Transmutation of the Lighter Elements in Stars

Abstract

THE formula given by Gamow (Zeits. f. Phys., 52, p. 512; 1928), for the probability that an α-particle will penetrate the nucleus of an atom with which it collides, can be readily adapted to the case of proton-impacts. These have only half the charge of an α-particle, and for the same energy twice the velocity, so that under conditions approaching thermodynamical equilibrium they have an enormously greater penetrating-power. We have investigated the possibility that in the interior of stars the process should actually occur with appreciable frequency, and we find that for the heaviest elements the probability is extremely small. For the lightest, however, we obtain an average life varying roughly from 10 seconds for helium to 100 years for carbon in a fairly typical case. The protons that are most effective, when their number is taken into account, are those with from three to four times the most probable velocity of the Maxwell distribution.