#### Topic: How to compute astrophysical reaction rates from experimental data

Usually, reaction cross sections or astrophysical S-factors are quoted in experimental papers. In order to use the data in astrophysical calculations, it is necessary to convert the given values to astrophysical reaction rates. This is not straightforward because there are two problematic points:

1) The data usually cover only a limited energy range and may be largely spaced;

2) error bars have to be considered.

These points pose difficulties for computing the rate by numerically solving the relevant integral (see, e.g., the definition of the nucleus-nucleus reaction rate).

In order to facilitate the task I provide the FORTRAN 90/95 program 'exp2rate.f90' which automatically takes care of these points.

The main features of the program are:

1) Cross sections or S-factors can be used as input. If cross sections are given, the S-factors are additionally computed and written to file. *Internally, S-factors are used in the integration for better accuracy.*

2) The data is interpolated in the integration. It can be chosen whether a linear or a spline interpolation is used.

3) **The rates are only computed for a valid range of temperatures defined by the data.** The valid temperature range is *automatically* determined from *numerical* considerations.

4) **The experimental error bars on both data and energy are taken into account.** This yields a rate with error bars!

Experimentalists are especially invited to make use of this program to provide derived reaction rates *with error bars* in their papers.

For further details see the instructions contained in the comment section at the beginning of the program.

**Special note:** Sometimes the approximate formula for the Gamow peak given in Eqs. 4.21 and 4.25 of the Rolfs & Rodney book "Cauldrons in the Cosmos" is used to determine the relevant energy/temperature range. However, this is an *approximation* which decreases in accuracy with increasing charge of the particles and only applies for constant S-factors! The above program *numerically* determines the actual Gamow peak using the provided data and therefore is *more accurate*.