The configuration-interaction method has been used to calculate the wave functions and energies for the ground state and some selected excited states of the atoms B to Ne. A systematic way of selecting atomic orbital basis and configurations has been developed and is reported in some detail. The calculated total correlation energies range from 95 to 97% of the empirical correlation energy. Calculated term energies of the carbon atom are within 2% of the spectroscopic values. The correlation energies were analyzed in terms of contributions from various classes of configurations, and these contributions were compared with results of previous work. The energy contributions from the class of configurations of triple and higher electron excitations are estimated to be of the order of (3-4)% of the total correlation energy, which is larger than previous estimates of (1-3)% for these atoms.

Channel interaction is shown to have a substantial effect of "spectral repulsion" that distorts the photoionization spectrum near the threshold of a weak channel. This effect is illustrated by calculating numerically the cross section of the $3s\to \epsilon p$ transition of Ar, taking into account its coupling with the $3p\to \epsilon d$ transition. The result is very different from that obtained by an independent-particle approximation. Examples calculated by other authors on He, Ne, and Xe serve as additional illustrations.

By comparing the random-phase-approximation-with-exchange (RPAE) method of Amusia et al. for the calcuation of photoionization cross sections from closed-shell atoms with the reaction-matrix method, we obtain a simplified version of the RPAE by which we calculate the dipole-transition amplitude much as in the reaction-matrix method, yet with ground-state correlation effects included simultaneously. Calculation of photoionization cross sections for the $3p\to \epsilon d$ transition of Ar and $4d\to \epsilon f$ transition of Xe by this method yields a substantial improvement on the calculation by the reaction-matrix method and good agreement with RPAE and with experiment.

Absolute cross sections for the emission of the 3914-ÅA radiation of the ${\mathrm{N}}_2^{+}$ first negative system have been measured for ${\mathrm{F}}^{+}$, ${\mathrm{Ne}}^{+}$, and ${\mathrm{Na}}^{+}$ ions incident on a gaseous nitrogen target. The energy range covered was 30 to 100 keV. It is shown that for incident ${\mathrm{F}}^{+}$ and ${\mathrm{Ne}}^{+}$ the emission cross sections closely resemble in shape the corresponding charge-transfer cross sections for these ions with ${\mathrm{N}}_2$. In the case of ${\mathrm{Na}}^{+}$ the two cross sections bear little resemblance. These results are consistent with the magnitudes of the internal-energy change required for each of the processes. It is concluded that charge transfer is the dominant process for exciting the $B{}_{}{}^2{}_{}{}^{}\Sigma (v^{\prime }=0)$ state in the cases of ${\mathrm{F}}^{+}$ and ${\mathrm{Na}}^{+}$, while no such conclusion can be drawn for ${\mathrm{Na}}^{+}$.

Absolute ionization cross sections for the $L$ subshells of Au by proton bombardment (0.25-5.2 MeV) have been determined from data obtained using a Si(Li) detector and the presently available values for radiative transition probabilities, fluorescence yields, and Coster-Kronig factors. The measured cross sections are compared with values calculated by Choi using the plane-wave Born approximation (PWBA) with either relativistic or nonrelativistic hydrogenic wave functions for the Au electrons. Except at low energies ($\frac{{\eta }_L}{{\theta }_L^2}<0.2\mathrm{}$) where the uncorrected PWBA is questionable, the agreement is good. A plateau in the $2s$ ionization cross section attributable to the bimodal $2s$-electron wave function is observed in the region 0.5-1.0 MeV. Ionization by He ions (1-12 MeV) is similar, but significant differences in subshell behavior are observed.

Backscattering cross sections for the electron-impact $L_1$-shell ionization of Na, Mg, and S as well as the $L_{2,3}$-shell ionization of Mg, S, Cl, and Cu are reported. The use of target atoms chemisorbed on a metal surface allow measurement of the weak intensities in the backscattered region. The Burhop first Born approximation theory is shown to qualitatively describe the primary-electron energy dependence of these backscattering ionization cross sections. However, the theoretical cross sections are generally too low, particularly for the highest primary-electron energies studied.

