1. Rates of Nuclear Reactions in White-Dwarf Stars. 2. The Cooling of Neutron Stars

Citation

Wolf, Richard Alan (1966) 1. Rates of Nuclear Reactions in White-Dwarf Stars. 2. The Cooling of Neutron Stars. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FKB7-W110. https://resolver.caltech.edu/CaltechETD:etd-09232002-145100

Abstract

1. Rates of Nuclear Reactions in White-Dwarf Stars

In stellar matter as cool and dense as the interior of a white dwarf, the Coulomb energies between neighboring nuclei are large compared to the kinetic energies of the nuclei. Each nucleus is constrained to vibrate about an equilibrium position, and the motion of the nuclei in the interior of a white dwarf is similar to the motion of the atoms in a solid or liquid. A method is proposed for calculating the rate at which a nuclear reaction proceeds between two identical nuclei oscillating about adjacent lattice sites. An effective potential U[r﹏] derived by analyzing small lattice vibrations is used to represent the influence of the Coulomb fields of the lattice on the motion of the two reacting nuclei. The wave function describing the relative motion of the two reacting particles is obtained by solving a Schrödinger equation containing the effective potential U[r﹏]. From this wave function an expression for the reaction rate is derived. Applied to the p + p reaction, this method predicts a reaction rate about 100 times the original estimate made by Wildhack; applied to the C¹² + C¹² reactions, the present work implies a rate about ten orders of magnitude smaller than the rate calculated by the method previously suggested by Cameron.

2. The Cooling of Neutron Stars

The emission of neutrinos from neutron stars is studied, and those characteristics of neutron-star matter that affect cooling are investigated. The validity of the particle model (which we adopt) is discussed. The effects of strong interactions on the composition of neutron-star matter are described. The question of superfluidity in the neutron-proton gas is discussed, and the limit of stability of the nucleon-gas to formation of "nuclei" is estimated. Calculations of the rates of the cooling reactions n + n → n + p + e⁻ + ν̅_e and n + π⁻ → n + e⁻ + ν̅_e are presented; the rates of the closely related muon-producing reactions and the four inverse processes are also given. The calculated cooling rates indicate that a neutron star containing quasi-free pions would cool within a few days to a temperature so low that photon emission from the star's surface would be unobservable. Uncertainty about the properties of neutron-star matter prevents precise predictions about cooling rates, but it is possible to establish a lower limit on the cooling rate of a neutron star. This lower limit on the cooling rate implies that the discrete X-ray sources located in the direction of the galactic center are probably not neutron stars.

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