Assume a solved quantum-mechanical problem for the one-dimensional Schrödinger equation, which has a discrete spectrum. An algorithm is presented to calculate exactly the change in the original potential and eigenfunctions brought about by arbitrary changes in the positions of the original eigenvalues and/or the normalizations of the corresponding eigenfunctions. As a first example, we consider the modification of the harmonic oscillator and thereby obtain potentials for anharmonic oscillators with exact eigenvalues and eigenfunctions. Next, we introduce potentials in the one-dimensional box with rigid walls which alter the usual spectrum in a predetermined way. We also sketch the process of obtaining a change in the Coulomb potential which deletes the lowest eigenvalue for the zero-angular-momentum equation.

The ${}_{}{}^2{}_{}{}^{}P$ ($2s2s2p$) and ${}_{}{}^2{}_{}{}^{}D$ ($2s2p2p$) resonance structure observed in the electron-helium scattering experiments has been investigated using a saddle-point technique. For ${}_{}{}^2{}_{}{}^{}P$ we obtain for the energy — 0.796 93 a.u. with an 82-term wave function. This agrees well with the experimental result. In the past, the ${}_{}{}^2{}_{}{}^{}D$ structure was thought to be a Feshbach resonance. In this calculation, we show that the $2s2p$ ${}_{}{}^3{}_{}{}^{}P$ target is repulsive to the third $p$ electron in the sense that the variational energy of the ${\mathrm{He}}^{-}$ system is monotonically increased as the $p$ electron approaches the target. Hence, the Feshbach resonance cannot be formed for this state. Some comments will be made concerning earlier theoretical calculations in the literature.

A model is investigated for doubly excited states, in which two electrons move on the surface of a spherical shell with restricted angular momentum to account for a hydrogenlike shell structure. Hybridized two-electron wave functions are constructed for the short-range part of the intrashell interaction potential using a modified version of hybridization theory originally developed by Pauling for molecules. The highest energy level obtained by this approach is identified as being invariant under SO(4) rotations on the restricted-shell basis, and is thus seen to be compatible with the SO(4) structure and rotation-vibration levels in a recent "supermultiplet" theory of doubly excited states. The highest energy level in each shell has ${}_{}{}^1{}_{}{}^{}S$ symmetry, and is interpreted as a "perfect pairing" level which maximizes the electron density at values of the interelectronic angle ${\theta }_{12}=0\mathrm{}°$, and hence is an exact eigenstate of a $\delta$-function interaction between the two electrons. Formulas are described for the explicit ${\theta }_{12}$ dependence of related ${}_{}{}^1{}_{}{}^{}S$ states for SO(4), and these give rise to approximate decoupling of the radial Schrödinger equation for two electrons in the same shell.

We show that our generalization of the Fermi-Segrè formula to arbitrary angular momentum, as well as a different expression obtained by Bouchiat and Bouchiat, can both be understood as limiting cases of a common form. This new expression, which connects energy and normalization, makes no explicit reference to inner, outer, or excited states properties, or to the degree of ionization of the atom. The expression also indicates that for given nuclear charge energy and the square of the normalization scale with ionic charge in the same way through an isonuclear sequence.

A perturbation study of the $1s^2\mathrm{ns}{}_{}{}^2{}_{}{}^{}S,1\mathrm{}{s}^2\mathrm{np}{}_{}{}^2{}_{}{}^{}P$, and $1s^2\mathrm{nd}{}_{}{}^2{}_{}{}^{}D$ states of three-electron atoms has been made (for $n=3\mathrm{} \mathrm{to} 7$). Second- order energy coefficients for these states are calculated, and estimates of the relativistic corrections to low orders in $Z$ are also obtained. Transition energies computed with these results, however, are not of high accuracy when compared to the experimental data, particularly for low-$Z$ members of the isoelectronic sequence. Introduction of higher-order energy coefficients can correct this deficiency, but these coefficients are difficult to compute. A semiempirical fitting of the experimental data is used here to obtain estimates of these higher-order coefficients with little computational effort. These, in turn, yield transition energies in excellent agreement with experiment.

We have observed fine-structure intervals in Cs I using high-resolution Fourier spectroscopy. Improved values are reported for the $5,6{}_{}{}^2{}_{}{}^{}D$ and $4-9{}_{}{}^2{}_{}{}^{}F$ terms and are shown to be consistent with recent laser fluorescence measurements of the $10-17{}_{}{}^2{}_{}{}^{}F$ intervals. The results are compared with previous measurements. A three-term expansion in odd powers of $\frac{1}{n^{*}}$ is shown to describe all of the $4-17{}_{}{}^2{}_{}{}^{}F$ fine-structure intervals. The state of experimental and theoretical work on the doublet structure in the alkali metals is briefly reviewed.

