations using simple approximations are discussed for ${\mathrm{H}}_2^{+}$, one of the simplest systems displaying channel structure. Comparison with the exact, Born-Oppenheimer results of Wind show that the non-Hermitian-equation, channel-component values of the equilibrium separation and total binding energy are accurate to within 2%, while the dissociation energy is accurate to 10%. The resulting wave function is identical to that arising from the simplest MO calculation, for which these numbers are less accurate than the preceding by at least a factor of 3. We also show that identical particle symmetry for the ${\mathrm{H}}_2^{+}$ case reduces the pair of coupled (two-channel) equations to a single equation with an exchange term. Similar reductions will occur for larger numbers of identical particles, thus suggesting application of the formalism to atomic structure problems. A detailed analysis of the present numerical results, their general implications, and possible applications is also given.

Charge-exchange total cross sections for the ${\mathrm{B}}^{+3\mathrm{}}$ + He and ${\mathrm{C}}^{+4\mathrm{}}$ + He systems have been calculated in the velocity range $v=(1-10)\mathrm{}\times {10}^7$ cm/sec. Ab initio potential-energy curves and coupling-matrix elements were computed and employed in the impact-parameter classical-coupled equations that describe the collision to obtain the cross sections. For the ${\mathrm{B}}^{+3\mathrm{}}$ + He system, our calculations are in excellent agreement with experimental results with the finding that the single-electron-transfer cross section rises rapidly to a maximum of 1.45×${10}^{-15\mathrm{}}$ ${\mathrm{cm}}^2$ at $v=5.5\mathrm{}\times {10}^7$ cm/sec. For the ${\mathrm{C}}^{+4\mathrm{}}$ + He system, however, we find that the double-electron-transfer process is more important than the single-electron-transfer process. For example, at $v=5\mathrm{}\times {10}^7$ cm/sec, the double-electron-transfer cross section is found to be 0.6×${10}^{-16\mathrm{}}$ ${\mathrm{cm}}^2$ vs 5.5×${10}^{-17\mathrm{}}$ for the single-electron transfer. This is in disagreement with an experiment of Crandall which gave the single-charge-transfer process as dominant. However, the more recent experiment reported by Crandall, Olson, Browne, and Shipsey verifies the double charge transfer as the dominant process for low energies.

A local, complex potential is used to compute differential cross sections, spin polarizations, and total nonelastic cross sections for electrons incident on inert gases at energies ranging from 20 to 3000 eV. Excellent comparison with experimental data is achieved in most cases. In addition to Hartree-Fock wave functions, the input to the model involves two parameters. The strength $W$ of the imaginary potential is determined by fitting the total nonelastic cross section. The static polarizability $\alpha$ is well known from independent determinations.

A theoretical coupled-channels investigation of $e$-C${\mathrm{O}}_2$ scattering is reported for incident electron energies from 0.07 to 10.0 eV. The fixed-nuclei approximation is made with the molecule in the ground $X{}_{}{}^1{}_{}{}^{}\Sigma _{\mathrm{g}}^{+}{}_{}{}^{}$ state and the nuclei frozen at their equilibrium positions. The $e$-C${\mathrm{O}}_2$ interaction potential consists of an ab initio electrostatic Hartree potential, an approximate local exchange potential, and a semiempirical polarization potential. The coupled-channel equations are formulated in a body-fixed reference frame using single-center coordinates and are solved by means of an integral-equations algorithm. Convergence of the highly anisotropic interaction potential and of the expansion of the scattering function are discussed. The asymptotic decoupling approximation and the Born approximation are also studied and found to be unsatisfactory methods for computing quantitatively accurate cross sections for low-energy $e$-C${\mathrm{O}}_2$ collisions. Converged coupled-channel total integrated, momentum-transfer and differential cross sections are presented, and the former are compared with experimental results, with special attention given to low scattering energies (≲0.1 eV).

Measurements of the target thickness dependence of the target x-ray production yield for incident heavy ions at 1.71 MeV/amu are reported for thin solid Cu targets. The incident ions were F, Al, Si, and S. The charge states of the incident ions were varied in each case to study the target x-ray production for projectiles which have initial charge states $q$ of $q=Z_1$, $q=Z_1-1\mathrm{}$, and $q<\mathrm{}{Z}_1-1\mathrm{}$. The target thicknesses were varied from 3 to 85 μg/${\mathrm{cm}}^2$. In each case the Cu $K$ x-ray yields exhibit a complex exponential dependence on target thickness. A three-component model which includes contributions to the target x-ray production due to ions with zero, one, and two $K$ vacancies is developed to describe the observed target $K$ x-ray yields. The three-component model is fitted to the individual data for each projectile, and the cross sections for both the target and projectile are determined. The fits to the target x-ray data give a systematic representation of the processes involved in x-ray production for heavy ions incident on solid targets.

