We obtain a uniformly valid leading-order approximation for the two-body correlation function of a gas which is not in thermodynamic equilibrium. We demonstrate that the correlation length is finite, of the order of the mean-free path, even without the inclusion of three-body collisions. The new result, which is in sharp contrast to previous calculations, is obtained by correcting an inconsistency in Bogoliubov's expansion method.

Compounds containing a first-row atom are shown to have an important additional contribution to the nonlinear optical susceptibility $d_{\mathrm{ijk}}$. Inclusion of this effect explains the anomalous sign of $d_{33}$ for ZnO and leads to excellent agreement with experiment.

The phase transition in the Ising model has been studied as a function of an applied transverse field, by Green's function and series-expansion methods. The critical indices are probably independent of the applied field except at $T=0\mathrm{}$ where they appear to be related to those of the Ising model in one higher dimension.

Transient absorption spectra produced by pulsed electron excitation at low temperature have been identified as due to transitions originating in the lowest triplet states of the self-trapped exciton. The current model, comprising an electron plus a self-trapped hole, is shown to provide electronic configurations for the higher excited states which give a good account of the principal features of the spectra.

The partition function for a spin ½ in a magnetic field coupled to a set of bosons is shown to be exactly equal to that of a one-dimensional gas and also, in a delicate limit, to that of a one-dimensional Ising model. Both of these are peculiar in that they must provide a free energy which is an intensive quantity. For special values of the parameters in the Hamiltonian, the partition function is equal to that first derived by Anderson and Yuval, and by Hamann, for the Kondo problem.

Isospin forbidden resonances ($\Delta T=1\mathrm{}$) have been observed in the reaction ${}_{}{}^{93}{}_{}{}^{}\mathrm{Nb}(p,\alpha ){}_{}{}^{90}{}_{}{}^{}\mathrm{Zr}$. Angular distributions to the $0^{+}$ ground state measured at the $4^{+}$ (59-keV) and $2^{+}$ (334-keV) analog resonances indicate that the $2^{+}$ isospin analog state is formed via a pure $d_{\frac{5}{2}}$ capture whereas the $4^{+}$ isospin analog state is formed by a coherent admixture of $d_{\frac{5}{2}}$, $s_{\frac{1}{2}}$, and $d_{\frac{3}{2}}$ components.

The excitation function at 90° c.m. has been measured between 7.5 and 27.5 MeV c.m. The prominent gross structure observed in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$- ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ is not seen in the present case, and the absolute cross section falls to much lower values at high energies. The results of the comparison of the two systems are discussed in terms of angular momentum restrictions on configurations directly coupled to the elastic channel.

The threshold singularities of internal bremsstrahlung spectrum in the pion-charge-exchange reaction are used for the identification of the reaction mechanism.

Lifetimes of low-lying levels in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$ have been investigated using the reaction ${}_{}{}^{54}{}_{}{}^{}\mathrm{Fe}(\alpha ,n){}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$ and the Doppler-shift attenuation method. The lifetimes are not in agreement with single-particle predictions and, together with the presence of new low-lying levels in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Ni}$, confirm the presence of core excitation of ${}_{}{}^{56}{}_{}{}^{}\mathrm{Ni}$.

In magnetic fields $B\sim {10}^{12}$ G, characteristic of neutron-star models for pulsars, the ionization energy of atoms is a few hundred electron volts and is a slowly increasing function of $Z$. This may greatly affect the nuclear abundances of matter lifted off the stellar surface by electric fields.

Using a wire-spark-chamber deuteron spectrometer, we have measured the missing-mass (MM) spectrum up to ∼ 1.5 GeV in the reaction $\mathrm{pp}\to d+\mathrm{MM}$ for deutrons produced at 0° in the laboratory and incident momenta of 3.8, 4.5, and 6.3 $\frac{\mathrm{GeV}}{c}$. Production cross sections for $\pi$ and $\rho$ are reported. Evidence of ${\pi }_N\mathrm{}\left(980\right)\mathrm{}$ production with mass 975 ± 6 MeV and width ${60}_{-10\mathrm{}}^{+16\mathrm{}}$ MeV is presented. No other statistically significant enhancements were found.

The branching ratio for the process $K^{+}\to {\pi }^{+}+\gamma +\gamma$ is shown by a counter-spark-chamber experiment to be less than 4 × ${10}^{-5\mathrm{}}$ of all decay modes, assuming a phase-space pion energy spectrum. A limit of 4 × ${10}^{-6\mathrm{}}$ is established for the process $K^{+}\to {\pi }^{+}+\gamma$. The apparatus was sensitive to pions in the kinetic energy range 117-127 MeV.

We have measured the nuclear capture rate of negative muons by deuterons in $\mu d$ atoms. The experiment was performed by stopping negative muons in a target of ultrapure gaseous hydrogen at 7.6 atm with 5.2% deuterium and looking at the outgoing neutrons. The result is ${\Lambda }_{\mathrm{expt}}=451\mathrm{}\pm 70$ ${\sec }^{-1\mathrm{}}$.

The photoproduction of ${\rho }^0$ mesons from hydrogen and carbon has been measured at 3.5 GeV using polarized photons from coherent bremsstrahlung produced by 10-GeV electrons on a diamond crystal. Asymmetry ratios for carbon and hydrogen are measured and are consistent with the mainly diffractive nature of ${\rho }^0$ photoproduction. A small nondiffractive component is suggested in the case of hydrogen.

It is suggested that the sequence $\rho ,A_2,R,S,\cdots$ is a sequence of multipole resonances. Thus, the $A_2$ is a doubled resonance, the $R$ is a tripled resonance, and so on. This hypothesis is consistent with present experimental data. The multipole resonance hypothesis is related to narrow-width resonance models in which undesirable states are eliminated with the aid of satellite Veneziano terms. The high-energy behavior is similar to normal Regge Behavior.

Anomalous, possibly large real parts in the $T$ matrices for high-energy scattering of unstable particles are shown to be a dynamical consequence of instability. This effect is estimated to be quite large in the case of the photoproduction and elastic scattering of ${\rho }^0$ mesons from nucleons and can be interpreted as a breakdown of the simple "${\rho }^0$-photon analogy."

The creation of $M_L$ alignment due to the foil excitation process is demonstrated with the observation of zero-field quantum beats in He $3{}_{}{}^3{}_{}{}^{}P-2{}_{}{}^3{}_{}{}^{}S$ 3880-Å, hydrogen ${\mathrm{H}}_{\alpha }$, and hydrogen ${\mathrm{H}}_{\beta }$ emission.

The time-decay spectra of positrons annihilating in helium gas from 4.6 to 30°K have been obtained and it is found that the spectra exhibit a large variation with respect to a small change in temperature. Many-body effects are discussed in connection with the data.

This Letter reports the results of ionic-mobility measurements in the four simple liquids He I, ${\mathrm{N}}_2$, Ar, and C${\mathrm{Cl}}_4$. Periodic steps in the mobility, like those found earlier in liquid helium II, were found also in these four liquids. We found also a simple relation connecting the critical velocities to the temperatures of the investigated liquids.

Interactions between excitations in superfluid helium are investigated by Green's function techniques. In our model, a sharp peak appears in the two-excitation spectrum corresponding to a resonance of two rotons. Interaction of the resonance with the single-particle spectrum results in a hybridization and splitting of the one-particle spectrum into two distinct branches. These theoretical results are in agreement with recent neutronscattering and Raman-scattering experiments.