I get this or similar questions so often recently that I decided to write a short summary on this topic here.*The short answer is: No, only in a very limited manner.*

The long answer, of course, is more differentiated. I cannot easily show equations or graphs here, therefore I try a verbal summary without those. For further details, please take a look at the literature at the end of this post. Here I just combine and summarize what is detailed in those articles. A review of all relevant effects is also found in [1] and photodisintegration in the gamma-process is discussed in [12]. Tables of sensitivities of cross sections and stellar rates to various nuclear properties and all ground-state (g.s.) contributions to the stellar rate (see below) are given in [10].

1. Experiments vs rates

The fact that photodisintegrations play a role in certain astrophysical processes often gives rise to the misconception that a photodisintegration measurement will directly help with determining the astrophysical reaction rate [7,8]. This is not the case. The reason is that, even when exciting the nucleus to an astrophysically relevant energy (and this is important because at higher energies so many additional effects are coming into play that it becomes difficult to impossible to extract the ones relevant in the astrophysical energy range), the photon-induced transition from the ground state with subsequent particle emissions is only a tiny fraction of all transitions appearing in the astrophysical case [1-4,10-13].

The majority of the relevant gamma-transitions have lower gamma-energy (about 2-4 MeV) and start at an already excited state of the nucleus (and therefore will probably also select different spin and parity quantum numbers) [1,2]. The ground state contribution to the stellar photodisintegration rate is always very small, often less than a percent [1,3,8,10-12]. Therefore, it is always recommended to measure the capture because there the ground state contribution is larger and thus the rate can be better constrained by experiment (although some theory may still be necessary) [1,3,10,13].

(The situation may be different for nuclei with very low particle separation energy (or reaction Q-value) but these nuclei are far from stability and not yet accessible by experiments [2,10].)

Why is this so? The reasons are somewhat hard to visualize without checking the equations. Three components act together [1]:

a) The principle of detailed balance in nuclear reactions states that there is a simple relation between forward and reverse reaction between a discrete initial and a final state. The cross sections are related by a simple phase space factor.

b) In astrophysics, most nuclei are in thermal equilibrium with the surrounding plasma and therefore are present also as excited nuclei, not just nuclei in their ground states. The fraction of nuclei in a specific excited state is given by its spin and a Boltzmann population factor depending on the energy of the excited state Ex and the plasma temperature: P=(2J+1)*exp(-Ex/(kT))

c) The projectile (or gamma) energies are also thermally distributed in a plasma. Obviously, the same energy distribution must act on a nucleus in the ground state and one in an excited state. This implies that the respective energy distributions (for example, Maxwell-Boltzmann or Planck distributions) are shifted relative to the ground state energy E0 and extending to higher excitation energy E0+Ex when acting on an excited state.

It is important to realize that a), b), and c) apply to all initial *and* final nuclei simultaneously in a reaction in an astrophysical environment.

Already from the notion that a capture reaction (with positive Q-value) releases gammas to a wider range of final states than particles (e.g. neutrons) are released in its reverse (photodisintegration) reaction we can see that a larger number of gamma transitions are relevant than particle transitions [2] (see also chapter 3 below). Astrophysical rates obey reciprocity between forward and backward reactions (in a rate all reactions on ground and excited target states are included and integrated over the energy distribution of the projectiles). This can be found by combining the principle of detailed balance a) and the thermal population of target states c). It also is easy to show that also in this case the number of participating transitions is larger in the exit channel of a reaction with positive Q-value [1,10,11].

Sometimes it leads to confusion when only looking at the Boltzmann population factors of the excited states as given in b). They seem to give similar weights to excited states in the initial and final channel. However, it is incorrect to take only these factors as a measure of the importance of initial states. Rather, folding these factors with the shifted energy distributions of the projectiles (or gammas) of c) and expressing everything in an energy scale relative to the ground state leads to a transformed weight: W=(2J+1)(1-Ex/Eeff), where Eeff is in the effectively relevant energy range for an astrophysical rate (aka the Gamow window) [1]. This has two implications. Firstly, it is a linear weight, more slowly declining than the exponentially declining Boltzmann factor. Secondly, the weight is relative to the Gamow energy which is higher in a reaction with negative Q-value. (When this energy is EG in the capture, then it is EG+|Q| in the photodisintegration.) Therefore, the weights decline more slowly and reach higher in the case of photodisintegration than in the case of capture.