We have measured total cross sections for the collisional depopulation of high-lying $\mathrm{nP}$ states ($12\le n\le 22$) of rubidium induced by thermal collisions with ground-state rubidium or rare-gas atoms. It is observed that for $n\ge 14$ the rubidium-rare-gas cross sections do not vary with the principal quantum number, contrary to previous hypotheses. Our results are discussed using the simple argument of quasifree behavior of the valence electron involving either an elastic-scattering or a binary-encounter approach. However, the disagreement observed between the experimental and the computed cross sections suggests that a three-body approach is generally needed for a good understanding of collisional processes involving highly excited states.

Energy straggling of 5.486-MeV $\alpha$ particles in Al foils has been measured as a function of energy loss using foil thicknesses corresponding to the range $0.01<\mathrm{}\frac{\Delta E}{E}<0.1\mathrm{}$. The thickness uniformity of the foils has been investigated by proton backscattering, electron microscopy, and by mechanical surface profiling. The estimated effect of foil nonuniformity on the straggling results is small. The results are in excellent agreement with the Bethe-Livingston theory.

Beams of ${\mathrm{H}}_2^{+}$ and ${\mathrm{H}}_3^{+}$ produce x rays, respectively, with 4% and 8% smaller yields per proton than a ${\mathrm{H}}^{+}$ beam of kinetic energies between 90 and 150 keV/amu. These effects are accounted for quantitatively by the enhanced stopping power of Al for ions moving in tight clusters.

Fission-fragment energy loss in Ag was measured as a function of atomic number. The data for Ag along with our previously reported data for Ni were compared to various theoretical and semiempirical methods for predicting stopping powers. The results of our stopping-power studies in solids indicate that the average atomic-number dependence predicted by Northcliffe-Schilling and Moak-Brown is correct. However, evidence for $Z_1$ oscillations consistent with previous work for low-velocity ions was found.

The ${}_{}{}^3{}_{}{}^{}P\to {}_{}{}^1{}_{}{}^{}D$ electron-impact excitation cross section within the ground configuration of doubly ionized oxygen is calculated in the distorted-wave approximation. An essential element of the present treatment is that we do not assume orthogonality between core and scattering orbitals of the same angular symmetry. Resonance structures are included through the use of quantum defect theory. Near threshold the effect of an isolated autoionization resonance in the dominant ${}_{}{}^2{}_{}{}^{}D_{}^o{}_{}{}^{}$ partial wave is found to be important, in agreement with previous close-coupling results.

The production of thermal muonium in a vacuum region has been investigated using an array of 200 thin (∼1000 Å thick) gold foils exposed to a stopping ${\mu }^{+}$ beam. By examining the observed time dependence of the ${\mu }^{+}$-decay spectra in various transverse magnetic fields, we estimate that the lower limit of the probability of muonium formation by these gold foils placed in vacuum was 0.28±0.05.

Coupled-channel equations which include the momentum-transfer terms and which are intended for application over proton energy range 1-1000 keV are derived for completely stripped positive ions in helium. In particular, a realistic nine-parameter wave function is employed to obtain from the general equations direct and exchange matrix elements for the specific reaction $X^{i+}+\mathrm{He}\left(1\mathrm{}{}_{}{}^1{}_{}{}^{}S\right)\to X^{\mathrm{}(i-1\mathrm{})+}\mathrm{}\left(\mathrm{nl}\right)+{\mathrm{He}}^{+}\mathrm{}\left(1s\right)\mathrm{}$ in which four target states are incorporated. The resulting simple expressions for the elements are calculable via the standard Gauss-Legendre and Gauss-Laguerre quadratures. In presenting the final expressions for the elements, the ease of directly programming them for a computer has been a primary consideration. The limitation of the calculation is discussed.

The direct and charge-exchange scattering is studied in the ${\mathrm{He}}^{+}$ + ${\mathrm{H}}_2$ collision system. Charge exchange, which is investigated at energies from 0.5 to 3.0 keV and at angles out to 12°, rapidly becomes the most important collision process as the scattering angle increases. At least two dominant channels contribute to the charge exchange. Direct scattering is studied at 1.0, 2.0, and 3.0 keV and at small angles. The direct scattering shows ${\mathrm{He}}^{+}$ energy-loss spectra having four peaks representing elastic scattering and inelastic processes resulting from vibro-rotational excitation of the ground and electronically excited states of ${\mathrm{H}}_2$ and ${\mathrm{H}}_2^{+}$. It is shown that the collision involves the entire molecule and that there is negligible coupling between the electronic and vibro-rotational excitation. Reduced cross-section plots for the observed direct scattering exhibit a behavior suggesting that the inelastic processes result from interactions occurring at particular interparticle separations.

$K$-shell x-ray production cross sections for Ge, Rb, Y, Zr, and Ag have been measured for incident ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$ ions in the energy range 7-35 MeV. Ionization cross sections are calculated from atomic $K$-shell fluorescence yields and compared with the plane-wave Born approximation (PWBA) theory modified to include the effects of increased target binding energy, Coulomb deflection of the incident projectile, target polarization, and relativistic $K$-shell electron velocities. Experiment and theory are in very good agreement and indicate that the PWBA with modifications is quite appropriate for the projectile-target combinations and energy range for the measurements presented in this report.