The dependence of the one-electron eigenvalues and the total energy on the value of the parameter $\alpha$ in the Hartree-Fock-Slater (HFS) theory is considered. When the HFS wave function is used in the HFS Hamiltonian and in the Hartree-Fock Hamiltonian (HF) different trends occur. When the Latter correction to the wave function is used, different results are obtained. $E^{\mathrm{HF}}\left({\alpha }_{\mathrm{HF}}\right)$ is lower when Latter's correction is not used, and $E^{\mathrm{HF}}\left({\alpha }_{\mathrm{ta}}\right)$ is lower when it is used. Use of the ${\alpha }_{\mathrm{ta}}$ of Gopinathan et al. given better ionization energies compared to experiment. No unique "best" $\alpha$ can be chosen.

It is shown that the Aharonov-Bohm scattering cross section diverges. This presents a problem since the range of the scattering force (Lorentz force) is finite. The cross section found by Aharonov and Bohm (AB) results whether one takes an incident wave function corresponding to particles moving in the incident direction, as was done by AB, or just takes the incident state to be a plane wave. The mechanism by which a localized force results in an infinite cross section is not clear. This is an apparent contradiction to recent proofs that electrodynamics is a local theory.

Potential energies have been computed for the ground states of HeH, He${\mathrm{H}}^{-}$, NeH, and Ne${\mathrm{H}}^{-}$ using the configuration-interaction method. The Ne${\mathrm{H}}^{-}$ potential curve is found to cross into the HeH continuum at $R=2.70\mathrm{}{a}_0$ with a threshold energy of 1.34 eV. In contrast, the Ne${\mathrm{H}}^{-}$ state is found only to merge with the NeH continuum at $R\approx 2.25a_0$ at an energy of 2.7 eV. These calculations suggest the threshold-energy collisional electron detachment for Ne${\mathrm{H}}^{-}$ can be best described by the complex potential method, while the Ne${\mathrm{H}}^{-}$ detachment mechanism is more akin to a charge transfer to the continuum process.

Inelastic quasi-projection-operator calculations of autoionization states of the three-electron ions of oxygen and silicon are carried out for states below the $n=3\mathrm{}$ manifold of the respective two-electron parent (i.e., ${\mathrm{O}}^{6+}$ and ${\mathrm{Si}}^{12+}$). Wave functions contain up to 40 configurations; calculations are completely ab initio. In the case of O VI calculated results agree with experimental results to within experimental error (∼ ±2 eV). For Si XII it is necessary to include relativistic effects; where formulas are available [states ($1s2s^{p}2p^q$) for which $p+q=2\mathrm{}$] our results are again in agreement with experiment for $2S^e,{}_{}{}^2{}_{}{}^{}P_{}^o{}_{}{}^{}$, and ${}_{}{}^2{}_{}{}^{}D_{}^e{}_{}{}^{}$ states. Our results for some of the higher states do not agree with tentative identifications proposed by Träbert et al.; alternative identifications are suggested.

A theory of collisionally aided radiative excitation (CARE) for three-level systems in the weak-field limit is presented. Cross sections for the excitation of three-level atoms by two off-resonant pulsed radiation fields in the presence of collisions with structureless perturbers are calculated. Analytic expressions for the cross sections as functions of atom-field detunings are obtained under usual classical-trajectory and rotating-wave approximations using perturbation theory for various regions of detunings. Examples for the resulting excitation line shapes are given mostly for van der Waals potentials. A dressed-atom picture of the CARE processes is discussed. Emphasis is put on an interesting effect arising from the interference between the "stepwise" and the "direct" channel of excitation. Such an interference effect manifests itself as modulations in the total excitation cross section as a function of relative interatomic speed in some cases.

Cross sections for electron-impact ionization from the ground states of four ions in the helium isoelectronic sequence have been calculated in the distorted-wave Born-exchange approximation. The results are in good agreement with available experimental data. Exchange in the scattering matrix element was found to be important in the determination of accurate cross sections. An isoelectronic plot of the scaled cross section permits ready interpolation of the nonrelativistic ionization cross section for any ion in the helium sequence in the incident electron energy range 1-5 times threshold.

