Rachel simulated yield output

''This page uses the output of Rachel version 1, which is more intuitive than that of the beta versions.''

The output to the terminal from a "simulated yields" calculation has the following format:

The simulation output now uses the standard definition of efficiency, and the default efficiency curve for any detector can be adjusted by the user.  The user will find prompts for the details of the planned beam run, and estimated absolute measured counts will be calculated and displayed.  The display format looks like the following:

<pre>
Experiment 1
Target excitation by Z,A = 54,136 at 517 MeV. Mean scattering angle = 45.0 deg.
Detector 1
Single crystal at theta, phi = 45.0, 45.0 deg. Solid angle = 0.06 sr.
This simulation does not include random gaussian scatter.  Counts represent the cross sections calculated by Gosia.      
       Transition             |  Gammas incident      |                     Fraction of |         Observed Counts        
                              |  on Ge detectors      | Gamma               Incident    |                                
 Initial         Final        |                       | Energy **Detector   Gammas      |                                
    Band Spin     Band Spin   | Counts    *Error      | (keV)   Efficiency  Detected    | Rate(Hz)   Counts  ***Error    
-------------------------------------------------------------------------------------------------------------------------
     gsb  1.5      gsb  0.5     4.662e+06  2.332e+05     100.0  0.00049     0.09962       1.075e+00  4.644e+05  6.815e+02
     gsb  2.5      gsb  0.5     1.570e+07  7.848e+05     200.0  0.00179     0.36853       1.339e+01  5.784e+06  2.405e+03
       a  2.5      gsb  0.5     1.079e+04  5.647e+02     250.0  0.00189     0.38907       9.719e-03  4.199e+03  6.480e+01
       a  2.5      gsb  1.5     9.816e+02  7.705e+01     150.0  0.00135     0.27823       6.322e-04  2.731e+02  1.653e+01
       a  2.5        b  3.5     4.689e+05  2.376e+04      75.0  0.00015     0.0312        3.387e-02  1.463e+04  1.210e+02
</pre>

The "Observed Counts" are calculated using the efficiency curve from the detector library or a detector created by the user.  The "Detector Efficiency" <math>\epsilon</math> is the usual definition.  Possion counting errors are based on the observed counts, while additional error on the ''total'' efficiency-corrected counts may be added by the user.


===Accuracy checking===

The predicted absolute counts (cross sections) for p-<math>\gamma</math> events were checked against perturbation calculations for weakly-coupled two-state systems where the perturbation method is valid.  Both the total count rates and solid angle factors have been re-checked in version 2.0.8.beta and agree with the perturbation calculations where they are applicable.  Many tests of fits to simulated yield data without the optional random error scatter resulted in <math>\chi^2</math> values very close to zero, as expected.

The ''intrinsic'' efficiency has been estimated more accurately in version 2.0.8.beta.  This will make a noticeable change in the "Raw counts" column.

===Simulated data passed to Gosia===

Note that Rachel operates Gosia such that efficiency-corrected "incident gamma" counts are passed to Gosia, but first they are divided by the solid angle of each Ge detector to match Gosia's calculation of yield per unit solid angle.  (This is true in Rachel versions >= 2.0.7.beta; in earlier versions this solid angle factor was neglected, which usually did not result in accuracy errors.)  All yields sent to Gosia are then multiplied by <math>4\pi</math> so that weak transitions have counts >=1.  This overall multiplicative constant of <math>4\pi</math> has no effect on fitting.  Refer to the page [[Normalization_of_yield_data | Normalization of yield data]] for more detail.