The photodetachment spectra of ${\mathrm{P}}^{-}$ and ${\mathrm{Te}}^{-}$ are measured in the wavelength region where excitation of the first excited state of P and the ground state of Te becomes energetically possible. A crossed ion-laser beam apparatus is used to measure relative total cross sections from the production of neutral atoms, while the ${\mathrm{P}}^{-}$→P ground- and excited-state partial cross sections are separately determined by means of kinetic energy analysis of the photoelectrons. The spectra allow determination of the P and Te electron affinities (EA), which are found to be 0.7464(4) and 1.9708(3) eV, respectively. The fine-structure intervals of the negative ions are found to be $\Delta E_{J(2-1)\mathrm{}}\left({\mathrm{P}}^{-}\right)=181\mathrm{}\left(3\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, $\Delta E_{J(2-0)\mathrm{}}\left({\mathrm{P}}^{-}\right)=263\mathrm{}\left(3\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, and $\Delta E_{J(\frac{3}{2}-\frac{1}{2})}\left({\mathrm{Te}}^{-}\right)=5008\mathrm{}\left(5\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Comparison is made with previous measurements and values which are predicted from extrapolations. A comparison of the ${\mathrm{P}}^{-}$ multichannel measurements is made with equivalent measurements involving alkali negative ions on the basis of channel coupling. In addition, the relative strengths of the various fine-structure level transitions in ${\mathrm{P}}^{-}$→P are determined; the observed strengths agree much better with the predictions of a geometrical model, than with those made by a statistical-weight argument.

A new measuring technique which can detect a single atom of a given kind, even in the presence of ${10}^{19}$ or more atoms of another kind, with good space and time resolution, was utilized to study the density fluctuation of less than 100 cesium atoms in a small volume of space filled with inert gases. Repeated measurements of the absolute number of atoms in a defined volume at an arbitrary time were recorded for the first time in order to obtain a statistical distribution giving the fluctuation of the number of atoms around the mean value. Numerous other physics applications of the one-atom detector are briefly described.

Laser-induced fluorescence from a beam of xenon ions has been used to determine the hyperfine structures of two levels from the $5p^{4}5d$ and $5p^{4}6p$ excited configurations of ${}_{}{}^{129}{}_{}{}^{}\mathrm{Xe}_{}^{+}{}_{}{}^{}$ and ${}_{}{}^{131}{}_{}{}^{}\mathrm{Xe}_{}^{+}{}_{}{}^{}$. The coupling constants (in MHz) were found to be as follows: $A_{129}\left(6p{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}\right)=-1667.5\mathrm{}\pm 18.7$, $A_{129}\left(5d{}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{}{}_{}{}^{}\right)=-515.7\mathrm{}\pm 8.9$, $A_{131}\left(6p{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}\right)=487.5\mathrm{}\pm 5.2$, $B_{131}\left(6p{}_{}{}^4{}_{}{}^{}P_{\frac{5}{2}}^o{}_{}{}^{}\right)=-107.2\mathrm{}\pm 52.3$, $A_{131}\left(5d{}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{}{}_{}{}^{}\right)=149.4\mathrm{}\pm 3.2$, and $B_{131}\left(5d{}_{}{}^4{}_{}{}^{}D_{\frac{7}{2}}^{}{}_{}{}^{}\right)=76.1\mathrm{}\pm 27.5$. The data also yielded values for the very small isotope shifts.

The small dipole moment of Ge${\mathrm{H}}_4$ induced by centrifugal distortion of the tetrahedral structure is measured by three experimental techniques using coincidences between the ${\nu }_2$ $Q\left(11\right)E$ transition of Ge${\mathrm{H}}_4$ and infrared C${\mathrm{O}}_2$ laser lines: (1) the Stark shift of the infrared-microwave double resonance, (2) infrared-infrared double resonance using modulation sidebands, and (3) laser Lamb-dip Stark spectroscopy. The observed results demonstrate the power of these methods in measuring small Stark shifts. From the observed shifts, Watson's centrifugal dipole moment has been determined to be ${\theta }_z^{\mathrm{xy}}=(3.33\mathrm{}\pm 0.05)\times {10}^{-5\mathrm{}}$ D for the ground vibrational state. For the excited state the Stark shift was found to be smaller than the ground state by a factor of 9, indicating approximate cancellation between rotation- and vibration-induced dipole moments for the rotational level in the ${\nu }_2$ vibrational state of Ge${\mathrm{H}}_4$.

The projectile energy dependence of apparent two-electron, one-photon x-ray transitions is determined from x-ray spectra resulting from collisions of nickel ions with thin nickel targets. Hartree-Fock energy calculations show that the observed projectile energy dependence can be attributed to the production of $L$-shell vacancies. It is also demonstrated that these transitions are fundamentally many-electron processes which cannot be described in terms of independent-particle models alone. Theoretical transition probabilities based on the non-closed-shell many-electron theory of Sinano$\stackrel{\mathrm{̌}}{\mathrm{g}}$lu yield a $K{\alpha }^h$ ($K\alpha$ hypersatellite) to $K\alpha \alpha$ branching ratio for nickel of 6700.