Second-order correlation energies for some ions of the Ne isoelectronic series are evaluated within the framework of the Rayleigh-Schrödinger Hartree-Fock perturbation theory (RS-HEPT). The variational-perturbation method is applied. Pair functions of definite orbital and spin symmetry are expressed in the form of partial-wave expansions. Special attention is paid to the determination of the $Z$ dependence of both the partial-wave increments to the pair energies and the second-order pair energies, which represent very close approximation to the "all-external" pair-correlation energies. It is found that the partial-wave increments depend in a strictly monotone way on the nuclear charge, whereas the $Z$ dependence of the pair energies is more complicated. A comparison with relevant results of the most extensive variational computation for ${\mathrm{F}}^{1-}$ confirms our previous conclusion that for Ne-like atoms the RS-HFPT yields very accurate correlation energies. A very accurate value for the electron affinity of F (3.534 eV) has also been obtained.

The Bethe formula for the stopping power for bare ions is extended to the collisions between partially stripped ions and neutral atoms. The resulting formulas can be presented in the same form as the original Bethe formula by replacing the nuclear charge of the projectile $Z$ and the mean excitation energy $I$ by $Z_{\mathrm{eff}}$ and $I_{\mathrm{eff}}$, respectively. Both $Z_{\mathrm{eff}}$ and $I_{\mathrm{eff}}$ contain contributions from excitations (including ionizations) of the target by the projectile, excitations of the projectile by the target, and mutual excitations. They are defined in terms of projectile and target properties that can be calculated from first principles. Expressions for $Z_{\mathrm{eff}}$ and $I_{\mathrm{eff}}$ reduce to those in the Bethe formula for bare incident ions. Formulas for atom-atom and ion-ion collisions are also presented. Comparison with experimental data on Ar ions in Ar gas indicates that the new formula is reliable for projectile energies greater than a few MeV/amu.

Range distributions of nitrogen ions implanted in solid targets have been studied as a function of target material and projectile energy and for both atomic- and molecular-ion species. These profiles were determined by a nuclear resonance reaction technique in which the ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}$($p$,$\gamma$)${}_{}{}^{15}{}_{}{}^{}\mathrm{O}$ reaction at 1058 keV was used. At a single energy of 800 keV, ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{+}{}_{}{}^{}$ ions were implanted in 24 elemental targets from carbon through lead. From these range distributions electronic stopping powers were inferred which show the familiar periodic structure with target atomic number. For three targets, iron, nickel, and zirconium, the energy dependence of the range distributions was studied for incident ${}_{}{}^{14}{}_{}{}^{}\mathrm{N}_{}^{+}{}_{}{}^{}$ ions from 200 to 2000 keV. The data suggest that the electronic stopping power has the same energy dependence for each target and is consistent with being proportional to velocity. For these three targets and for gold also, the range distributions were determined for both atomic and molecular nitrogen-ion beams of equal energy per atom. The data suggest that at higher particle energies the molecular beam gives rise to slightly more shallow distributions.

Electron capture to the $K$ shell of projectiles from the $K$ and other subshells of multielectron target atoms is studied in the intermediate energy region using the single-active-electron approximation and the two-state, two-center atomic eigenfunction expansion method. It is concluded that the theoretical capture cross section is not sensitive to the atomic models used at high collision energies where the projectile velocity $v$ is near or greater than the orbital velocity $v_e$ of the active electron. For $v<\mathrm{}{v}_e$, however, a proper atomic potential such as the Herman-Skillman potential is needed to represent the target atom. The insufficiency of various simple Coulomb model potentials is illustrated. Capture cross sections for a few collision systems are obtained and compared with experimental data when available to illustrate the reliability of the present model.

Two new approaches to the inclusion of target charge-polarization effects in electron-scattering calculations are presented and tested. The first approach is an energy-dependent polarization potential based on an $r^{-6\mathrm{}}$ nonadiabatic correction to the adiabatic polarization potential. The second approach is a matrix effective potential which includes the nonadiabatic dynamics of the polarization effect at all $r$. The two approaches are tested by comparing them to accurate phase shifts and differential cross sections for electron-helium scattering for impact energies 12-400 eV.

In a relativistic density-functional theory the importance of the transverse photon contribution to the exchange potential in the high-density regime is pointed out. A neutral atom ${}_{}{}^{92}{}_{}{}^{}\mathrm{U}$ is studied and its orbital energies calculated in the present scheme are compared with previous calculations based on relativistic Hartree, Dirac-Slater, and Dirac-Fock schemes and with experimental values from (electron spectroscopy for chemical analysis) ESCA studies. The present scheme is also used to calculate the orbital and total energies of some highly stripped ions of the Li isoelectronic sequence which occur as impurities in controlled thermonuclear plasma. These energies are found to be in close agreement with more involved Dirac-Fock results. Also, the relativistic effects significantly increase in going from ${\mathrm{C}}^{3+}$ to ${\mathrm{W}}^{71+}$ because the electronic density reaches values for which relativistic effects become large.