Finally, folding the actual astrophysical weights W with the relevant gamma transition strengths (which are - close to stability - roughly about halfway between the ground state and the particle separation energy [2]) shows that the ground state contribution to astrophysical photodisintegration rates is small.

2. Implementation in reaction networks

For this and other (numerical) reasons, in astrophysical reaction network calculations only reactions with positive Q-value are included (also only measurements of such, with few exceptions) and the reverse direction is calculated using the reciprocity of stellar rates (which can be derived from a)+b)+c) above) [1]. Therefore, even if a measurement of a rate with negative Q-value would be able to constrain the astrophysical rate, it would have to be converted to its reverse first before being used in an astrophysical calculation [1,3,10,13].

3. Relevant energies

There are two important types of energies appearing in capture/photodisintegration studies. They are also connected.

The first type of relevant energy range are the projectile energies which give most of the contributions to the reaction rate integral. These are always given relative to the ground state of the target nucleus. They also specify the most important formation energies of the compound nucleus. The simple formula for the Gamow window of a reaction is only applicable to light nuclei, for intermediate and heavy targets, the reaction rate integrand (for the stellar rate including thermally excited target states) has to be examined [9]. The maxima and widths of the integrands are tabulated for a large number of nuclei (see this topic). The tables are for reactions with positive Q-value. As pointed out above, the relevant energy window (relative to the ground state of the final nucleus) for the reverse reaction can be computed easily by adding the Q-value to the tabulated energy window.

The other interesting energy range is that of the gamma-energies determining the gamma-width appearing in the reaction cross section. This is not necessarily the one given by the Gamow window. Rather, the Gamow window determines the excitation energy range in which the compound nucleus is formed and from which it decays (by gamma and/or particle emission). Although transitions from EG+Q to an excited state with Ex above the ground state are weaker because the relative gamma energy EG+Q-Ex is smaller, there are more levels available due to the exponentially increasing level density with increasing Ex. Thus, there is a competition between the decreasing individual gamma strengths and the increasing level density, leading to a maximum in the summed gamma strengths at about 3-4 MeV below EG+Q [2]. (This may only be different in nuclei with low level density up to EG+Q (perhaps because of a small Q) where single gamma transitions are important.) This is only slightly modified by the linear weights W acting on the excited state transitions in the astrophysical rate.

4. How can experiments help?

From the above, it is found that photodisintegration (with real photons or by Coulomb excitation) cannot directly constrain the astrophysical reaction rate. Capture reactions are much better suited for this as their ground state contribution to the stellar rate is much larger than for photodisintegrations. See [10] for complete tables of g.s. contributions across the nuclear chart; it can be seen that STELLAR photodisintegration rates almost always have extremely tiny g.s. contributions (with very few exceptions [13]). Therefore what is measured is closer to the value required in astrophysics. Nevertheless, further corrections from theoretical calculations may still be needed.

A (g,n) experiment thus tests the g-ray strength function (or gamma width) at much larger gamma-ray energy than the one of the g-rays actually contributing mostly to the STELLAR photodisintegration rate. In the past, a few (g,n) cross sections were measured (see, e.g., [6-8]) and an astrophysical rate was derived by renormalizing the predicted rate by the same factor as found when comparing the measured result with a prediction in the same model as used to calculate the rate. This implicitly assumes that any discrepancy found between experiment and theory for the much larger gamma energy of the g.s. photodisintegration equally applies also to the actually relevant transitions with smaller relative energy (or are due to the particle transitions in the exit channel). Usually, this is not a good assumption because the photon strength function behaves differently at low energy and the allowed partial waves in the particle transitions may have different relative angular momentum than the ones appearing in the astrophysical rate. Therefore the experiment does not really constrain the astrophysical rate.

