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Rates of Nuclear Reactions in Solid-Like Stars

Wolf, Richard A. (1965) Rates of Nuclear Reactions in Solid-Like Stars. Physical Review, 137 (6B). B1634-B1643. ISSN 0031-899X. http://resolver.caltech.edu/CaltechAUTHORS:20120829-160903541

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Abstract

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. We propose a solid-state method 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 the Schrödinger equation containing the effective potential U(r). From this wave function, we derive an expression for the reaction rate. The rates of the p+p and C^(12)+C^(12) reactions calculated using this solid-state method are typically 1 to 10 orders of magnitude smaller than those calculated by the method previously suggested by Cameron.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRev.137.B1634DOIUNSPECIFIED
http://link.aps.org/doi/10.1103/PhysRev.137.B1634PublisherUNSPECIFIED
Additional Information:© 1965 The American Physical Society. Received 9 November 1964; published in the issue dated March 1965. Supported in part by the U. S. Office of Naval Research [Nonr-220(47)] and the National Aeronautics and Space Administration [NGR-05-002-028]. National Science Foundation Predoctoral Fellow in Physics. I am grateful to Dr. J. N. Bahcall for his skillful guidance of this work and for his countless illuminating suggestions. Discussions with Professor R. F. Christy and Professor E. E. Salpeter have also been most helpful. I would like to thank H. Van Horn for informing me about his extensive work on the same problem and for calling my attention to several important papers.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)Nonr-220(47)
NASANGR-05-002-028
NSFUNSPECIFIED
Record Number:CaltechAUTHORS:20120829-160903541
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120829-160903541
Official Citation:Wolf, R. A. (1965). "Rates of Nuclear Reactions in Solid-Like Stars." Physical Review 137(6B): B1634-B1643.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:33696
Collection:CaltechAUTHORS
Deposited By: Aucoeur Ngo
Deposited On:30 Aug 2012 15:00
Last Modified:26 Dec 2012 16:05

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