The conversion of atomic helium ions into molecular ions was studied in pure helium and in helium-neon mixtures containing between 0.1 at.% and 50 at.% neon. The experiments showed that the termolecular conversion reaction, ${\mathrm{He}}^{+}+2\mathrm{}\mathrm{He}\to \mathrm{He}_2^{}{}_{}{}^{+}+\mathrm{He}$, is augmented by the four-body conversion reaction ${\mathrm{He}}^{+}+3\mathrm{}\mathrm{He}\to \mathrm{products}$, where the products could include either $\mathrm{He}_2^{}{}_{}{}^{+}$ or $\mathrm{He}_3^{}{}_{}{}^{+}$ ions. Conversion rate coefficients of (5.7 ± 0.8) × ${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$ and (2.6 ± 0.4) × ${10}^{-49\mathrm{}}$ ${\mathrm{cm}}^9$ ${\sec }^{-1\mathrm{}}$ were found for the termolecular and four-body conversion reactions, respectively. In addition, rate coefficients for the following ${\mathrm{Ne}}^{+}$ conversion reactions were measured: ${\mathrm{Ne}}^{+}+\mathrm{He}+\mathrm{He}\to {\left(\mathrm{HeNe}\right)}^{+}+\mathrm{He}$, (2.3 ± 0.1) × ${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$; ${\mathrm{Ne}}^{+}+\mathrm{He}+\mathrm{Ne}\to {\left(\mathrm{HeNe}\right)}^{+}+\mathrm{Ne}$ or $\mathrm{Ne}_2^{}{}_{}{}^{+}$ + He, (8.0 ± 0.8) × ${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$; and ${\mathrm{Ne}}^{+}+\mathrm{Ne}+\mathrm{Ne}\to \mathrm{Ne}_2^{}{}_{}{}^{+}+\mathrm{Ne}$, (5.1 ± 0.3) × ${10}^{-32\mathrm{}}$ ${\mathrm{cm}}^6$ ${\sec }^{-1\mathrm{}}$. All rate coefficients are at a gas temperature of 295 K.

The $K\alpha$ satellite spectra of F emitted from several fluorides irradiated with photons and electrons were examined in some detail. A relative intensity of the first satellite to the diagram line revealed a systematic change depending upon the Pauling bond ionicity or the covalency of fluorides used. Such a change can well be explained by substantial F $L$-shell vacancy relaxation prior to the $K$-hole filling for an x-ray emission. The probability for the $L$-vacancy rearrangement, and the $L$-shell width are discussed quantitatively.

We have applied the second Born approximation with the Coulomb Green's function to the calculation of the cross section for electron capture from a hydrogenlike ion of high atomic number $Z_T$ by a bare ion of atomic number $Z_P$ moving with a high speed $v$. With the aid of a peaking approximation, which is valid when $\frac{\hslash v}{e^2}\gg Z_P$ and $Z_T\gg Z_P$, we reduced the second Born amplitude to a one-dimensional integral which was evaluated numerically for $1s\to 1s$ capture. It was found that by using the Coulomb Green's function, rather than the free Green's function, the second Born cross section is greatly reduced (and is comparable in size to the first Born cross section) when $\frac{\hslash v}{e^2}\lesssim Z_T$.

Measurements are reported for the impact parameter ($b$) dependence of $K$-vacancy production probabilities [$P_K\mathrm{}\left(b\right)\mathrm{}$] in collisions of 54.4- and 90-MeV Ni with targets of Ni, Ge, and Rb. The shape of $P_K\mathrm{}\left(b\right)\mathrm{}$ is found to be qualitatively similar to that expected for the $2p\pi -2p\sigma$ rotational-coupling mechanism, but the maximum found at large $b$ is shifted to smaller $b$ in comparison with the predicted adiabatic maximum. This behavior is investigated systematically by applying a simple scaling law within the $2p\pi -2p\sigma$ rotational-coupling model on these and all published $P_K\mathrm{}\left(b\right)\mathrm{}$ data of nearly symmetric collision systems.

The continuum—intermediate-states approximation has been adapted for application to charge-exchange collisions between high-energy structured projectiles. A critical test of the scheme is provided by the reaction $\mathrm{H}\mathrm{}\left(1s\right)+\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}\to {\mathrm{H}}^{-}\left(1\mathrm{}{s}^2\right)+{\mathrm{H}}^{+}$; the overall agreement with the limited experimental data is encouraging.