A new second-order representation of the Dirac equation is presented. This representation which is exact for a hydrogen atom is applied to approximate analytical self-consistent-field calculations for atoms. Results are given for the rare-gas atoms from helium to radon and for lead. The results compare favorably with numerical Dirac-Hartree-Fock solutions.

An analysis of the three-electron problem in hyperspherical coordinates is begun by generalizing the adiabatic method developed by Macek and Lin. Approximate potential curves are constructed for Li and ${\mathrm{H}}^{--}$. The relationship between the hyperspherical and shell-model quantum numbers is presented for the $s^3$ configurations.

The probabilities of differently ionized products following inner-shell-vacancy creation are calculated with account taken of Auger, Coster-Kronig, and radiative transitions. Results of calculations are presented for argonlike ions with different nuclear charges, both in the isolated state and in a plasma environment.

A linked-cluster expansion that has been derived previously to calculate expectation values for Jastrow-type wave functions is applied to variational calculations for closed-shell atoms. In the calculation the Hartree-Fock ground state is multiplied by a correlating factor $\Pi g\left(r_i\right)\Pi f\left(r_{\mathrm{ij}}\right)$ and the functions $f$ and $g$ determined variationally. Only the lowest-order direct terms are included in the calculation so that the variational principle is not strictly valid. The calculation is carried out in momentum space in order to simplify the treatment of the kinetic energy operator. The variational principle leads to a Fredholm equation of the first kind for the correlating factor. Parametrized forms of the correlating factor are given for the cases considered. It is found that the direct terms calculated overestimate the correlation energy of the atoms considered but estimates of the exchange terms indicate that these would largely account for the differences. It is found that it is not adequate to include only the two-particle functions $f$ in the correlating factor, but the one-particle function $g$ must also be included. The atoms considered are He, Be, Ne, Mg, and Ar.

The methods of calculation of overlap integrals over a reduced Bessel-function basis set have been reviewed. Some new results were obtained, and the numerical aspects of existing formulas were investigated. Also, analytical expressions for multiploe integrals over reduced Bessel functions have been derived.

In this paper general working equations for the Morse ${(r-r_e)}^l$ matrix elements are given. These equations can be used to calculate the diagonal ($m=n$) matrix elements and, for the off-diagonal ($m\ne n$) elements, are simpler to use than the ones currently available in the literature. Also, in this paper a new approach is given which allows one to obtain simple formulas, in closed form, for the off-diagonal matrix elements. Explicit expressions are given for $l=1, 2, \mathrm{and} 3$.

The quadrupole antishielding factors ${\gamma }_{\infty }$ for the ions ${\mathrm{Na}}^{+}$, ${\mathrm{Mg}}^{2+}$, and ${\mathrm{Cl}}^{-}$ have been calculated by solving differential equations in nonorthogonal Hartree-Fock perturbation theory. The results are compared with the values of ${\gamma }_{\infty }$ obtained in other calculations. The agreement in all the cases except ${\gamma }_{\infty }(3p\to p)$ of ${\mathrm{Cl}}^{-}$ is quite satisfactory. It is believed that the discrepancy in the latter case is perhaps due to the different zero-order wave function used in the present calculation.

Kinetic-energy distributions of ion fragments from electron-impact bombardment of ${\mathrm{H}}_2$, ${\mathrm{D}}_2$, and HD have been measured at electron energies between 30 and 100 eV. In the case of ${\mathrm{H}}_2$ these distributions at 90° are interpreted as resulting from excitation of two autoionizing states of ${\mathrm{H}}_2$ (${}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ and ${}_{}{}^1{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$) and one repulsive state of ${\mathrm{H}}_2^{+}\left({}_{}{}^2{}_{}{}^{}\Pi _u^{}{}_{}{}^{}\right)$. The shapes of the kinetic-energy distributions for ${\mathrm{H}}^{+}$ from ${\mathrm{H}}_2$ and ${\mathrm{D}}^{+}$ from ${\mathrm{D}}_2$ are substantially different, and a strong preference for ${\mathrm{H}}^{+}$ over ${\mathrm{D}}^{+}$ fragments from HD was observed.