Studying the behavior of gamma strength functions itself helps the predictions of astrophysical rates, both for captures and photodisintegrations. As mentioned above, the relevant gamma energies are of the order of 3-4 MeV [2]. Changes in the strength function within this energy range directly affect astrophysical capture and photodisintegration rates, changes outside that range are of smaller importance [2,12]. Unfortunately, this gamma-energy range can only be accessed indirectly, requiring a combination of experiment and theory. For example, (g,g') data can help to constrain the low-energy gamma-strength or -width. The (g,n) data cannot be used for this by themselves. Recent experiments (e.g., [14]) realized this and fit theoretical (g,g') data with theoretical models to use such models for the calculation of the stellar photodisintegration rate. Note that in such experiments also any (g,n) cross section, if measured, does not contribute much to the actual constraint of the stellar rate.

Because of the relevance of reactions proceeding on thermally excited target states in an astrophysical plasma, it is important to study (particle) transitions from these excited states. This can be done by studying the inverse transitions to such excited states in a particle exit channel. Photodisintegrations can achieve this, as can inelastic particle scattering (e.g., (n,n') [5,11,12]). One has to be careful in the interpretation of such experiments, however, because starting from a specific ground state introduces a selection of possible quantum numbers (relative angular momenta) which may be different from the astrophysically relevant ones. Nevertheless, this may allow testing the predictions of particle transitions to/from excited states by theoretical models and also the predicted ratios to the ground state transitions (e.g., (g,n1)/(g,n0), (g,n2)/(g,n0), ...; (g,a1)/(g,a0), (g,a2)/(g,a0), ...). [12]

(Additional information required in predictions of captures and photodisintegrations are low-lying discrete states and nuclear level densities above those discrete states.)

What is essential in all kind of experiments is to really measure within the relevant energy region! The gamma strength function has to be known around 3-4 MeV [2]. The compound formation energy is given by the Gamow window [9]. For neutron captures, the upper end of the relevant energy window is at most at 0.2 MeV, even at the high plasma temperatures encountered in explosive burning environments. This translates into an excitation energy of the compound nucleus of S_n+0.2 MeV (with the neutron separation energy S_n). The energy window of charged particles is shifted to slightly higher energy due to the Coulomb barrier but does not exceed a few MeV [1,9]. Measuring at much larger energy than the astrophysical one does not yield much relevant information in most cases. This is because at higher energy the cross sections show a different sensitivity to photon- and particle-strengths than at astrophysical energies and higher partial waves also play a role [1,10]. Furthermore, additional reaction mechanisms may occur which are not appearing in the astrophysical energy range [1]. At high energy, so many additional effects are coming into play that it becomes difficult to impossible to extract and compare the ones relevant in the astrophysical energy range.

5. Conclusion

Much can be learned from photodisintegration experiments (including experiments with real photons and Coulomb excitation). However, it should be clear that there are severe limitations in this method regarding astrophysical rates. Without further information (such as (g,g') data), a (g,n) measurement cannot be used to constrain the astrophysical rate or to even only test the reliability of model predictions of such rates. Data showing the relative particle emission to g.s. and excited states, though, may test to a certain extent the prediction of thermal modification of the stellar capture reaction. The situation is similar in photodisintegrations emitting charged particles. If measurements could study, however, charged particle emission below the Coulomb barrier, this would constrain the rate because at low relative energy, the cross section is determined by the charged particle width. Unfortunately, such cross sections are very small and outside the reach of current methods, especially for unstable nuclei.

*Of course, new ideas for directly measuring relevant quantities are welcome.*

For further details see:

[1] T. Rauscher, *The Path to Improved Reaction Rates for Astrophysics*, Int. J. Mod. Phys. E 20 (2011) 1071 (arXiv:1010.4283; the arXiv version includes a table of contents)

[2] T. Rauscher, *Astrophysical relevance of gamma transition energies*, Phys. Rev. C 78 (2008) 032801(R) (arXiv:0807.3556)

[3] T. Rauscher, G. G. Kiss, Gy. Gyürky, A. Simon, Zs. Fülöp, E. Somorjai, *Suppression of the stellar enhancement factor and the reaction 85Rb(p,n)85Sr*, Phys. Rev. C 80 (2009) 035801 (arXiv:0908.3195)

