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Starting with the lowest-order unscreened QED matrix element for electron-positron pair production by heavy charged particles, the paper calculates the cross section for this process differential in all independent variables and valid for all pair energies small compared to the incident particle energy. Integration over the possible emission angles of one of the pair members gives an expression that is valid for low-energy pairs that can be compared with previous work based on the Weizsaecker-Williams method. Integration over the possible angles of the other pair member then yields an expression identical to one derived by Racah. The high energy-transfer limit of the expression for the cross section integrated over electron and positron angles is found to be identical to that of Kelner in the unscreened case.

A calculation of the total cross section for direct electron-positron pair production by heavy ions is described. It combines the use of the Weizsaecker-Williams method for low-energy transfers and existing calculations for high-energy transfers. Higher-order corrections to the total cross section are calculated based on the Weizsaecher-Williams method and existing results for pair production by photons.

A comparison is conducted between an exact numerical calculation and two approximate analytic expressions for the Mott correction to energy loss of heavy ions. A complete tabulation of the Mott correction is presented together with a comparison of some of the approximate expressions for the Mott correction due to Ahlen (1978) and Morgan and Eby (1973). Comparison is made with results of an experimental calibration of the HEAO-3 Heavy Cosmic Ray experimental chambers at the Bevalac.

A Lagrangian is constructed which gives Newtonian gravity in the lowest-order approximation in an isotropic universe and also predicts the correct advance of the perihelion with the proper choice of a constant governing the ratio of inertial to gravitational mass. The situation considered is that of a test particle orbiting a central body with external mass at rest and distributed isotropically at large distances from the central body. In the theory developed, the perihelion advance is due to a small contribution to the test-particle inertial mass by the central attracting body rather than to a failure of the inverse-square law of attraction. Some interesting Machian features of this theory are that: (1) the local value of the gravitational constant is determined by the mass distribution of the external matter; (2) the orbits are fixed, and the perihelion advances unambiguously with respect to the external-mass distribution; (3) there are no vestiges of absolute space; (4) the perihelion precession arises from the inertial interaction of the test particle with the central mass; (5) the local rest mass is really determined by the mass distribution of the rest of the universe; and (6) a limited form of the equivalence principle is inherent in one of the equations.