Lowest-order Effects Research Articles

Weak Corrections to the Magnetic Moments of Leptons

A calculation of the contribution of the weak interactions to the magnetic moments of the leptons is reported. An intermediate vector boson is assumed, and lowest order effects are calculated. The radiative corrections to these results are estimated by making use of the summation technique introduced by Lee. The contributions are small compared to the uncertainties in the experimental values of the magnetic moments. For the muon the changes in the magnetic moment are at least an order of magnitude smaller than the contributions of the strong interactions. If the muon's neutrino has a relatively large mass, its induced magnetic moment will affect the neutrino scattering cross sections calculated by Bernstein and Lee.

Fermi Normal Coordinates and Some Basic Concepts in Differential Geometry

Fermi coordinates, where the metric is rectangular and has vanishing first derivatives at each point of a curve, are constructed in a particular way about a geodesic. This determines an expansion of the metric in powers of proper distance normal to the geodesic, of which the second-order terms are explicitly computed here in terms of the curvature tensor at the corresponding point on the base geodesic. These terms determine the lowest-order effects of a gravitational field which can be measured locally by a freely falling observer. An example is provided in the Schwarzschild metric. This discussion of Fermi Normal Coordinate provides numerous examples of the use of the modern, coordinate-free concept of a vector and of computations which are simplified by introducing a vector instead of its components. The ideas of contravariant vector and Lie Bracket, as well as the equation of geodesic deviation, are reviewed before being applied.

Pairing model for Pr-isotopes

The interaction between neutrons and protons filling different major shells is treated as a perturbation within the framework of the pairing force model. The lowest order effect is to keep the pairing model equations unchanged; only the single nucleon energies to be used therein are modified by an amount dependent on the number of the opposite kind of nucleons and the zero-rank component of the n-p potential. This effect produces the observed ground-state spins of Pr 141, 143, 145. The quasi-neutron-quasi-proton interaction, which contains the effect from the higher multipole components of the n-p potential, must be diagonalised to attempt a detailed fit to the spectra. This is particularly true for the odd nuclei Pr 142, 143. There are two competing configurations for the ground state of Pr 144, a diagnolisation between which is now in progress.