[4] T. Rauscher, P. Mohr, I. Dillmann, R. Plag, *Opportunities to constrain astrophysical reaction rates for the s-process through determination of the ground state cross sections*, ApJ 738 (2011) 143 (arXiv:1106.1728; note: although this focuses on s-process neutron capture, the same considerations with respect to the ground state contribution to the stellar rate can be applied to photodisintegration reactions)

[5] M. Mosconi, M. Heil, F. Käppeler, R. Plag, A. Mengoni, *Neutron Physics of the Re/Os clock. II. The (n,n') cross section of 187Os at 30 keV neutron energy*, Phys. Rev. C 82 (2010) 015803

[6] K. Sonnabend, P. Mohr, K. Vogt, A. Zilges, A. Mengoni, T. Rauscher, H. Beer, F. Käppeler, R. Gallino, *The s-process branching at 185W*, ApJ 583 (2003) 506 (arXiv:astro-ph/0209527)

[7] P. Mohr, K. Vogt, M. Babilon, J. Enders, T. Hartmann, C. Hutter, T. Rauscher, S. Volz, A. Zilges, *Experimental simulation of a stellar photon bath by Bremsstrahlung: the astrophysical gamma-process*, Phys. Lett. B 488 (2000) 127 (arXiv:nucl-ex/0007003)

[8] P. Mohr, T. Rauscher, K. Sonnabend, K. Vogt, A. Zilges, *Photoreactions in Nuclear Astrophysics*, Nucl. Phys. A718 (2003) 243

[9] T. Rauscher, *Relevant energy ranges for astrophysical reaction rates*, Phys. Rev. C 81 (2010) 045807 (arXiv:1003.2802)

[10] T. Rauscher, *Sensitivity of astrophysical reaction rates to nuclear uncertainties*, Ap. J. Suppl. 201 (2012) 26 (arXiv:1205.0685)

[11] T. Rauscher, *Formalism for inclusion of measured reaction cross sections in stellar rates including uncertainties and its application to neutron capture in the s-process*, Ap. J. Lett. 755 (2012) L10 (arXiv:1207.1664; note: although this applies the derived formalism to s-process neutron capture, the same considerations with respect to the ground state contribution to the stellar rate can be applied to any other reaction, including stellar photodisintegration reactions)

[12] T. Rauscher, N. Dauphas, I. Dillmann, C. Fröhlich, Zs. Fülöp, Gy. Gyürky, *Constraining the astrophysical origin of the p-nuclei through nuclear physics and meteoritic data*, Rep. Prog. Phys. 76 (2013) 066201 (arXiv:1303.2666)

[13] T. Rauscher, *Suppression of Excited-State Contributions to Stellar Reaction Rates*, Phys. Rev. C 88 (2013) 035803 (arXiv:1308.5816)

[14] H. Utsonomiya, et al., *Photoneutron cross sections for Mo isotopes: A step toward a unified understanding of (g,n) and (n,g) reactions*, Phys. Rev. C 88 (2013) 015805

Approximation formulas for charged and neutral projectiles are given in textbooks but those are insufficient for the application to intermediate and heavy targets.

A large scale study of the proper energy windows has been published in *Physical Review C* **81**, 045807 (2010), including an extended table with the actual energy windows. It was found that the relevant energy range can be shifted by several MeV (or sometimes tens of MeV) with respect to the energies obtained from the standard approximations. Although the results were obtained with cross sections averaged over many resonances, the derived energy windows are also applicable to resonant reactions, where they show the energy range of relevant resonances (although the individual contribution of resonances, i.e., how much each resonances contributes within the window, cannot be estimated).

It is recommended that the energy windows are taken from this table instead of using the standard approximation.

(see also this topic)

]]>This is a brief outline of how to proceed, including some general warnings of what can go wrong. Some of the remarks were written with fitting rates to the 7-parameter format used in REACLIB in mind. However, they should also apply to fitting any other format.

Part A: General remarks

1) For details on the definition of rates and the 7-parameter REACLIB format, see ADNDT 75, 1 (2000).

