A theoretical calculation is presented for absorption-line profiles of alkali-metal atomic spectra. The red- and violet-satellite bands caused by interactions with noble-gas perturbing atoms are discussed in detail. The statistical theory is used in calculating absorption profiles. It is shown that the pair-distribution function between atoms has an important, and temperature-dependent, influence on the red-satellite bands.

A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.

The expression for the absorption coefficient in two-photon resonance transitions is deduced under general conditions. No particular restrictions are imposed on the level system or on the frequencies and intensities of the fields. The following cases are considered: (i) a two-level system (with and without singularities) irradiated by a single wave and (ii) a three-level system irradiated by two waves. Some theoretical and experimental disagreements reported by authors of previous papers are examined and clarified by the present theory.

Beams of bare carbon nuclei were produced at 25 and 35 MeV using the Bell-Rutgers tandem Van de Graaff accelerator. Hydrogenic atoms, ${\mathrm{C}}^{5+}$, were formed by electron pickup in dilute argon gas. About 2.2% of the ${\mathrm{C}}^{5+}$ beam is found to be in the metastable $2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state. On entering a magnetic field, the metastables are Stark quenched by the motional electric field $\left(\frac{\gamma }{c}\right)\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}}$. The quench-radiation decay length was determined by counting ${\mathrm{C}}^{5+}$ Lyman-$\alpha$ quanta as a function of distance traversed in the field. Windowless electron multipliers and thin-window gas-flow proportional counters were used to detect the 33.8-Å radiation. The decay length, as a function of field and energy was used to determine the Lamb shift ($2{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}-2\mathrm{}{}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ splitting) with the aid of Bethe-Lamb quenching theory. The result is 780.1±8.0 GHz. Corrections due to beam deflection, background, $2{}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ state mixing, special relativity, and Zeeman effect are considered. Recent calculations are in agreement with the experimental result.

A new expansion of the wave function in Laguerre polynomials for hydrogenlike atoms in a magnetic field has been developed. This expansion reduces the Schrödinger equation to an infinite set of algebraic equations for which a fast, accurate, and unambiguous calculation of the bound states of a hydrogen atom in a magnetic field is possible. Four quantum numbers ($K, C, M, N$) are used to label the energy levels of the system in cylindrical coordinates. When the magnetic field is zero, the new labeling of the states is equivalent to the standard ($n, l, m$) quantum numbers obtained for the Coulomb potential in spherical coordinates. Numerical results are presented for the first 14 energy levels with principal quantum number $n=1, 2, 3$. Several energy-level crossings occur in the region $0<\mathrm{}\gamma <1\mathrm{}$, where $\gamma =\frac{\hslash {\omega }_c}{2\mathcal{R}}$ and $\mathcal{R}$ is the effective Rydberg energy.

The rotational spectrum of ${\mathrm{H}}_2$${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ in the ground vibrational state has been investigated by means of high-resolution microwave spectroscopy. We report the measurement of ten new rotational transitions in the 1.0- to 0.4-mm wavelength region. Among these are several low-$J$ lines which are of significance in the atmospheric absorption of electromagnetic radiation in the microwave region. The frequencies of newly observed transitions are (in MHz); $5_{1,5}$←$4_{2,2}$, 322 465.17; $4_{1,4}$←$3_{2,1}$, 390 607.76; $4_{2,3}$←$3_{3,0}$, 489 054.26; $6_{2,4}$←$7_{1,7}$, 517181.96; $6_{4,3}$←$5_{5,0}$, 520 137.32; $5_{3,3}$←$4_{4,0}$, 537 337.57; $1_{1,0}$←$1_{0,1}$, 547 676.44; $6_{4,2}$←$5_{5,1}$, 554 859.87; $5_{3,2}$←$4_{4,1}$, 692 079.14; and $2_{1,1}$←$2_{0,2}$, 745 320.20. Assignments were based on a weighted analysis of combined microwave and infrared data.

