Caughlan and Fowler 1988

THERMONUCLEAR REACTION RATES

In these pages, we reproduce and extend the Georgeanne R. Caughlan and William A. Fowler 1988 Thermonuclear Reaction Rate Collection. This collection includes analytic expressions for the (forward and reverse) rates of astrophysically important thermonuclear reactions involving low-mass (Z = 1 - 14, Hydrogen to Silicon) nuclei. It was published as Thermonuclear Reaction Rates V , Atomic Data and Nuclear Data Tables, Vol. 40, #2, 1988, p. 283-334 (hereafter CF88). These rates are based on experimental information prior to August 1987. Certain rates have since been updated. We have added a graphical interface to choose rates from the table of the isotopes, tabular values of the reaction rate on the same temperature grid as used in Caughlan and Fowler, as well as GIF and Postscript Plots of the reaction rates vs. temperature. We have added temperature derivatives of the forward and reverse reaction rates, useful for coupling the reaction rates to the hydrodynamics of astrophysical sites. The derivatives were calculated symbolically with Mathematica ®. We have also added downloadable FORTRAN programs for calculating both the reaction rates and their temperature derivatives.

Graphical Interface to choose reactions from the table of isotopes

Directory of CF88 Reaction Rates, with links to
Analytic Expressions, Tabular Values,
GIF and Postscript Plots, and Temperature Derivatives

FORTRAN Program to calculate all CF88 Reaction Rates

FORTRAN Program to calculate all Temperature Derivatives of CF88 Reaction Rates

Reaction Rate Update information

Copyright Information

Reaction Rate Details

We have assigned each rate and its inverse a number, corresponding to the order in which they appear in CF88.
We have written the rates and temperature derivatives in the form of a FORTRAN program.
The temperature range, unless noted, is 10⁶ to 10¹⁰ K, or T9 = 0.001 to 10.
Certain rates [H1(P,E+NU)H2, H1(E-P,NU)HE3, HE3(E-,NU)H3, HE3(P,E+NU)HE4, C12+O16] have maximum temperatures T9max below T9 = 10; for T9max < T9 < 10, we have set these rates equal to their values at T9max.
One rate [the reverse of HE4(A)BE8] has a minimum temperature T9min above T9 = 0.001; for 0.001 < T9 < T9min, we have set this rate equal to its value at T9min.
When necessary, we have explicitly carried through the multiplication implied in CF88's reverse reaction rate ("REV RATIO") terms. This is to avoid computational overflows at the lowest temperatures.
We have inserted rate coefficients to replace the CF88 notation "(0 to 1)", which multiplies individual terms in some reaction rates.

Units & Notation

Q	Q value for the reaction in MeV.
T9	Temperature of the reactants in units of 10⁹ K.
T9nm	Notation for (T9)^(n/m), [e.g. T932 = (T9)^3/2].
T9maxj	Maximum valid temperature of jth Reaction Rate (see CF88).
T9minj	Minimum valid temperature of the jth Reaction Rate (needed for reverse rate #26).
RHO	Density in units of g/cm³.
X	Mass fraction of hydrogen.
rcj	Rate coefficient of the jth reaction (varies from 0 to 1, initially set to intermediate value of 0.1).
fj	Rate of the jth reaction in (cm³/moles)^(N-1) /s, where N is the number of particles involved in the reaction.
rj	Reverse rate of the jth reaction in (cm³/moles)^(N-1) /s.
dfj	Temperature derivative of the rate of the jth reaction in (cm³/moles)^(N-1) /s /K.
drj	Temperature derivative of the reverse rate of the jth reaction in (cm³/moles)^(N-1) /s /K.

Last modified September 25, 1998.

Contributors to these Caughlan and Fowler Reaction Rate Compilation Pages:

Michael Smith, Physics Division, Oak Ridge National Laboratory
Zhanwen Ma, Chinese Institute for Atomic Energy
Barry H. Cain, U.S. Department of Energy
Mohini Gupta, University of Bombay

Research sponsored, in part, by the Oak Ridge National Laboratory, managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under contract number DE-AC05-96OR22464.

Any questions or comments should be directed to Michael Smith at msmith@mail.phy.ornl.gov