A model which describes the competition between chain melting and orientational ordering in a monomolecular layer of long-chain amphiphilic molecules is studied. This model is analogous to the Berker-Cardy-Nelson-Scalapino model for phase transitions in films of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$-${}_{}{}^4{}_{}{}^{}\mathrm{He}$ mixtures. Their Midgal-Kadanoff renormalization-group approach is applied to the present problem. It reveals two phase transitions. A first-order one, associated with the melting of hydrophobic chains and a Kosterlitz-Thouless-type transition linked to the existence of topological orientational order of the chains in the high-molecular-area region. Isotherms and coexistence curves in the region of the liquid-expanded liquid-condensed transition are calculated. The disagreement with experimental results suggests that the model does not adequately describe the phase transition. This is in contradiction with a previous suggestion based on mean-field considerations.

$X\alpha$ calculations (with exchange parameter $\alpha =0.7\mathrm{}$) are presented for ${\mathrm{Cr}}_2$ in which the constraint of inversion symmetry on the one-electron orbitals is avoided. The ground state is antiferromagnetic, ${}_{}{}^1{}_{}{}^{}\Sigma _{}^{+}{}_{}{}^{}$, with equilibrium separation 2.75 Å, vibrational frequency 110 ${\mathrm{cm}}^{-1\mathrm{}}$, and dissociation energy 1.0 eV. This is in qualitative agreement with the generalized-valence-bond calculation of Goodgame and Goddard.

Abraham, DeFacio, and Moses and Brownstein have given examples of pairs of potentials, which support no point eigenvalues, but which have the same scattering operator. These potentials all have δ-function contributions to them. In the present paper, a pair of potentials is given, neither of which has a $\delta$-function contribution, such that they both have the same simple scattering operator. Like the earlier examples, the new potentials violate the range condition of Faddeev and Deift and Trubowitz used in the proof of the one-to-one correspondence of potentials to scattering operators. Thus the present example is an addition to the list of long-range potentials with simple eigenfunctions and scattering operators.

We report the measurement of the depopulation cross sections of the $\mathrm{Na} \mathrm{ns}$ states from $n=5\mathrm{} \mathrm{to} 11$ by ${\mathrm{H}}_2$ and CO, using a time- and wavelength-resolved fluorescence approach. The cross sections rise to a plateau value of 60 and 160 Å for ${\mathrm{H}}_2$ and CO, respectively. The increased size of the cross sections relative to those for the rare gases is attributed to energy transfer to molecular vibration.

Continuum x rays induced by bombardments of a Be target with 20.14-MeV/amu protons and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ ions have been measured with a Si(Li) detector in the direction of 90° with respect to the incident beam. Differences in the x-ray-production cross sections multiplied by the x-ray energy $\hslash \omega \left\{\hslash \omega \right[\frac{{\sigma }_h\left(\hslash \omega \right)}{4-{\sigma }_p\left(\hslash \omega \right)}\left]\right\}$ and ratio of the cross sections $R\left(\hslash \omega \right) \left[\equiv \frac{{\sigma }_h\left(\hslash \omega \right)}{4{\sigma }_p\left(\hslash \omega \right)}\right]$ for the proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$-ion impact, where ${\sigma }_h\left(\hslash \omega \right)$ and ${\sigma }_p\left(\hslash \omega \right)$ are the x-ray-production cross sections for proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$-ion impact, respectively, were obtained as a function of the x-ray energy. Both the difference and the ratio show peaks in the region where the x-ray energy is equal to the relative kinetic energy between the projectile and the inner-shell electron to be scattered by the projectile. From the comparison with a theory of quasi-free-electron bremsstrahlung based on the impulse approximation, it is found that this peak corresponds to the maximum of the velocity-distribution function of the inner-shell electron. Furthermore, the contribution of the radiative electron-capture process in the case of proton and ${}_{}{}^3{}_{}{}^{}\mathrm{He}_{}^{2+}{}_{}{}^{}$ impact is clearly found.

In this Brief Report we extend the work on the frame-transformation method to give an analytic form for the relative intensities of rotational transitions in photodetachment and photoionization. The specific case of photoabsorption by a ${}_{}{}^1{}_{}{}^{}\Sigma$ species, resulting in a ${}_{}{}^2{}_{}{}^{}\Pi$ species and an $s$ electron, is treated analytically. The results are in good agreement with both threshold photodetachment cross sections and photoelectron spectra.

The velocity distribution of a monatomic gas in a very strong magnetic field (e.g., ${10}^7$ T) is computed two ways: with classical statistical mechanics and with rarified-gas kinetic theory. The same non-Maxwellian distribution is found in both cases. This anomaly arises from the saturation of the electrical polarization of the atoms by the enormous electric fields which they see when moving.

We show that, in the presence of an ion-acoustic turbulence, the electron velocity distribution function deforms irreversibly to a flat-topped shape in the central region and a nonthermal one in the tail region. The runaway part which behaves as $v^{-m}$, with $m=\frac{9}{2}$, is created with a completely specified production rate and is given by the turbulent collision frequency.

