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Title: S-matrix calculation of the triple-alpha reaction

Abstract

An S-matrix formalism is developed which can be applied to reactions in which electron screening is important, including three-body reactions and reactions involving weak interactions. The various regimes of the triple-alpha reactions are systematically discussed, and a new nonresonant regime at high densities is identified. Using the S-matrix formalism, an analytic expression is obtained for the screened triple-alpha reactions which is accurate for all temperatures and densities. The results are compared with those of Cameron (1959) and Nomoto et al. (1985), and the latter's expression for the unscreened reaction rate is verified. However, it is shown that the reaction rate in the pycnonuclear regime cannot be obtained from the unscreened rate using a screening factor, and that the results of Nomoto et al. therefore cannot be used in this regime. 25 references.

Authors:
;
Publication Date:
Research Org.:
Harvard-Smithsonian Center for Astrophysics, Cambridge, MA; Chicago Univ., IL
OSTI Identifier:
6086290
Resource Type:
Journal Article
Journal Name:
Astrophys. J.; (United States)
Additional Journal Information:
Journal Volume: 317
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALPHA REACTIONS; ANALYTICAL SOLUTION; ASTROPHYSICS; ABUNDANCE; ALPHA PARTICLES; ATOMIC PHYSICS; COMPARATIVE EVALUATIONS; COSMIC GAMMA BURSTS; HIGH TEMPERATURE; REACTION KINETICS; S MATRIX; STAR EVOLUTION; SUPERNOVAE; THERMONUCLEAR REACTIONS; CHARGED PARTICLES; CHARGED-PARTICLE REACTIONS; COSMIC RADIATION; ERUPTIVE VARIABLE STARS; IONIZING RADIATIONS; KINETICS; MATRICES; NUCLEAR REACTIONS; NUCLEOSYNTHESIS; PHYSICS; PRIMARY COSMIC RADIATION; RADIATIONS; STARS; SYNTHESIS; VARIABLE STARS; 640102* - Astrophysics & Cosmology- Stars & Quasi-Stellar, Radio & X-Ray Sources

Citation Formats

Fushiki, I, and Lamb, D Q. S-matrix calculation of the triple-alpha reaction. United States: N. p., 1987. Web. doi:10.1086/165284.
Fushiki, I, & Lamb, D Q. S-matrix calculation of the triple-alpha reaction. United States. https://doi.org/10.1086/165284
Fushiki, I, and Lamb, D Q. 1987. "S-matrix calculation of the triple-alpha reaction". United States. https://doi.org/10.1086/165284.
@article{osti_6086290,
title = {S-matrix calculation of the triple-alpha reaction},
author = {Fushiki, I and Lamb, D Q},
abstractNote = {An S-matrix formalism is developed which can be applied to reactions in which electron screening is important, including three-body reactions and reactions involving weak interactions. The various regimes of the triple-alpha reactions are systematically discussed, and a new nonresonant regime at high densities is identified. Using the S-matrix formalism, an analytic expression is obtained for the screened triple-alpha reactions which is accurate for all temperatures and densities. The results are compared with those of Cameron (1959) and Nomoto et al. (1985), and the latter's expression for the unscreened reaction rate is verified. However, it is shown that the reaction rate in the pycnonuclear regime cannot be obtained from the unscreened rate using a screening factor, and that the results of Nomoto et al. therefore cannot be used in this regime. 25 references.},
doi = {10.1086/165284},
url = {https://www.osti.gov/biblio/6086290}, journal = {Astrophys. J.; (United States)},
number = ,
volume = 317,
place = {United States},
year = {1987},
month = {6}
}