We present the first experimentally determined angular intensity distributions of helium ($n{}_{}{}^1{}_{}{}^{}P-1{}_{}{}^1{}_{}{}^{}S$) resonance photons with respect to the exciting electron beam. The angular intensity distributions were measured at selected electron-impact energies from 25 eV (near threshold) to 150 eV. Polarization fractions (II) were obtained by analyzing the data in terms of the theoretical relation between angular intensity distribution and II, i.e., $I\left(\theta \right)=I\left(90\right)\mathrm{}\times (1-\Pi {cos}^2\theta )$. The experimental values for II are compared with recent theoretical results and with previous experimental values for the ($3{}_{}{}^1{}_{}{}^{}P-1{}_{}{}^1{}_{}{}^{}S$) transition. Our results are slightly higher than the theoretical results for electron-impact energies from 80 to 150 eV, e.g., 0.36 vs 0.32 at 100 eV. Our values for II reach a maximum at ∼40 eV where II=0.55 and then decrease for lower electron energies, reflecting the increasing importance of cascade ($m{}_{}{}^1{}_{}{}^{}S-n{}_{}{}^1{}_{}{}^{}P$) transitions at lower electron energies.

The study of keV ${\mathrm{H}}^{+}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collisions has been extended to the production by electron transfer of highly excited states with principal quantum numbers between 13 and 28. A fast-proton beam was passed through thermally dissociated hydrogen gas, and the resultant fast excited atoms were observed using electric field ionization and proton-counting techniques. The incident proton energy range was from 7 to 60 keV. The observed cross section for production of such excited states possesses a broad maximum near 30 keV. The sum of cross sections over the observed principal quantum numbers is 0.00089 ${\mathrm{\AA }}^2$ at 7 keV, 0.0070 ${\mathrm{\AA }}^2$ at 30 keV, and drops again with energy to 0.0023 ${\mathrm{\AA }}^2$ at 60 keV. Possible error in our cross section scale is ± 30%. Thus the fraction of electron-transfer collisions producing these highly excited states varies from a maximum value of about 0.03% in the range 30-60 keV to the lower value of 0.01% at 7 keV, values not markedly different from those found for inert-gas target atoms; this is contrary to the predictions of the Brinkman-Kramers-Oppenheimer approximation. The data at 60 keV agree with recent calculations by Band using the coupled Born approximation. The present results for ${\mathrm{H}}^{+}$-Ar collisions and $13\le n\le 28$ are in agreement with previous investigations for $9\le n\le 15$, assuming that the Jackson-Schiff scaling rule is valid for this collision system.

Rigorous lower-bound $p$ -wave positron-hydrogen phase shifts are calculated below the positronium pick-up threshold. The wave function is expanded in terms of the two linearly independent D functions each multiplied by an associated Hylleraas-type radial function with two nonlinear parameters. Calculations have been done employing up to a total of 168 linear parameters, so that convergence can be examined and extrapolations in most cases performed to $N=\infty$. In addition, adiabatic and nonadiabatic corrections have been included. Results are found to be larger than Armstead's in all cases, near the upper edge of his estimated uncertainty. The calculation confirms as a byproduct that there are no $p$ -wave Feshbach resonances in this energy range.

Using the precision $s$- and $p$ - wave elastic-scattering wave functions obtained previously, we have calculated the annihilation rate for positrons colliding with hydrogen atoms below the positronium-formation threshold. The $s$-wave results agree well with those of Humberston, while the $p$-wave results, which are new, contribute about 20% of the total at the higher energies.

