The general form for the moments of the Van Hove incoherent scattering function is derived for a simple classical liquid with velocity-independent interatomic forces. With the additional assumption of additive central forces, explicit expressions are obtained for the coefficients which determine the asymptotic behavior of the moments at large momentum transfer $\kappa$. This enables one to obtain an exact asymptotic expansion of the scattering function in inverse powers of $\kappa$. The theory is applied in detail to the Lennard-Jones liquid at the triple point and to the hard-sphere fluid at arbitrary density. The results for these two cases are qualitatively different as a consequence of the fact that the atomic velocities are continuous functions of time in the former case and discontinuous in the latter. For example, the leading correction to the impulse approximation due to final-state interactions is proportional to ${\kappa }^{-2\mathrm{}}$ for the Lennard-Jones potential and to ${\kappa }^{-1\mathrm{}}$ for hard spheres. With decreasing $\kappa$ the scattering function changes from the Gaussian shape, characteristic of the impulse approximation at large $\kappa$, to the Lorentzian shape characteristic of simple diffusion at small $\kappa$. This change occurs in the hardsphere fluid when $\kappa l\sim 1$, where $l$ is the mean free path (including the Enskog factor).

The theory of Lekner for the scattering of excess electrons in fluid argon has been applied for densities lower than that at the triple point. We point out some discrepancies between the theory and recent experimental electron-mobility data in fluid argon.

The temperature-dependent correction to the Lamb shift of a single-electron atom exposed to black-body radiation at temperature $T$ is considered. At room temperatures, the correction for $Z>\mathrm{}1\mathrm{}$ is dominated by a shift, not considered before, of the $2s_{\frac{1}{2}}$ level, involving $2p_{\frac{3}{2}}$ as an intermediate state, and is given by $\frac{\pi {\alpha }^3{Z}^2{\mathrm{}\left(\mathrm{kT}\right)\mathrm{}}^2}{8m}$. This competes with another shift $\approx \frac{x{\mathrm{}\left(\mathrm{kT}\right)\mathrm{}}^4}{Z^4{\left(\alpha m\right)}^3}$ discussed by Walsh, where $x$ is a purely numerical but remarkably large coefficient of order 300.

The inclusion of dipole polarizability of the core for argon is shown to substantially improve the agreement between the theoretical and experimental photoionization cross sections for the ground-state configuration.

The recent specific-heat data of Bretz and Dash have been interpreted as evidence of two-dimensional inhomogeneous remnant Bose condensation in ${\mathrm{He}}^4$ submonolayer films. For specific heats and for adsorption isotherms we suggest quantitative relationships which would verify this point of view.

The energy dependence at threshold for the escape of two electrons with total angular momentum $L=1\mathrm{}$ is shown to be the same as that found for $L=0\mathrm{}$ by Rau, and classically by Wannier, for processes that leave the same residual ion. It is suggested that this threshold law will also hold for $L>\mathrm{}1\mathrm{}$.

A fully coupled Hartree-Fock variational method is used to calculate the hyperpolarizability of the He, Be, Ne, and Ar atoms. In these calculations the hyperpolarizability is inferred from the electric moment induced in the atoms for various finite values of the external static electric field. A formulation of the problem and the justification for the methods used is given. The nonlinear parameters of all the wave functions used in these calculations are presented along with a convergence test for the wave function of the helium atom. The nuclear dipole shielding factor, polarizability, and hyperpolarizability are tabulated for these atoms and the results are discussed and compared with previous theoretical and experimental results.

The equations of the coupled-pair many-electron theory (CPMET) are extended to incorporate the effect of both unlinked and linked triexcited clusters. The minimal basis correlation energy of the B${\mathrm{H}}_3$ molecule in the ground state is calculated using the ordinary as well as extended CPMET in various degrees of approximation, and the relative importance of linked and unlinked triexcited clusters is studied. The results afford an unambiguous conclusion for closed-shell systems that, in contrast to the situation with tetraexcited states, unlinked triexcited clusters are negligible relative to the linked ones. It is shown that the extended CPMET reproduces the full configuration-interaction results to a very high degree of accuracy.