2) It is essential to fit rates in the direction of *POSITIVE Q-value* unless absolutely no information is available for that reaction. Otherwise, any fit errors will be enhanced when computing the rate in the other direction by detailed balance. The fit parameters for the reverse direction can easily be computed from the relations given in Eq. (17) of ADNDT 75, 1 (2000). The fit parameters for both forward and backward reaction have to be included in REACLIB. It is also essential that both sets are derived from the *same fit of ONE direction* and application of Eq. (17) for the other direction! Separate fits of forward and backward reactions can NEVER be used, they are not consistent and may lead to numerically unstable network equations! This applies for all reaction networks, not just those using REACLIB.

3) Usually, fits are only valid in some temperature region. In REACLIB, this is T9=0.01-10. Nevertheless, *it is extremely important that the fits behave well also outside this range. They must not diverge and must not show unphysical oscillation patterns* (as sometimes obtained with polynomial fits). Specifically, charged particle rates should go to Zero for T9->0. Neutron capture reactions should become constant or go to zero for T9->0, depending on whether they are s-wave dominated or not.

Part B: Creating the required data set

1) Make sure the rate values (either from experiment or calculations) cover at least the temperature range of validity (see above) for the fit. Obviously, cross section data have to be converted to rates first. For the conversion and to check whether the covered temperature range is sufficient, my program exp2rate.f can be used (see also "How to compute astrophysical reaction rates from experimental data" in this forum). For interpolation (to obtain a more narrow energy/temperature grid for improved fitting) use, e.g. my small program interpolate.f (see also "How to obtain values at arbitrary energies/temperatures" in this forum).

2) If the obtained temperature range is not sufficient, the data have to be supplemented to cover the missing part(s). This has to be performed with extreme caution. Knowledge about reaction mechanisms, additional information, and a lot of experience are usually necessary in order to make an educated guess about the behavior of the cross section and rate. Renormalization of theoretical predictions (both for the Hauser-Feshbach and direct mechanism), inclusion of resonance information, simple extrapolations: Any combination of these may be necessary. Further details are beyond the scope of this description.

3) If distinct resonances are contributing, it may be helpful to split the data sets into the different contributions or to prepare analytic functions for the resonance contributions (e.g., as provided in Caughlan & Fowler, ADNDT 40 (1988) 283). However, limit the number of separate entries to *as few as possible* (see also C.8 below).

Part C: Fitting the data set

1) In the following, "data" refers to all sets of reaction rates prepared as in Part B, regardless of whether they stem from actual experimental data or theoretical calculations.

2) Usually, satisfactory fits of the astrophysical rates can only be achieved with fit routines that allow for different weights of the data points. When writing your own fitting program, allow for automatic setting of the weights according to some or all of the following rules. If the program cannot compute the weights automatically, iterations with modified weights have to be run manually.

3) The fit criterion should always include relative deviations of the rates as these can vary across many orders of magnitudes, i.e. (abs(fit-rate)/fit)**2.

4) A first run can use equal weights at all temperatures (w=1.0) or consider the experimental errors (as, e.g., included when having used the code exp2rate.f).

5) After the run, check the quality of the fit by inspecting the average deviation (or other fit criterion) AND by testing the behavior of the fit outside the fitted temperature range.

6) The truly complicated game starts when this first attempt does not yield good results. Then it becomes necessary to play around with the weights. Two cases should definitely get lower weighting:

a) Very slow rates, i.e. rates below 1.e-18 or 1.e-20 or so. Even at high density, those rates would be too slow to change anything within the time scale of astrophysical burning (or the lifetime of the Universe). Therefore it is not necessary to reach any accuracy in such a case and deviations even of several orders of magnitude are acceptable! (Unless they make the rate too fast.) The reason why such rates should not be discarded completely is because they serve as constraints to suppress divergences in the fit. It is possible to allow weights that are exponentially suppressed when the rates become smaller, e.g. w=(rate/1.e-18)**0.03. For the same reason, whenever comparing fits to data, *it is of no importance when there are large deviations for such slow rates*!!

b) Rates at high temperatures, i.e. rates at about T9=5 and above. At high temperatures, all rates attain equilibrium (with the exception of neutrino rates and decays). The rates then cancel out from the equilibrium abundance distribution. The abundances are just determined from spins and Q-values. Nevertheless, the rates have to be included in the network to compute the proper abundances from the relation of forward and backward reactions and to follow the freeze-out (or heat-up) properly. Due to the latter, the fit accuracy should be higher than for the slow rates, e.g. w=0.1.

