Computer Science – Numerical Analysis
Scientific paper
Jan 1995
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...438..300k&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 438, no. 1, p. 300-307
Computer Science
Numerical Analysis
5
Coulomb Potential, Nuclear Reactions, Reaction Kinetics, Schroedinger Equation, Stellar Interiors, Thermal Diffusion, Wave Scattering, Boltzmann Distribution, Monte Carlo Method, Numerical Analysis, Supernovae
Scientific paper
Pycnonuclear rates in dense Coulomb solids are calculated through an exact numerical solution to the Schroedinger equation for s-wave scattering between nearest-neighbor nuclei in the lattice potentials formulated through Monte Carlo sampling. Thermal enhancement factors over the ground-state pycnonulcear rates are thereby evaluated through explicit summation of the discrete contributions from excited states with thermal Boltzmann factors taken into account. The results are compared with those obtained earlier by Salpeter & Van Horn with fluid-like approximations based on a Wentzel-Kramers-Brillouin (WKB) approach and continuum saddle-point integrations. Those two sets of evaluations agree fairly well over the entire density-temperature domain of solids except in the vicinity of the melting conditions, where the present results may predict enhancement greater by a factor as large as 1021 than those of Salpeter & Van Horn. Validity of such a huge enhancement factor is reconfirmed separately through consideration of the harmonic and anharmonic lattice vibrations.
Ichimaru Setsuo
Kitamura Hikaru
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