The Cm $K$ x-ray spectrum from the decay of ${}_{}{}^{249}{}_{}{}^{}\mathrm{Cf}$ and the Cm $L$ x-ray, internal conversion, and $\gamma$ray spectra associated with the 42.9-keV $E2\mathrm{}$ transition in the $\alpha$ decay of ${}_{}{}^{250}{}_{}{}^{}\mathrm{Cf}$ were measured at high resolution. From these data accurate values for the binding energies of $K$, $L_1$, $L_2$, $L_3$, $M_1$, $M_2$, $M_3$, $M_4$, $M_5$, $N_1$, $N_2$, $N_3$, $N_4$, $N_5$, $O_2$, $O_3$, $O_4$, and $P_3$ electrons in Cm were obtained. Values were derived also for the $L$-subshell fluorescence yields in Cm: ${\omega }_1=0.28\mathrm{}\pm 0.06$. ${\omega }_2=0.55\mathrm{}\pm 0.02$, and ${\omega }_3=0.63\mathrm{}\pm 0.02$.

The Stark shift of the atomic-hydrogen hyperfine separation has been measured in a hydrogen maser, designed to study in particular the dependence of the shift on the angle $\theta$ between the external electric and magnetic fields. A method of designing shielded solenoids to produce arbitrary magnetic fields is presented. The result of the experiment is $\delta {\nu }_{\mathrm{stark}}=(-7.1\mathrm{}\pm 1.1)\times {10}^{-5\mathrm{}}{E}^2 (\theta =0)$ using electrostatic units for the electric field $E$, and $\frac{\delta {\nu }_{\mathrm{stark}}(\theta =0)-\delta {\nu }_{\mathrm{stark}}(\theta =\frac{\pi }{2})}{\delta {\nu }_{\mathrm{stark}}(\theta =0)}=-1\%\pm 10\%.$

We have measured the transition rate of the normally metastable helium $2{}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ state in the presence of a uniform electric field by observing the attenuation of a metastable beam of helium passing between parallel electric field plates. This attenuation, when combined with our measurement of the velocity distribution of the beam, yields a transition rate of $(0.926\mathrm{}\pm 0.020)F^2$ ${\sec }^{-1\mathrm{}}$, where $F$ is the field strength in kV/cm. This agrees well with our calculated value of $(0.920\mathrm{}\pm 0.030)F^2$ ${\sec }^{-1\mathrm{}}$ which is derived from a sum of oscillator strengths published by various workers.

The magnetic moment of the proton has been measured by observing simultaneously an electronic and a nuclear magnetic transition in atomic hydrogen. Observations were made with a hydrogen maser operating in a 3500-G field. A theory is presented for the transient response of a three-level system under conditions of double resonance including effects of cavity pulling, spin-exchange collisions, and frequency shifts due to motional field narrowing. The electron-proton $g$-factor ratio in hydrogen is found to be $\frac{g_j\left(\mathrm{H}\right)}{g_p\left(\mathrm{H}\right)}=\frac{{\mu }_j\left(\mathrm{H}\right)}{{\mu }_p\left(\mathrm{H}\right)}=-658.210\mathrm{}706\left(6\right)\mathrm{}$. This leads to a value of the proton moment in Bohr magnetons of $\frac{{\mu }_p}{{\mu }_B}=1.521\mathrm{}032181\left(15\right)\mathrm{}\times {10}^{-3\mathrm{}}$.