The asymptotic time behavior of the velocity autocorrelation function has been investigated by means of molecular dynamics with and without the presence of three-body forces, respectively. It turned out that the long-time tail is strongly influenced by three-body forces. The famous $t^{-\frac{3}{2}}$ law has been observed in the calculation with the presence of three-body forces.

The recently proposed functional of Takatsuka and McKoy, derived from the Schwinger-type Newton functional, is shown to follow from the usual Hulthén-Kohn variational principle. A generalization of their method becomes obvious in this approach and its better convergence is demonstrated on a simple example.

About 1% or more of iron was introduced into a hydrogen-filled theta pinch by a guninjection method. The Fe x density in the plasma was determined from the measured intensity of the Fe x forbidden (coronal) line at 6374.5 Å. Electron collisional excitation rate coefficients for Fe x were obtained from measurements of Fe x vacuum-ultraviolet line intensities, electron density and temperature, and Fe x density. The experimental rate coefficients are compared with theoretical results.

The exact solution of the Fano model, including both radiative recombination to the initial state (recycling) and off-diagonal phase-jitter relaxation, is obtained by two different methods. We derive a simple substitution rule stating that, by replacing $\pm i{\omega }_L\to \pm i{\omega }_L+{\gamma }_T$, the phase-jitter effects are included. The time dependence of the solution has a convolution form. The results for the electron spectrum exhibit an increasing elastic-peak line narrowing the faster the spontaneous decay becomes. For very fast spontaneous decay, the elastic linewidth saturates to ${\gamma }_T$. The relevant thresholds are discussed and demonstrated.

A new technique is proposed for the measurement of high-$Z$ Lamb shifts using ions created by a hot tokamak plasma. By using the laser resonance technique to measure the $2S_{\frac{1}{2}}2P_{\frac{1}{2} or \frac{3}{2}}$ energy splittings, it is possible to obtain a fractional accuracy of ${10}^{-4\mathrm{}}$${-10\mathrm{}}^{-3\mathrm{}}$. This would be a considerable improvement on existing measurements and would allow a clear test of current calculations.

We report the first measurement of the specific mass shift of the $5{}_{}{}^3{}_{}{}^{}P$ level between ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ and ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. A value $\Delta {\nu }_s=-1113.1\mathrm{}\pm 5.0$ MHz, twenty times more accurate than the best known theoretical value, was obtained by ultraviolet-infrared double-resonance laser spectroscopy of the $2{}_{}{}^3{}_{}{}^{}S-5\mathrm{}{}_{}{}^3{}_{}{}^{}P-13\mathrm{}{}_{}{}^{1,3}{}_{}{}^{}D$ transition.

A theory of spontaneous emission is presented which does not quantize the radiation field. By allowing the atomic electron's radiation-reaction field to act in the equation of motion for the atomic density operator, the theory accounts for sponteneous emission without leaving the Hilbert space of the atom. The theory is quite simple and leads to exactly the same relaxation terms in the density-operator equation of motion as those predicted by the quantum theory of radiation.

The influence of noise on laser operation is considered for swept-gain lasers and laser amplifiers in which the velocity of the gain medium must be decreased relative to the velocity of light in order to achieve lasing action. The noise is introduced through the tipping-angle approximation, which leads to a simple, if perhaps unrealistic, formulation of the problem. Such a laser is tuned by desynchronizing the gain medium with the optical pulse, which is the procedure used in the Stanford free-electron laser (FEL). In so doing, the FEL tunes over regions of true lasing (gain > loss), and over regions where the output is sustained by amplified spontaneous emission (noise driven). The power in the noise-driven regime is not necessarily small compared to the power in the lasing regime. These regimes are identified, the fluctuations are computed, and the connection with the FEL is discussed.

The Dirac equation for the hydrogen atom is solved exactly in momentum space chosen to be properly conjugate to the spherical polar variables of position space. The coupled first-order differential equations are readily solved to give functions which involve a sum over poles along the imaginary axis at $\frac{\mathrm{iZ}{p}_0}{N}$, where $N$ is the apparent principal quantum number.

A perturbation study of singly excited $S$, $P$, and $D$ states of two-electron atoms has been made. Perturbation expansion coefficients for the nonrelativistic energies are computed and estimates of the relativistic corrections to low orders in $Z$ are also obtained. A simple one-electron Lamb-shift correction is then combined with these results to yield theoretical transition energies in excellent agreement with experimental data for HeI through FeXXV.

The frequency dependence of the dipole electric polarizability and electric shielding tensors of hydrogen and fluorine nuclei in the HF molecule has been investigated by means of the lower approximations to the equation-of-motion method—namely, the single-transition approximation (STA), the Tamm-Dancoff approximation (TDA), and the random-phase approximation (RPA)—within the framework of dipole length, velocity, acceleration, and mixed formalisms. Some relations are proved, concerning the relative magnitude of TDA and RPA polarizabilities and Thomas-Reich-Kuhn sum rules in the various formalisms. An interdependence between dynamic polarizabilities and nuclear shielding factors has been found. Good agreement with experimental static shielding factors has been obtained in the RPA calculation.