The lowest order electromagnetic radiative corrections to electron-positron annihilation into neutrino and antineutrino and to neutrino scattering by electrons are calculated. The pair annihilation corrections are used to calculate the radiative corrections to stellar neutrino luminosities in the temperature range in which the zero order process gives the dominant contribution. The corrections to the neutrino-electron scattering cross section are those relevant to a proposed experiment detecting scattered electrons with more than a minimum recoil energy whether or not a bremsstrahlung photon is emitted.
\r\n\r\nThe results depend logarithmically on an ultraviolet cut-off in the same way as does the lowest order vacuum polarization diagram of electrodynamics. When the cut-off is taken to be on the order of the nucleon mass the luminosity is enhanced by as much as 10 percent below T ~ 10\u2079 \u00b0K and depressed by ~1 percent for T > 10\u2079 \u00b0K. The scattering cross section is depressed by ~4 percent for the incident neutrino energies ~8 - 14 MeV of the proposed experiment.
\r\n\r\nA characteristic distance, the neutrino charge radius, is associated with a charge distribution of the neutrino and depends on the cut-off. With the cut-off at the nucleon mass the charge radius of the electron neutrino is estimated to be two orders of magnitude smaller than the experimental limit. The possible effects of a charge radius larger than the estimate are also considered. It is found that interference between the electromagnetic and weak couplings could depress both the non-relativistic stellar luminosity and the scattering cross section, but that if the scattering cross section is found to be as large as expected' the luminosity must be also.
", "doi": "10.7907/QS3P-0P04", "publication_date": "1967", "thesis_type": "phd", "thesis_year": "1967" }, { "id": "thesis:3714", "collection": "thesis", "collection_id": "3714", "cite_using_url": "https://resolver.caltech.edu/CaltechETD:etd-09232002-145100", "type": "thesis", "title": "1. Rates of Nuclear Reactions in White-Dwarf Stars. 2. The Cooling of Neutron Stars", "author": [ { "family_name": "Wolf", "given_name": "Richard Alan", "orcid": "0000-0001-5291-4275", "clpid": "Wolf-Richard-Alan" } ], "thesis_advisor": [ { "family_name": "Bahcall", "given_name": "John N.", "clpid": "Bahcall-J-N" } ], "thesis_committee": [ { "family_name": "Unknown", "given_name": "Unknown" } ], "local_group": [ { "literal": "div_pma" } ], "abstract": "1. Rates of Nuclear Reactions in White-Dwarf Stars
\r\n\r\nIn 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 Schr\u00f6dinger 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 C\u00b9\u00b2 + C\u00b9\u00b2 reactions, the present work implies a rate about ten orders of magnitude smaller than the rate calculated by the method previously suggested by Cameron.
\r\n\r\n2. The Cooling of Neutron Stars
\r\n\r\nThe 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 \u2192 n + p + e\u207b + \u03bd̅e and n + \u03c0\u207b \u2192 n + e\u207b + \u03bd̅e 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.
", "doi": "10.7907/FKB7-W110", "publication_date": "1966", "thesis_type": "phd", "thesis_year": "1966" } ]