The static approximation, which neglects the distortion of the (complex) target, that is, virtual excitations, during the collision of a particle with the target, was shown previously to give an upper bound on the scattering length when the number of bound states supported by the static and true Hamiltonians are the same. It represents an underadjustment of the target to the field of the scattering particle. It is perhaps then to be expected that the adiabatic approximation, in which the target wave function is calculated for each value of the incident particle coordinate as if the incident particle were fixed at the given point and which represents therefore an overadjustment of the target to the field of the incident particle, might provide the opposite bound, the lower bound, on the scattering length. This possibility is explored for the determination of scattering lengths. The bound property is shown to hold in cases where both the true and adiabatic Hamiltonians support the same number of bound states; some (reasonable) subsidiary conditions must also be satisfied. Possible extensions of the formulation to scattering with nonzero energy and with exchange are briefly mentioned. The theory is then applied to $e^{+}\mathrm{H}$ and $e^{+}\mathrm{He}$ scattering at zero incident energy; a reasonably accurate bound for the latter system is obtained, but the adiabatic approximation gives only a very crude, though rigorous, bound on the $e^{+}\mathrm{H}$ scattering length. A connection between the generalized optical potential and the adiabatic potential is derived using projection-operator techniques, thus further clarifying the physical content of the adiabatic picture. Bounds are also obtained for atom-atom and ion-atom collisions; they are interesting only if the electron-proton mass ratio is not thought of as vanishingly small. Some consideration is given to $p\mathrm{H}$ scattering. Lower bounds on electron-atom scattering lengths are more difficult to obtain.

An exact closed expression for the form factor (and hence the generalized oscillator strength) for bound-free transitions of the hydrogen atom in highly excited states is derived by use of the Coulomb Green's function. The calculated densities of the generalized oscillator strength of the excited hydrogen atom with an initial principal quantum number $n_0=10\mathrm{}$ are 10.9(-5.0), 13.6(-4.0), 22.7(-3.0), 55.3(-2.0), 96.2(-1.0), 42.1(0.0), and 4.63(1.0) in ${\mathrm{Ry}}^{-1\mathrm{}}$ near the ionization threshold [for $\frac{E}{I\left(n_0\right)}$ = 1.0001]. Here a figure in parentheses denotes the value of $\ln \left(n_0^2{q}^2\right)$, where $q$ is the magnitude of the momentum transfer, $E$ the excitation energy measured from the state $n_0$, and $I\left(n_0\right)$ the ionization potential. Using these results, we draw the Bethe surface, i.e., a three-dimensional plot of the density of the generalized oscillator strength as a function of $E$ and $\ln q^2$. This surface gives a quantitative understanding for the entirety of the inelastic process of this excited atom by charged particles. The validity of the binary-encounter theory is quantitatively discussed. The Born sections for excitations $n_0\to n_0+1\mathrm{}$, $n_0\to n_0+2\mathrm{}$, $n_0\to 2n_0$ transitions) and ionization are evaluated for the case of $n_0=10\mathrm{} \mathrm{and} 20$. Finally, an application of this form factor to the collisional of the highly excited atom with a molecule is briefly mentioned.

Time-dependent studies of the vacuum-ultraviolet emissions in krypton were performed using 250-keV electrons. Measurements as a function of pressure were made at the wavelengths of the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ and ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ resonance lines and the 1250- and 1425-Å continuum emissions. The suggest that at early decay times the ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$ atomic state is responsible for the 1250-Å molecular radiation. From the time-dependent studies it is proposed that the ${}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ state is converted to a highly excited molecule by two-body collisions. This molecule undergoes rapid vibrational relaxation resulting from two- and three-body collisions. The vibrationally relaxed molecule then radiates the 1425-Å continuum. At high pressures (about 1000 torr) the vibrationally relaxed molecule decays with a nearly pressure-independent lifetime of about 0.30 μsec.

Extensive configuration-interaction calculations have been carried out to determine electron affinities of the first-row atoms, B to F. Calculated electron affinities in eV with the observed values in parentheses are 0.15, 1.11(1.25), -0.52, 1.13(1.461), and 3.12(3.448), for B, C, N, O, and F, respectively. Our best estimates, based on an empirical extrapolation which makes use of the known C, O, and F affinities, for B and N electron affinities are 0.24 and -0.19 eV, respectively. Detailed analysis of the results in terms of contributions from various classes of configurations shows that the $K$-shell and $KL$-intershell correlation-energy contributions to these electron affinities are negligibly small, and that about 15% of the total correlation contribution comes from the triple and higher electron-excitation configurations. Symmetry-adapted pair-correlation calculations have been carried out for O, ${\mathrm{O}}^{-}$, F, and ${\mathrm{F}}^{-}$ to study convergence patterns for the correlation energy and electron affinity with respect to the orbital basis used to construct the configurations. Such pair-correlation calculations are known to overcompute the correlation energy. The excess energies, which correspond to pair-pair interaction energies neglected in the pair-correlation calculations, were roughly constant over a range of orbital basis sizes, with magnitudes about twice the energy contributions from the configurations of triple and higher excitations omitted in the pair-correlation calculations. Accordingly, this approximation should overestimate the electron affinity if a complete orbital basis is used.

