Non-conservative Terms Research Articles

Rocket measurements of energetic particles: 2. Electron results

Fluxes, energy spectrums, and angular distributions of electrons with energies greater than 150 kev have been measured by five detectors on each of two rockets fired along a magnetic field line near L = 5.6. The flux above 150 kev increased with altitude along the field line to a value near 105 electrons/cm2 sec at an altitude of 400 km. The angular distributions were peaked at a pitch angle near 90° with a width less than the detector entrance aperture of 20°. The flux coming down the field line was about 1% of that mirroring and 3 times that coming up the field line. The energy spectrums were functions of altitude and pitch angle, the e-folding energy varying between about 55 and 280 kev. There were no significant intensity fluctuations on a time scale of several milliseconds to 1 second. Sinusoidal-like intensity fluctuations of a factor of 2 and a period near 19 seconds were observed. The qualitative features of the angular distributions and energy spectrums are explicable in terms of atmospheric diffusion of the electrons. Detailed properties of the 19-second periodicity require that an electron source be essentially on the field line of observation and that at least some of the electrons come directly from the source with insignificant atmospheric diffusion. The data are interpreted in terms of the nonconservation of the adiabatic invariants in the equatorial plane, resulting in the scattering from an equatorial reservoir of electrons observed at low altitudes. The data can also be explained in terms of low-altitude acceleration mechanisms or of the nonconservation of the adiabatic invariants along the entire length of the field line.

Estimate of a Parity Non-conserving Contribution to +-Meson Production by Polarized Protons

Results of parity nonconserving interactions of the first order in the weak coupling constant G are applied to p-N production of pions. These interactions are combined with strong pseudoscalar interactions to give a parity nonconserving term in the differential cross section. The calculation is performed in terms of general isotopic spin factors; results are evaluated explicity for pi /sup +/production by polarized protons incident on nucleons. It is predicted that these parity nonconserving contributions to pi /sup +/ pro duction are too small to be observed experimentally. (L.N.N.)

On parity conservation in strong interactions

The analogy in respect toγ5 invariance between the two component Dirac equation for the neutrino and the Schremp-Gursey type equation describing bayrons is used in order to express the lagrangian for strong interactions as the sum of two types of parity non-conserving terms formally similar to those adopted for weak interactions. These terms however, when suitably grouped, may be shown to compensate each other in order that parity is always conserved and the conventional lagrangian is obtained; the compensation is a consequence of the fact that the number and disposition of the baryon states in the elementary particle scheme is such as to allow this grouping of compensating pairs; the original asymmetry remains only detectable in the mass differences between baryons which may naturally be thus interpreted as a consequence of it.

Gravitational motion and radiation — I

A method is established to solve Einstein’s equations by successive approximations, uniqueness and compatibility at each step being secured by imposing de Donder’s condition on the field. This turns out to restrict the freedom of choice of the sources in a way that determines their laws of motion, directly from the field quantities, without any use of integration around singularities. If the approximation parameter is the reciprocal velocity of light, the first non trivial approximation results in the constancy of the rest mass, and in Newton’s law of attraction. The next step shows that there is no first-order correction to these laws. The third approximation then gives a small correction to the rest mass, which is found to be increased by the presence of other bodies. There is also a second-order correction to the acceleration (not explicitly evaluated here) which causes the perihelion advance in the two-body problem. Te fourth approximation involves a contribution from the radiation field. It is found that in order to fulfil de Donder’s condition, we must introduce into the field a term which is linear in the sources, although it does not appear in the so-called «linear approximation». This result may cast some doubts on the validity of the latter. In a further paper, we shall solve still higher approximations by means of an improved technique, and find that the fifth-order correction to the acceleration involves a non-conservative term. This last result may be taken as evidence for the reality of gravitational radiation.

The hyperon decays and the structure of interactions

Experiments have shown that, in cases of the weak fermion interactions and π-decay interaction, the coupling constant for the parity conserving term and that for the parity non-conserving term are almost equal to each other. Assuming that this is the situation in every case of the weak interactions, we show that the Λ-decay interaction is of the derivative (vector and axial vector) coupling type. This belongs to the 2nd kind interactions, as do the weak fermion interactions. We discuss various features which stem from the basic assumption that all the weak interactions violating the parity conservation belong to the 2nd kind. A result coming from this basic assumption is the universality of the coupling constants for the weak interactions. The two-neutrino decay of K is forbidden as it should be. The situation for the processes π, K → e+ ν and e+ ν+ γ is much better than in the case of the weak interactions of the 1st kind. A dimensional analysis is used to obtain information on the strength of interactions in each energy region. It suggests that the weak interactions belonging to the 2nd kind predominate over all the other interactions in the high energy region corresponding to a scale smaller than 10 −20 cm. The violation of the parity conservation may be due to some feature of space for such small distances. It is suggested that multiple production of leptons may occur at extremely high energies. The high energy behaviour of the strong interactions like the π-nucleon coupling is briefly discussed; the nucleon Compton wave-length may characterize a region where the strong interactions behave in a way different from ordinary notions. In this sense, we may meet various strata of nature in high energy regions.

Hyperon Decays and Characteristics of Interactions between Elementary Particles

The weak interactions describing decays of elementary particles have some regularity and universality. The Fermi-type weak fermion interaction with the same universal coupling constants for parity conserving and nonconserving terms has explained successfully the nuclear beta decay and μ-e decay. As for the pion and K-meson decays, it also seems that the universal weak boson fermion interaction of gradient type with the same amount of even and odd parts is more desirable than the direct type coupling. As for the hyperon decays, recent observations on the angular assymmetries have appeared to emphasize a similar tendency. Calculated results are presented in tables and figures.

Polarization effects in beta decay accompanied by internal bremsstrahlung

The calculations were performed under the assumption of the two- component neutrino theory, although the generalization for an arbitrary admixture of the parity nonconserving terms modifies the results for the polarizations only by a constant factor. The method and notation used were previously applied by Cutcosky to the calculation of the spectra and angular distributions of internal bremsstrahlung gamma rays. The bremsstrahlung effect tends to increase the efiect of the electron polarization, independently of the coupling assumed. (M.H.R.)