Discrepancies between Physically and Chemically Determined Atomic Weights for the Elements between Silver 47 and Iodine 53

Abstract

P REVIOUSLY, it was shown 1 that C -N reactions can also explain the energy generation of the two well-known giant stars, Capella A and t Aurigae K, if they are built on the Gamow shell-source model, 2 and that in their envelopes the hydrogen content must be ^35 percent by weight if helium is neglected. Based on this chemical composition and the C -N reactions, possible structures of stars, which have given masses, 8 MQ and MQ, but dehydrogenized isothermal cores of various masses have been investigated.Under widely different assumptions as to luminosity, L, and radius, R, the usual four equations of stellar equilibrium 3 for p (pressure), T (temperature), M(r) (mass inside the radius r), and L{r) (energy flow across the surface of radius r) are numerically integrated inward. The following assumptions are made: In the envelopes the hydrogen content is 35 percent and the remainder is a Russell mixture which contains 1 percent of carbon and nitrogen, while in the cores hydrogen is replaced by helium; for the mean molecular weight, n, and the opacity, values tabulated by Strongren 4 and Morse 6 are used; in the convective regions, temperature gradients are given by the formula of an adiabatic change of matter and radiation. 3 Values of p, T } and M(r) at the points where L{r) vanishes are compared with those of the Emden solutions of the isothermal cores. Here, it is convenient to use the functions U, F, and \j/ (measure of electron degeneracy), which determine the core's solutions apart from the homologous transformations, defined bywhere p, p g , and /u e are density, gas pressure, and mean molecular weight of the electron, respectively. In our case, suitable conditions for the outer and inner solutions are given by the continuity of U/p, V/fi, and ^-f-logeC/WV). Appropriate solutions thus obtained by interpolation determine L, R, and internal conditions of stars in a series of one parameter ^c > the value of ^ at the center. The results are similar for the two masses as shown in Figs. 1 and 2. Calculated ranges of tp e are from -5.4 to +23.3 for 8 MQ and from -2.3 to +11.5 for MQ. They correspond to slight increases of the core's temperatures, from 3.5 X10 7 to 5.2X10 7°K for 8MQ and from 2.1 X10 7 to 2.4X10 7°K for Mo, and large increases of the central densities, from 10 to 5.1 X10 5 g/cm 3 for 8 M 0 and from 1.5X10 2 to 5.5X10 4 g/cm 3 for M Q. For minimum values of \p e > the core's masses M* are nearly zero and the stars lie within the main sequence. L and R increase with \j/ e when ^c<0 (perfect gas state), and then •-o 0 / / / / Mo -__ -__8M^^ --^^ __ FIG. 1. Luminosity-radius relations for stars of masses, 8 M Q and M Q.change abruptly when ^c-0 (incipient degeneracy). Further increases of \j/ c (strong degeneracy) give rapid increases of R, while increases of M* are relatively small and consequently the Eddington's relation L^R~* is approximately satisfied. Together with the earlier results, 1 these will give the general features of giants of any mass. Further, from their observed distribution and the ...