S. B. Treiman

The Physics of Time Reversal

A filler for a continuous cigarette filter rod is formed by feeding a wide band of filaments of filter material on to a slower moving surface, to which suction is applied so that the band is axially shrunk and the filaments crimped. The band is then narrowed to the desired width of the filler whilst retaining the crimp in the filaments, preferably by the use of a plasticiser.

Mandelstam representation for potential scattering

Abstract A proof of the Mandelstam representation for the scattering amplitude in the case of nonrelativistic potential scattering is given for a certain class of potentials. Fredholm theory and the Lehmann representation are employed in the proof. The unitarity condition is used to provide an iteration procedure for the exact determination of the weight function appearing in the Mandelstam representation, independent of the number of subtractions required in the latter. The analytic properties of the partial wave amplitudes can be easily read off from the Mandelstam representation. It is shown that in cases where the partial wave amplitudes can be represented by dispersion integrals without subtractions, they are uniquely determined, together with the energies of any bound states, in terms of the first Born approximation and the Mandelstam weight function, which is in principle known. In these circumstances, in effect, the Mandelstam representation and unitarity, together with the first Born approximation, completely define the nonrelativistic scattering problem in a way which replaces the Schrodinger equation. Some approximation methods are discussed and compared with exact solutions for s -wave amplitudes.

Coulomb corrections in allowed beta transitions

Abstract Complete expressions, with all Coulomb effects taken into account, are given for the distribution functions for allowed beta decay, including recoil, nuclear orientation, and electron polarization effects. The expressions are general in that no assumptions are made as to invariance with respect to space inversion, charge conjugation, or time reversal. Simple arguments based on the behaviour of the various momenta and angular momenta under space inversion and time reversal are used to elucidate which combinations of vectors will appear when the different symmetry laws are violated, and the modifications of these arguments necessary because of the Coulomb interaction in the final state are pointed out. Various tests of time reversal invariance, previously suggested, are re-evaluated in view of the results for the Coulomb corrections.

Axion Emission in Decay of Excited Nuclear States

Abstract Decay of an excited nuclear state by axion emission can be related, under certain circumstances, to an isotopically analogous β decay process. All strong interaction and nuclear complications for the former reaction are therefore fixed by data on the latter, so that the axion rate can be reliably predicted up to open parameters of the underlying weak interaction model. This is illustrated, in the framework of a simple axion model, with the example of decay of 12 C ∗ (15.1 MeV). For plausible values of the parameters, the ratio of axion to gamma decay widths is of order 10 −5 . Some aspects of decay of the axion itself are commented on; and we also briefly discuss possible alternative models of axion interactions.

Thermalization of baryon asymmetry

Abstract In an expanding and cooling universe, baryon asymmetry generated through baryon-and CP -violating interactions in the early high temperature stages will tend at later stages to thermalize toward a situation of reduced baryon asymmetry. We analyze this thermalization effect in the context of the SU(5) model of grand unification. The thermalization is characterized by distinctive eigenmodes. For SU(5) we observe that there is one particular mode that does not thermalize at all.

A model for weak trimuon production

Abstract Neutrino-induced trimuon events have been interpreted by several authors as arising from cascade decay of a new lepton produced directly in neutrino reactions. We incorporate this idea in a gauge scheme based on the group Su(2) × SU(2) × U(1).

Electron-positron collisions and the C-invariance question

Abstract The implications of charge conjugation invariance are reviewed for hadronic processes induced by e + −e − collisions. Attention is called to certain features which follow from one photon exchange and which afford the possibility of refining C -invariance tests in a statistically economical way.