Level-crossing measurements have been made on the $A{}_{}{}^1{}_{}{}^{}\Pi$ state of CO by observing the fluorescence of resolved rotational features of the (1,0) and (2,0) bands of the fourth positive system in a magnetic field. Each of the rotational features studied is comprised of three unresolved lines, one each from the $P$, $Q$, and $R$ branches of the system. The field-dependent part of the fluorescence consists of a superposition of three Lorentz curves which have halfwidths proportional to $g_{J^{\prime }}{\tau }_{J^{\prime }}$, the product of the Lande $g$ factor and the lifetime of the state. The relative contributions of each line to the level-crossing signal are evaluated by simulating spectra which reproduce both the band spectrum of the lamp used for excitation and the spectrum of the fluorescence. Lifetimes of the vibrational levels are obtained by assuming that the $g$ factors can be computed from the case (a) coupling scheme for unperturbed rotational states and then finding the value of ${\tau }_{J^{\prime }}$ which produces the best fit to the data. The results from the present work are $\tau (v^{\prime }=1)=10.4\mathrm{}\pm 0.8$ nsec, $\tau (v^{\prime }=2)=8.5\mathrm{}\pm 1.0$ nsec. Data from the $J^{\prime }=22\mathrm{}$ to $J^{\prime }=25\mathrm{}$ rotational states of the $v^{\prime }=1\mathrm{}$ level clearly show the effects of the perturbation which couples the $a^{\prime }{}_{}{}^3{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$ and the $A{}_{}{}^1{}_{}{}^{}\Pi$ states. The averaged result for the matrix element which couples the two states is found to be $\delta =2.7\mathrm{}\pm 0.9$ ${\mathrm{cm}}^{-1\mathrm{}}$.

A semiempirical model for electrons in atoms, which improves upon the Thomas-Fermi model in two ways, is proposed. It gives the correct wave-mechanical electron density near the nucleus and an exponentially decreasing density (as required by Hartree-Fock calculations) at large distances from the nucleus. We have calculated the diamagnetic susceptibility, polarizability, and potential at the nucleus for various $Z$ values and these results have been compared with available experimental data. The agreement between the two sets of results is found to be more satisfactory than that obtained by earlier statistical or semistatistical models. The model is also extended to positive ions. The calculated values of second-ionization energies for atoms with large $Z$ are found to be in very good agreement with experimental data.

An exact analytic calculation is presented for the cross section of the nonrelativistic Compton-type inelastic scattering of photons by electrons bound in the ground state of a hydrogenlike atom. The matrix element of the process was taken to be of the Kramers-Heisenberg-Waller form. It was integrated by the Coulomb-Green's-function method, developed previously by the author in connection with Rayleigh scattering. This is based on replacing the sum over intermediate states by the Green's function which is expressed in terms of the integral representation in momentum space given by Schwinger. The final continuum-state wave function was also described by an integral representation. Thus the evaluation of the matrix element requires the carrying out of momentum-space integrations, followed by two contour integrations. Its final form was expressed in terms of hypergeometric functions of four variables of Lauricella's type $F_D$. At small photon energies, where the dipole approximation is valid, the result simplifies considerably. The low-energy end of the scattered-photon spectrum is considered in detail in connection with the infrared divergence problem. The shape of the spectrum is discussed and a comparison with previous results is given.

The dipole approximation of the nonrelativistic cross section for Compton scattering by electrons bound in the ground state of a hydrogenlike atom, obtained by the present author, is computed and discussed. In this approximation the cross-section differential with respect to the angles and energy of the scattered photon is proportional to $C_1+C_2{cos}^2\theta$, where $\theta$ is the scattering angle of the photon. The coefficients $C_1$, $C_2$ are combinations of Appell functions $F_1$, depending on the atomic number $Z$ and the energies of the initial and final photons ${\kappa }_1$, ${\kappa }_2$ by means of the dimensionless variables $k_i=\frac{{\kappa }_i}{Z^2\mathcal{R}}$, $i=1, 2$, where $\mathcal{R}$ is the rydberg. In order to compute the Appell functions, these were first continued analytically and expressed in terms of other hypergeometric functions of two variables, which under our circumstances admit convergent series expansions. These were then summed numerically. The incident photon energies considered lie in the interval $1.05\le k_1\le 20$. For each value $k_1$ the coefficients $C_1$ and $C_2$ were computed for a number of values of $k_2$ ($0\le k_2\le k_1-1\mathrm{}$). Special attention was given to the end points $k_2=0\mathrm{}$ and $k_2=k_1$. $C_1$ and $C_2$ turn out to be monotonically decreasing functions of $k_2$ presenting the infrared-divergent behavior $\frac{1}{k_2}$ for $k_2\to 0$. The limitations of the result due to retardation corrections are considered.