A model is derived for the differential cross section for ($e,2e$) reactions on atoms, leaving the residual ion in an excited state. The eigenstates of the ion are described by the shell model with configuration interaction. In the case of argon, $3s^{-1\mathrm{}}$ spectroscopic factors are independently determined. They describe the probability that each of the three ion eigenstates whose ($e,2e$) angular correlation has the $3s^{-1\mathrm{}}$ shape, contain the $3s^{-1\mathrm{}}$ configuration. Two Hartree-Fock single-particle models are compared. The spectroscopic factors add to 1 for both, but only one correctly predicts the experimental single-hole energy level.

Absolute cross sections have been measured for the $K$ -shell ionization of Al, V, Fe, Cu, Y, Mo, Ag, and Sn by $\alpha$-particle bombardment over the 1-5-MeV energy range. Characteristic x-ray radiation produced by the ion impact was detected by a cooled Si(Li) detector. Experimental results are compared with ionization cross sections calculated using the plane-wave Born approximation, the semiclassical approach, and the binary-encounter approximation (BEA). The present results agree most favorably with the BEA calculations. Comparisons of cross sections obtained from separate thick- and thin-target measurements show excellent agreement.

A line-integral representation for a transform of the free-particle Green's function is derived. This representation gives rise to a line-integral equation for the Yukawa-potential scattering amplitude. The second term in the Born series is recovered by iterating the equation once. Generalization to superpositions of Yukawa potentials and angular-dependent potentials is discussed.

Using the Thomas-Fermi distribution for the electronic charge in an atom, Landau and Lifshitz have shown that Born's formula for scattering applied to the elastic scattering of electrons yields the scattering cross section

$\sigma =\left(\mathrm{const}\right)\left(\frac{Z^{\frac{4}{3}}}{v^2}\right),$

where $v$ is the velocity of the incident electrons. This relation gives, for the $Z$ dependence of the transmitted intensity of electrons from a radioactive source through different absorbers, an equation of the form

$\frac{t}{A}=K{Z}^{-\frac{4}{3}},$

where $t$ is the thickness in mg/${\mathrm{cm}}^2$ of the absorber needed to obtain a given transmitted intensity, $K$ is the mass of the atom of the absorber and $A$ is a constant. Experimental results for the scattering of positrons by atoms in their passage through thin metallic foils indicate that the same relation is also valid for positron scattering in the range 300 keV to 2 MeV. A simple interpretation of this relationship is also given.

Cross sections for the ionization of atoms by the impact of heavy, charged particles are expressed as a function of the impact parameter $b$ of the incident projectile. The ionization probability $P\left(b\right)\mathrm{}$, which is obtained in a peaked-binary-encounter approximation (BEA), is compared to several recent experiments and to the semiclassical Coulomb approximation (SCA). At high energies the BEA and plane-wave SCA models give the same result, the shape of which is proportional to a simple function of $\frac{2b}{a}$ ($a$ is the atomic radius). The functional form is independent of both projectile and target for isotropic target-electron distributions. At low energies the BEA and SCA models give similar but not identical results. The scaling properties at low energies are the same for both models. Comparison to experimental results at intermediate energies does not strongly favor either model at this time. Typically, the shape of $P\left(b\right)\mathrm{}$ is within ∼ 50% of experiment. A table of $P\left(b\right)\mathrm{}$ for the BEA model is given which, together with scaling laws, may be used to find $P\left(b\right)\mathrm{}$ for arbitrary projectiles and targets at various energies.

A new method for calculating quantum-mechanical reactance matrices (and hence cross sections) for rearrangement collisions is discussed and tested. This method avoids the integral kernels which usually appear in the coupled differential equations describing the wave function for rearrangement scattering. The method is applied to an example rearrangement scattering problem (elastic and inelastic electron-hydrogen-atom scattering) with good results.