Gamows Calculation of the Neutron Stars Critical Mass Revised

It has at times been indicated that Landau introduced neutron stars in his classic paper of 1932. This is clearly impossible because the discovery of the neutron by Chadwick was submitted more than one month after Landaus work. Therefore, and according to his calculations, what Landau really did was to study white dwarfs, and the critical mass he obtained clearly matched the value derived by Stoner and later by Chandrasekhar. The birth of the concept of a neutron star is still today unclear. Clearly, in 1934, the work of Baade and Zwicky pointed to neutron stars as originating from supernovae. Oppenheimer in 1939 is also well known to have introduced general relativity (GR) in the study of neutron stars. The aim of this note is to point out that the crucial idea for treating the neutron star has been advanced in Newtonian theory by Gamow. However, this pioneering work was plagued by mistakes. The critical mass he should have obtained was $6.9,M_odot$, not the one he declared, namely, $1.5 M_odot$. Probably, he was taken to this result by the work of Landau on white dwarfs. We revise Gamows calculation of the critical mass regarding calculational and conceptual aspects and discuss whether it is justified to consider it the first neutron-star critical mass. We compare Gamows approach to other early and modern approaches to the problem.

Collective electronic pulsation around giant nuclei in the Thomas-Fermi model

Based on the Thomas-Fermi solution for compressed electron gas around a giant nucleus, $Zapprox 10^6$, we study electric pulsations of electron number-density, pressure and electric fields, which could be caused by an external perturbations acting on the nucleus or the electrons themselves. We numerically obtain the eigen-frequencies and eigen-functions for stationary pulsation modes that fulfill the boundary-value problem established by electron-number and energy-momentum conservation, equation of state, laws of thermodynamics, and Maxwells equations, as well as physical boundary conditions. We choose a proton number of $Z=10^6$ and assume the nucleons in $beta$-equilibrium at nuclear density. Similar systems with non-spherical geometry are hypothesized to exist in the lower crust of neutron stars, commonly referred to as textit{pasta equation of state}. The lowest modes turn out to be heavily influenced by the relativistic plasma frequency induced by the positive charge background in the nucleus. We discuss the possibility to apply our results to dynamic nuclei using the spectral method and mention mechanisms that could stimulate such dynamics in the astrophysical context.