A dielectric model of diatomic molecules has been used to calculate the ground-state force constant and the dipole moment. An attempt is made to use atomic parameters only, but the calculations show that this is not possible with the model. Good agreement with experiment is obtained when one molecular parameter is adjusted, e.g., the position of the bond charge.

The $c$-state eigenfunctions of the Schrödinger equation for an electron in a Hulthén potential are shown to form a basis for an irreducible unitary representation of SO(2, 1). The properties of this SO(2, 1) are then applied to a study of the difference between the Hulthén potential and a screened Coulomb potential. Results compare well with those obtained by Lam and Varshni using a direct integration.

The first-order (FO) wave functions for the second period of atoms have been analyzed in terms of natural spin orbitals (NSO). The FO function is constructed to account for the same polarization effects as are accounted for by the unrestricted Hartree-Fock method (UHF), but the FO function has the correct symmetry. The strongly occupied NSO and the UHF orbitals contain the same kind of symmetry admixtures. The agreement between the first NSO determinant and the UHF wave function is bad for the contact term but good for the other expectation values that contribute to hyperfine structure. The FO function accounts also for internal and semi-internal correlation effects. The direct contributions through pair correlations (PC) from the "NSO sea" have been calculated. They agree for B with the values calculated from the 187-term function in our earlier paper. The PC correction to the contact term is of the same magnitude as the contact term itself. Furthermore, there is a large PC correction to the electric field gradient at the nucleus for B and C connected with the internal $s^2\to p^2$ correlation. The remaining PC effects are rather small but lead almost always to a decrease of the $〈{{\mathcal{r}}_x}^{-3\mathrm{}}〉$ expectation values. Since the expected increase of the $〈{{\mathcal{r}}_x}^{-3\mathrm{}}〉$ expectation values due to all-external correlations is not taken into account by the FO function, this function yields, at least for B and C, too small $〈{{\mathcal{r}}_x}^{-3\mathrm{}}〉$ values. The FO function is also missing important self-consistency effects. The quadrupole moment of the ${\mathrm{C}}^{11}$ nucleus is estimated to be $\pm 0.0333b$ on the basis of our analysis and experimental results.

A number of properties of the bound eigenstates of an electron in an exponential cosine screened Coulomb potential, $V\left(\mathcal{r}\right)=-\left(\frac{e^2}{\kappa \mathcal{r}}\right)e^{-qr}cos\left(q\mathcal{r}\right)$, are studied. Perturbation and variation methods are used to calculate the eigenvalues. Detailed results are presented for the first four $s$ states. For each state there is a critical value of the screening parameter ${\delta }_c$ above which no bound states with negative energy exist. The value of ${\delta }_c$ for the ground state is obtained from a two-parameter variational calculation. The total number of different energy levels is finite for any value of the screening parameter $\delta$ greater than zero, and is found to be approximately linearly dependent on $\frac{1}{{\delta }_c}$, The square of the number of bound $s$ states is also shown to be linear with $\frac{1}{{\delta }_c}$, Positive-energy states are also discussed.

A perturbation calculation, based on restricted Hartree-Fock approximation, is carried out to second order in the residual interaction for the electric field gradient at the nucleus of Li $2{}_{}{}^2{}_{}{}^{}P$. It is shown that the second-order wave function is not required for the calculation of the second-order correction. We find that the second-order correction is nearly equal and opposite to the first-order (Sternheimer) correction.

Electron-bremsstrahlung cross-section values differential in photon energy and angle are given for a bombarding energy of 0.2 MeV. Measurements were made for photon energies from 0.02 to 0.06 MeV with a Ge(Li) spectrometer and from 0.06 to 0.2 MeV with a NaI-crystal-scintillation spectrometer for photon emission angles of 10°, 20°, 30°, 45°, and 60°. Targets of Al, Cu, and Au were used. Comparisons are made to the Born-approximation values.

The Auger group rates and fluorescence yields are presented for $Z=35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 83, \mathrm{and} 85$ for a vacancy in either the $3p$ shell or the $3d$ shell. The present calculations have been performed with the nonrelativistic Hartree-Fock-Slater model with the exchange approximation of Herman, Van Dyke, and Ortenburger. The theoretical fluoresence yields can be used in converting the experimental $M$-shell x-ray production cross sections by protons and $\alpha$ particles to the cross section for $M$-shell vacancy production.