7) At the same time (with every new fit and change of weights) it has to be assured that the fit still behaves properly outside the fitted range and does not diverge. Divergences and oscillations again may be treated by modified weights. Another trick is to supply additional data points at very low and very high temperature and assign low weights to them. The values of these additional data points are obviously only crude extrapolations or educated guesses but because of their low weights, they should not change the fit in the valid region too much. They merely serve as constraints to prevent divergence.

a) Neutron capture: Additional values at low and high energy can be obtained by assuming s-waves (constant reaction rates) or p-waves (rate proportional to T).

b) Charged particles in the entrance or exit channel: For positive Q-values, the behavior will be dominated by the entrance channel because of the higher energy of the ejectile in the exit channel. Then the temperature dependence of the rate can be estimated from the penetration through the Coulomb barrier. However, when the projectile is a neutron, the Coulomb barrier has to be accounted for in the exit channel at the proper energy (neutron energy + Q-value). Barrier penetrations can either be estimated from a simple WKB approximation or by employing a formula similar to what was used in the fits by Woosley et al. in ADNDT 18 (1976) 305 and 22 (1978) 321.

8) It may prove difficult to fit single resonance contributions. In that case, the fit may be split up in two or more functions for the different contributions (see B.3) which are fitted separately. In REACLIB, additional entries (with the same 7-parameter format) appearing for the same reaction are simply added up. Therefore, make sure that the total rate can be constructed from the sum of the different contributions. Usually, Hauser-Feshbach rates (obtained from calculations in the compound nucleus reaction model) are easy to fit and do not require such splitting. Generally, the number of REACLIB entries should be *as few as possible* because it is computationally expensive to evaluate a large number of entries. For large reaction networks it is preferrable to have only one or (at most) two entries, even if this leads to a lower fit accuracy. *The true art of fitting is to get the best compromise between accuracy and the least number of separate entries for a rate!* The only exception is the fitting of nonresonant and resonant contributions to a rate; these should always be fitted separately because they are treated differently when applying screening effects. Ideally, even in this case one limits the fits to one entry each for the resonant and the nonresonant part.

9) After modifying weights and/or supplying additional data points, the fit has to be redone (go to C.5 above). The above procedure can be automatized to a certain extent. However, manual interference may be necessary for some cases.

D. Partition functions

1) Finally, partition functions (see Eq. (12) in ADNDT 75 (2000) 1) have to be supplied for relating forward and backward reactions. They are not included in the fits and have to be supplied separately. For REACLIB, they are included in the file WINVN. It includes partition functions up to T9=10. For higher temperatures, you may check out Ap. J. Suppl. 147 (2003) 403.

**Good luck!**

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*.

It is easy to use: Download the program 'interpolate.f90' and compile it. The values to be interpolated have then to be presented in the file 'interpol.dat' as x and y values, (you can just copy/paste the NON-SMOKER output into a text file).

A second file 'interpolate.tab' contains a table of the desired x values for which we want to compute interpolated values. The x values defined in that file should not lie outside the x range defined by the data; *this is interpolation, not extrapolation*!

Run the program and the computed values are written to the standard output.

**Hint:** For rapidly increasing or decreasing functions spanning several orders of magnitude (like astrophysical reaction rates or charged particle cross sections) it is always *more accurate* to interpolate the logarithm of the y values and recompute the values after interpolation. This can be done in two ways:

1) put x,log(y) in 'interpol.dat' and take the exponential of the returned value;

2) put 'log' as the first line in 'interpol.dat'; the code internally automatically takes the logarithm and performs the exponentiation before returning the value!

For further details see the comments in the code.

**Note 1:** NON-SMOKER automatically chooses an energy grid optimized to calculate the reaction rates on the standard temperature grid. It is more widely spaced when the cross section is smooth and can be interpolated easily and more densly spaced when a strong variation of the cross section occurs (at channel openings). Thus, the default cross sections are ideally suited for interpolation.

**Note 2:** There is an option in NON-SMOKER(WEB) to change the default energy grid. It is not advisable to use this option in order to extract results at the desired energies because the numerics of the calculations depend on this grid and a different grid can lead to different cross sections! Use the above program instead!