A new approach is suggested for dealing with the many-body aspects of resonance broadening of spectral lines in gases. A Liouville-space formalism is used in which the absorption by $N$ identical molecules undergoing resonance-exchange collisions is described by an $N$-dimensional projection operator in Liouville space. In the impact approximation, under conditions in which the Doppler shift of resonance frequencies can be neglected, it is shown that the effect of resonance collisions is to modify the linewidth expression obtained by ordinary foreign-gas-type theories. The shape of isolated lines remains, however, Lorentzian. Only a combined effect of Doppler and collision broadening causes appreciable deviations from the Lorentzian shape near the line center, but these deviations are not peculiar to resonance broadening.

Multiplet theory for a single configuration for symmetric wave functions is developed and applied to the $s^2$, $\mathrm{sp}$, $p^2$, $s^3$, $s^{2}p$, $s{p}^2$, $p^3$, $s^4$, $s^{3}p$, $s^2{p}^2$, $s{p}^3$, and $p^4$ configurations. Orthonormal eigenfunctions of $L^2$ and $S^2$ are given for these configurations in terms of symmetric products of one-particle functions with $\Sigma m_l=\Sigma m_s=0\mathrm{}$. With these eigenfunctions, the deuteron structure of molecules with up to four deuterons can be studied. The multiplets of the deuterides are compared with the multiplets of the hydrides. The difference between the multiplet structures imply that ${\mathrm{D}}_2$O can make three deuteronic electric dipole transitions where ${\mathrm{H}}_2$O can make only one protonic electric dipole transition; N${\mathrm{D}}_3$ can make three deuteronic electric dipole transitions and two deuteronic electric quadrupole transitions where N${\mathrm{H}}_3$ can make only one protonic electric dipole transition; and C${\mathrm{D}}_4$ can make three deuteronic electric dipole transitions and two deuteronic electric quadrupole transitions where C${\mathrm{H}}_4$ has no allowed protonic transitions.

An experiment is described in which the two transitions $\alpha a(m_J=+\frac{1}{2}\to +\frac{3}{2})$ and $\alpha b(m_J=+\frac{1}{2}\to +\frac{1}{2})$ were employed to measure the interval ${(\Delta E-\mathcal{S})}_{\mathrm{H}}$. Hydrogen atoms in the metastable state are produced by bombarding molecular hydrogen with electrons within a waveguide in a magnetic field. An rf electric field in the guide induces electric dipole transitions from this state to the $2P$ states, and the 1216-Å radiation produced in the decay of the $2P$ state is detected. The frequency of the rf field is held constant, and the magnetic sublevels of the states involved are tuned by varying the magnetic field. When the resonance condition is met, the intensity of 1216-Å light increases. Precision measurements of signal versus magnetic field are fitted by least squares to a line-shape formula described in detail. Potential sources of systematic error and experimental searches for them are described. Small shifts are detected upon changing the electron-beam current and gas pressure, and an extrapolation is made to remove them. The weighted average of results from the two transitions is ${(\Delta E-\mathcal{S})}_{\mathrm{H}}=9911.377\mathrm{}\left(26\right)\mathrm{}$ MHz. A comparison is made with other recent experiments which have measured the same interval.

Experiments in collisional transfer of excitation, as well as theoretical considerations, have shown that singlet-triplet mixing occurs for $\mathrm{nF}$ states of helium. In this work the helium fine structure has been calculated using polarized orbitals to determine the amount of mixing and its dependence on the state ($\mathrm{nl}$) of the excited electron, and on the polarization of the orbital of the inner electron. Results are presented for $n=3\mathrm{}-10$ and $l=2\mathrm{}(n-1\mathrm{})\mathrm{}$. All $P$ states gave poor results because of a large exchange effect involving the polarization term in the wave function. However, the $3{}_{}{}^3{}_{}{}^{}D$ and $4{}_{}{}^3{}_{}{}^{}D$ levels showed improved agreement with experiment for the fine structure. The singlet-triplet mixing is essentially zero for $l=2\mathrm{}$, is significant for $l=3\mathrm{}$, and is virtually complete for $l\ge 4$. It is also found that the mixing decreases slightly with increasing $n$.