Absolute cross sections have been measured for the reaction $\mathrm{H}\mathrm{}\left(2s\right)+T\to {\mathrm{H}}^{+}+T+e$, where $T$ represents ${\mathrm{N}}_2$, Ar, and He. The measurements were carried out for impact energies in the 20-120-keV range. The experimental results for impact on He and ${\mathrm{N}}_2$ are in general agreement with calculations based on the method of Bates and Walker. The calculation for impact on Ar overestimates the experimental stripping at the lowest energies but approaches satisfactory agreement at the highest energies. A few cross sections are presented for electron capture into the stable ${\mathrm{H}}^{-}$ state for $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ impact on these gases. The capture cross sections are small and are about 7% of the total capture cross sections by protons having the same energy.

A study has been made of ${\mathrm{H}}_2^{+}$ dissociation by impact on targets of He, Ar, ${\mathrm{H}}_2$, and ${\mathrm{N}}_2$. Cross sections were measured for the angular distributions of metastable hydrogen, protons, and neutral hydrogen atoms resulting from dissociation. Projectile energies are in the range 4-12 keV; the angular range of the measurements extended from 0.5° to 5.0°. The angular distributions of metastables are consistent with their formation through excitation of the ${\mathrm{H}}_2^{+}$ projectile into the $2s{\sigma }_g$ and $3p{\sigma }_u$ repulsive states of ${\mathrm{H}}_2^{+}$. In all cases the dissociation cross section appears to be strongly peaked towards small angles between the internuclear axis of the molecule and the direction of the ${\mathrm{H}}_2^{+}$ projectile; in the case of $\mathrm{H}\mathrm{}\left(2s\right)\mathrm{}$ formed by dissociation on He, the cross section appears to vary as approximately the square of the cosine of that angle. Angular distributions vary quite markedly from one target to another.

Molecular stopping cross sections ${\epsilon }_{\alpha }$ of $\alpha$ particles of energy 0.3-2.0 MeV have been measured (probable error 0.9-2.1%) in gaseous (or vapor) C${\mathrm{F}}_4$, ${\mathrm{C}}_2$${\mathrm{F}}_6$, ${\mathrm{C}}_3$${\mathrm{F}}_8$, ${\mathrm{C}}_4$${\mathrm{F}}_8$, C${\mathrm{Cl}}_4$, CCl${\mathrm{F}}_3$, C${\mathrm{Cl}}_2$${\mathrm{F}}_2$, CH${\mathrm{Cl}}_2$F, CBr${\mathrm{F}}_3$, ${\mathrm{C}}_2$${\mathrm{Br}}_2$${\mathrm{F}}_4$, ${\mathrm{C}}_2$${\mathrm{H}}_3$Br, ${\mathrm{C}}_2$${\mathrm{H}}_5$Br, and ${\mathrm{C}}_2$${\mathrm{H}}_5$I. Atomic stopping cross sections for F, Cl, Br, and I have been calculated (probable error 2.3-4.4%) by application of the Bragg additive rule. It is found that carbon $\epsilon \left(\mathrm{C}\right)$ calculated from gaseous fluorocarbons agrees with previous measurements by Chu and Powers of $\epsilon \left(\mathrm{C}\right)$ for carbon in solid form but disagrees with $\epsilon \left(\mathrm{C}\right)$ calculated from gaseous hydrocarbons by Bourland, Chu, and Powers. Consistent results are found by using either of two alternatives: (i) Use hydrocarbon gas $\epsilon \left(\mathrm{C}\right)$ and experimental ${\epsilon }_{\mathrm{expt}}$ (${\mathrm{H}}_2$) in hydrogen-enriched C-H-Br or C-H-I compounds, and use solid carbon $\epsilon \left(\mathrm{C}\right)$ everywhere else; or (ii) use solid carbon $\epsilon \left(\mathrm{C}\right)$ in all compounds, but use an ${\overline{\epsilon }}^{\prime }$ (H) which disagrees by as much as 21% from $\frac{1}{2}{\epsilon }_{\mathrm{expt}}$ (${\mathrm{H}}_2$). A plot of ${\epsilon }_{\alpha }$ vs the atomic number $Z_2$ of the stopping medium shows that the halogen measurements at $Z_2=9, 17, 35, \mathrm{and} 53$ agree well with the existing theory and other experimental measurements for neighboring $Z_2$ values.