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The steady-state transport in a prism bounded by partially absorbing walls of emissivitye at temperaturesT1 andT2 and containing fixed scattering centers is obtained exactly in the limit of sufficiently low temperature that onlyS-wave scattering is important and Boltzmann statistics are valid. The integro-differential equations are solved and boundary conditions satisfied by using the techniques of singular integral equations. The properties of the thermodynamic quantities are discussed.

The solution is obtained to the quantum mechanical linearly damped harmonic oscillator subjected to a time dependent driving force. This solution allows the calculation of interesting quantum quantities such as the Green’s function and the transition amplitudes between harmonic oscillator states. The specific results for a harmonic driving force are given.

The solution to the linear Heisenberg equations which result from the most general quadratic time dependent Hamiltonian is developed. The Green’s function is obtained, and the transition amplitudes between harmonic states are calculated.

The solution to the steady-state transport in a prism containing fixed scattering centers and bounded by partially absorbing walls of emissivitye and different temperatures has previously been expressed in terms of a singular integral equation. This equation contains parameters to be evaluated from the boundary equations. A plausible solution to the boundary equations is obtained here.

A formalism for a time-dependent harmonic oscillator is presented. The quantum-mechanical solution is developed and the Green's function is derived. Particular examples of runaway and dissipative behavior are considered.

The electromagnetic radius of the neutrino is calculated by use of dispersion relations. If an intermediate vector boson is used, $$\left\langle {x^2 } \right\rangle = - 6\frac{{g^2 }}{{2\pi ^2 }}\frac{1}{{3m_B^2 }}\left[ {\log \frac{{m_B^2 }}{{m_1^2 }} + \frac{1}{6}} \right]$$ . If no intermediate vector boson is used, $$\left\langle {x^2 } \right\rangle = - 6\left( {\frac{G}{f}} \right)^2 \frac{1}{{4\pi ^2 }}\left( {\frac{{m_1^2 }}{m}} \right)^2 \frac{1}{{3m_\pi ^2 }}\left[ {\log \frac{{m_\pi ^2 }}{{m_1^2 }} - \frac{4}{3}} \right]$$ .

A theory of the intermediate vector boson is proposed, in which the boson field can be described by a renormalizable Lagrangian in an indefinite-metric space. The circumstances under which an indefinitemetric space can be consistently applied are discussed. It is shown that for very massive bosons (M∼2500 proton masses) the indefinite metric of the space does not conflict with requirements of probability conservation. The coupling constant for the lepton-intermediate boson interaction is approximately given byg 2∼10−1 in this theory.

The effects of a quadratic interaction term in a quantum field theory are studied. It is found that the exact and bare Hilbert spaces are orthogonal. Thus, if such terms occur in a theory, they must be treated exactly prior using the Dyson expansion to calculate the effects of residual interactions.

Cross section for electron and muon neutrino- antineutrino pair production by photons, using intermediate boson theory

The motion of neutrinos in ihe presence of charged matter is analyzed. Implications for stellar neuirino emission are considered.

A stable neutral meson is described. Strong and weak interactions, and experiments designed to observe this particle are discussed. Finally, it is shown that if a scalar or pseudoscalar boson is odd under charge conjugation, it is stable or extremely long lived in the absence of neutral lepton currents.

A solution is presented for the steady-state transport in a prism containing fixed scattering centers, and bounded by walls of temperatures ${T}_{1}$ and ${T}_{2}$ having emissivity e. S-wave scattering, specular reflection, and Boltzmann statistics are assumed. Numerical results are obtained for the thermodynamic quantities over the full range of the Knudson number.

The isobar model for the system p + pi /sup +/ is in reasonable accord with the gross features of the momentum distribution for pions emitted in proton- proton collisions, and also in pion photoproduction from nucleons. Some consequences which follow for near-threshold production of the isobar by piors if the model is taken seriously are sbown. (A.C.)

The production of pi mesons by pi mesons has been reported for energies of 960 Mev and 1 Bev. In one. the pi /sup -/ from the process pi /sup -/ + p yields pi /sup -/ + p + pi /sup 0/ emerges predominantly fast, whereas it is predominantly slow in the other. A possible explanation is given for a model which leaves the interpretation of the first pion spectrum unaltered but which could fit the second spectrum owing to the rapid onset of another process. The ratio of fast to slow pi /sup -/ production is given as limits for T states of 0, 1. and 2. The ratio of the pi + pi /sup -/ reactions to the pi /sup -/ + pi /sup 0/ reactions is given for the case T = 1. (B.O.G.)

THE 21-cm. hyperfine emission from the neutral hydrogen atom has an exceedingly narrow natural width, corresponding to a transition probability of 2.84 × 10−15 sec.−1. Consequently, in principle, small variations in its frequency resulting from gravitational effects offer a method to measure gravitational potential in our Galaxy, provided that they are not too small compared with the temperature broadening. The galactic disk is well known to emit 21-cm. radiation, and from its observed Doppler shifts the radial dependence of its rotational velocity has been deduced. Because the true Doppler shifts of galactic rotational motion are large, it may be difficult to detect the expected gravitational shift, which also looks like a Doppler shift. But, in principle, the two effects may be separated because the true Doppler shifts have opposite signs at the same radius on opposite sides of the galactic centre, whereas the gravitational frequency shift has the same sign.

An equation of motion for neutrinos in matter is presented. Solutions are obtained for neutrino motion in uniformly rotating current distributions. Implications for stellar neutrino emission are considered.

An ambiguity is pointed out in the interpretation of an expermient by Stein (Phys. Rev. Letters 2, 473(1959)) on the polarization of the recoil proton in photoproduction in the vicinity of the second resonancehgt he found that at 90 deg cm the polarization was quite large, in fact, the polarization seemed to increase to what appears to be a maximum at or near the second resonance. (W.D.M.)