Electron-photon angular correlations between electrons which have excited the $2{}_{}{}^1{}_{}{}^{}P$ state of He and photons from the $2{}_{}{}^1{}_{}{}^{}P\to 1{}_{}{}^1{}_{}{}^{}S$ transition have been studied for 100-, 200-, and 500-eV incident electrons. Values of $\lambda$ and $\left|\chi \right|$ obtained from these measurements are compared to values which have been obtained in other experiments and calculations. The results are in good agreement with the recent distorted-wave calculation of Madison. The values of $\lambda$ and $\left|\chi \right|$ from all experiments have been combined to examine the behavior of the Fano-Macek alignment and orientation parameters for electron energies from 40 to 500 eV.

Cross sections for the stripping of one electron from ${\mathrm{Ar}}^{+}$, ${\mathrm{Ar}}^{2+}$, and ${\mathrm{Ar}}^{3+}$ ions in single collisions on argon atoms have been measured. The measurements were made at energies from 2 to 15 keV per incident-ion charge. The growth-rate method has been used to check that the single-collision condition is realized. Cross sections are then deduced. During the collision, incident ions are scattered out of the acceptance angle of the analyzing device: An estimate of losses is made, and corrected cross sections are proposed. Comparisons to previously published data are attempted: For ${\sigma }_{1,2}$ one value at 6 keV exists which is in fair agreement with our value; for ${\sigma }_{2,3}$ our value at 30 keV coincides with the single ${\sigma }_{2,3}$ value existing.

Distorted-wave-approximation calculations are reported for the excitation of the $b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ and $B{}_{}{}^1{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$ states of ${\mathrm{H}}_2$ by electron impact. A discrete-basis-set method is used to obtain the electron-molecule continuum wave functions. Differential and integrated cross sections are presented from near threshold up to 60-eV electron impact energy. Comparison is made with other theoretical results and experimental data.

Absolute total electron scattering cross sections for ${\mathrm{N}}_2$ from 0.5 to 50 eV have been measured with an estimated uncertainty of ±3% using a transmission time-of-flight method previously described. The results are compared to previous experimental results and to recent calculations. The positions of the ${}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ resonance peaks were determined with much greater accuracy (± 15 meV) than in previous transmission measurements. The structure reported by Golden (1966) below the ${}_{}{}^2{}_{}{}^{}\Pi _g^{}{}_{}{}^{}$ resonance was clearly not present, indicating that, if real, these features are not a property of the ${\mathrm{N}}_2$ ground vibronic state. The shape resonance predicted at 11 eV by Dill and Dehmer (1977) was not seen, perhaps because it was too weakly manifested in the total cross section. A weak broad band centered at 25 eV may be interpreted as being due to a ${\sigma }_u$ shape resonance as predicted by Dehmer, Siegel, Welch, and Dill.

Spectral distributions of bremsstrahlung produced by ${}_{}{}^{204}{}_{}{}^{}\mathrm{Tl}$ $\beta$ particles in thick targets of Perspex, aluminum, copper, tin, and lead have been measured in a sandwich geometry. The contributions of internal bremsstrahlung produced along with the $\beta$ particles have been determined by magnetic field deflection as well as the $Z=O$ extrapolation method. Experimental results agree with Bethe-Heitler Born-approximation theory, corrected for Coulomb-field effects for low- and medium-$Z$ targets, but show 25% positive deviation for high-$Z$ targets. Again it is found that the bremsstrahlung produced in low-$Z$ targets like Perspex is comparable with internal bremsstrahlung, and the corrections for its contribution to measurements by earlier workers can lead to large uncertainties.

Total differential cross-section ratios for scattering of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{Li}}^{+}$ ions incident on bismuth-zinc and gold-carbon systems have been measured. The energy dependence of the cross sections was measured for each species at a fixed laboratory backscattering angle (${\varphi }_{\mathrm{lab}}=170\mathrm{}°$), using an amorphous carbon target implanted with 10-keV ${\mathrm{Zn}}^{+}$ and ${\mathrm{Bi}}^{+}$ at a depth of ∼2.7 μg/${\mathrm{cm}}^2$. Angular distributions (${\varphi }_{\mathrm{lab}}=15\mathrm{}°, \dots , 170°$) were measured for helium ions at four different energies, using selfsupporting vacuum-deposited polycrystalline carbon and gold foils. For the case of backscattering, the cross-section ratios $\frac{{\left(d\sigma \right)}_{\mathrm{Bi}}}{{\left(d\sigma \right)}_{\mathrm{Zn}}}$ deviate significantly from both the Rutherford-scattering law and the Lindhard, Nielsen, and Scharff differential-scattering cross section. The deviations of the absolute cross sections from the Rutherford cross sections amount to 3.5% for 1-MeV and 16% for 0.2-MeV helium on bismuth. The experimental results are in good agreement with exact classical differential-scattering cross sections based on the Lenz-Jensen and Dirac-Hartree-Fock-Slater atomic potentials. Simple analytical formulas describing the energy and angular dependence of the cross sections are presented.