This work has been digitalized and published in 2013 by Verlag Zeitschrift für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namensnennung 4.0 Lizenz. Neutron Star Matter and Neutron Star Models H. Heintzmann Institut für Theoretische Physik der Universität Köln W. Hillebrandt, M. F. El Eid, and E. R. Hilf Institut für Kernphysik der Technischen Hochschule Darmstadt (Z. Naturforsch. 29 a, 933 —946 [1974] ; received January 16, 1974) Various methods to study the ground state of neutron star matter are compared and the cor responding neutron star models are contrasted with each other. In the low density region o < 1014grcm -3 the nuclear gas is treated here by means of a Thomas Fermi method and the nuclei are described by the droplet model of Myers and Swiatecki. For o > 1014 gr cm“3 both standard Brueckner theory with more realistic interaction (one-boson-exchange) potentials and the semiphenomenological theory of Fermi liquids (together with the standard Reid softcore potential) are applied to neutron star matter. It is shown that while the high mass limit of neutron stars is hardly affected, some properties of lowmass neutron stars such as their binding depend sensitively on these refinements. Various tentative (but unreliable) extensions of the equation of state into high density regime Q > 1015 gr cm-3 are investigated and it is shown that the mass limit for heavy neutron stars lies around 2.5 solar masses. It is further shown that a third family of stable (hyperon) stars is not forbidden by general relativistic arguments if there is a phase transition at high densities. 1. Introduction The discoveries of radio pulsars1 and x-ray sources in close binary systems2 and particularly the unique radio-optical-x-ray and y-ray pulsar in the crab nebula3 have stimulated renewed interest in the final stages of stellar evolution. Today it is believed that an ordinary star can end its life in at least three different ways: 1) A white- (and later black-) dwarf star, if the final mass M does not exceed the Chandra sekhar limit ( ¥ ^ 1 . 4 M 0). 2) A neutron star, if the final mass does not exceed a certain other limit which will be discussed below. 3) A (white or) blade hole provided the final mass exceeds this latter limit. Apart from these final states there might exist others e. g. hyperon stars. A great number of authors have calculated the properties of neutron star matter and neutron star models including the composition and the equation of state at both low and high density4-13, the cooling process and the problem of energy dissipa tion 14_20, the superfluidity of neutrons and pro- Reprint requests to Dr. W. Hillebrandt, Institut für Kernphysik der Technischen Hochschule Darmstadt, D-6100 Darmstadt, FRG, Schloßgartenstraße 9. tons 21’ 22 and the possible existence of a neutronic quantum crystal 23. Our motivation for reconsidering here neutron star matter and neutron star models is the follow ing: More realistic nuclear forces than used so far have been derived from meson theory which rely only on the experimentally measured coupling strengths and meson masses. We consider model-extensions of the high density regime of neutron star matter such as a possible quantum crystal and different hadronic equations of state to study their effect on a possible third family of stable stars or effects of anisotropy. We pay special attention to the equation of state at low densities to see how the minimum mass of a stable, bound neutron star is affected by the equa tion of state. We try to analyse the effects of alternative theo ries of gravitation on the properties of neutron star models. The present paper is divided into three main sec tions. In section two we will treat neutron star mat ter from a microscopic point of view and discuss limiting cases for the equation of state. In section three the macroscopic structure of neutron stars is studied and the fourth section tries to establish a link between theory and observation.