Fusion reactions in multicomponent dense matter

D. G. Yakovlev, L. R. Gasques, A. V. Afanasjev, M. Beard, and M. Wiescher

Phys. Rev. C 74, 035803 – Published 27 September 2006

Abstract

We analyze thermonuclear and pycnonuclear fusion reactions in dense matter containing atomic nuclei of different types. We extend a phenomenological expression for the reaction rate, proposed recently by Gasques et al. [Phys. Rev. C 72, 025806 (2005)] for the one-component plasma of nuclei, to the multicomponent plasma. The expression contains several fit parameters which we adjust to reproduce the best microscopic calculations available in the literature. Furthermore, we show that pycnonuclear burning is drastically affected by an (unknown) structure of the multicomponent matter (a regular lattice, a uniform mix, etc.). We apply the results to study nuclear burning in a $^{12} C −^{16} O$ mixture. In this context, we present new calculations of the astrophysical $S$ factors for carbon-oxygen and oxygen-oxygen fusion reactions. We show that the presence of a C-O lattice can strongly suppress carbon ignition in white dwarf cores and neutron star crusts at densities $ρ ≳ 3 \times 10^{9}$ g cm $^{- 3}$ and temperatures $T ≲ 10^{8}$ K.

Received 13 March 2006

DOI:https://doi.org/10.1103/PhysRevC.74.035803

Authors & Affiliations

D. G. Yakovlev

Ioffe Physico-Technical Institute, Poliekhnicheskaya 26, RU-194021 Saint Petersburg, Russia and Department of Physics & Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA

L. R. Gasques

Department of Physics & The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556, USA

A. V. Afanasjev

Department of Physics and Astronomy, Mississippi State University, P.O. Drawer 5167, Mississippi 39762-5167, USA

M. Beard and M. Wiescher

Department of Physics & The Joint Institute for Nuclear Astrophysics, University of Notre Dame, Notre Dame, Indiana 46556 USA

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Issue

Vol. 74, Iss. 3 — September 2006

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Images

Figure 1
Top: Astrophysical $S$ factors as a function of the center-of-mass energy $E$ for the ${}^{12}C$ + ${}^{12}C$ , ${}^{12}C$ + ${}^{16}O$ , and ${}^{16}O$ + ${}^{16}O$ reactions. Solid lines correspond to the BP model calculations; various symbols are experimental data. Bottom: Gamow-peak energy ranges for these reactions in the thermonuclear regime vs temperature $T$ of stellar matter. See text for details.Reuse & Permissions
Figure 2
Temperature-density diagram for ${}^{12}C$ - ${}^{16}O$ matter. Straight lines show temperature $T_{l}$ of the appearance of ion liquid, melting temperature $T_{m}$ of ion crystal, and ion plasma temperature $T_{p}$ . Solid lines refer to pure carbon matter, long dashes to C-O matter with equal particle fractions of C and O, and short dashes to pure oxygen matter. Three shaded strips show the regions important for C+C burning (in pure carbon matter), C+O burning (in C-O mixture), and O+O burning (in pure oxygen matter). Each strip is restricted by upper and lower lines along which the burning time equals 1 year and $10^{6}$ years, respectively (see the text for details).Reuse & Permissions
Figure 3
Rates of pycnonuclear C+C, C+O, and O+O reactions vs density for the optimal burning model. Dot-and-dashed lines show C+C burning in a pure carbon crystal and O+O burning in a pure oxygen crystal. Other lines are for the C-O mixture ( $x_{C} = 0.5$ ); solid lines refer to a uniform BIM; long-dashed lines are for a regular C-O bcc crystal; dots are for phase-separated matter. Inset shows the same curves for the C+C reaction on a larger scale; thicker short-dashed lines give the maximum and minimum reaction rates for the uniform C-O mixture in the ion-sphere model ( $α_{λ} = 1$ ); thin short-dashed lines are the same but allow for the variation of $α_{λ}$ (see text for details).Reuse & Permissions
Figure 4
C+C reaction rate vs temperature at $ρ = 5 \times 10^{9}$ g cm $^{- 3}$ . Dot-and-dashed line is the optimal model for pure carbon matter; other lines are for a C-O mixture with $x_{C} = 0.5$ . Solid line is the optimal model for a uniform mixture; long-dashed line is for the regular bcc C-O crystal at low temperatures (vertical part indicates the melting point). Thicker short-dashed lines give the maximum and minimum reaction rates for the uniform C-O mixture in the ion-sphere model ( $α_{λ} = 1$ ); thinner short dashed-lines are the same but allow for deviations from the ion-sphere model (see text for details).Reuse & Permissions
Figure 5
Carbon ignition curves in ${}^{12}C$ - ${}^{16}O$ matter. Dot-and-dashed line is the optimal model for carbon burning in pure carbon matter. Solid and dotted lines are optimal models for uniform C-O mixtures with $x_{C} = 0.5$ and 0.1, respectively. Other lines are for C-O BIMs with $x_{C} = 0.5$ . Short-dashed lines give the highest and lowest theoretical ignition curves for uniform mixtures. Long-dashed line is for the C-O bcc crystal at low temperatures.Reuse & Permissions

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