Simulation (experiment planning)

==Introduction==

In Gosia, 'simulation' can mean simply performing a Coulomb excitation calculation with known matrix elements and initial guesses at the unknowns.  This would generally involve an 'OP,INTI' integration over the laboratory solid angle of the particle and Ge detectors.  The Gosia output can then be translated into expected counts of each decay transition in a planned beam run.

==Calculation of expected yields==

The expected total p-gamma counts can be obtained from the Gosia output as follows.  The output of the integration gives cross sections in mb mg/cm^2/sr in the "YIELD" column:

<pre>
                                                  INTEGRATED YIELDS

     EXPERIMENT  5  DETECTOR  1
     ENERGY RANGE  967.500--- 985.000 MEV   SCATTERING ANGLE RANGE  24.000--- 31.000 DEG

     NI     NF     II     IF     YIELD     NORMALIZED YIELD

     21      2    3.0    2.0   0.13010E+01   0.94604E-01
     21      3    3.0    4.0   0.27412E+00   0.19933E-01
     21     20    3.0    2.0   0.16659E-03   0.12114E-04
     20      1    2.0    0.0   0.14124E+01   0.10270E+00
     20      2    2.0    2.0   0.15701E+01   0.11417E+00
     20      3    2.0    4.0   0.36551E-01   0.26578E-02
      5      4    8.0    6.0   0.13752E+02   0.10000E+01
      4      3    6.0    4.0   0.49997E+02   0.36356E+01
      3      2    4.0    2.0   0.10556E+03   0.76756E+01
      2      1    2.0    0.0   0.35444E+02   0.25774E+01
               ********* END OF EXECUTION **********
</pre>

In these yields, the 1/sr units refer to the solid angle subtended by the Ge detector numbered '1' in the Gosia input file.  To convert these yields to the expected counts during a beam run, the following formula can be used:

<math>N = 10^{-30} P (N_{Av} / A) Y \epsilon  \Delta\Omega</math>

where N is the total p-gamma count expected in the laboratory, P is the total incident number of beam particles during the experiment, <math>N_{Av}</math> is Avogadro's number, A is the mass of the beam particle in g/mol, Y is the yield of the desired transition from the YIELD output, <math>\epsilon</math> is the absolute efficiency for the corresponding gamma-ray energy, and <math>\Delta\Omega</math> is the solid angle subtended by detector #1 above.  ''Note that this is equivalent to the formula given in the OP,INTI and OP,INTG sections of the Gosia manual.''

==Test-fitting matrix elements==

Once estimated counts are calculated, these can be fed back into Gosia as simulated data to perform a test fit of the desired measurements (matrix elements).  This is done by assigning counts as in the section above (on an arbitrary scale) and corresponding predicted error bars and entering them into Gosia's file #3.  The format of this file is given in the Gosia manual section XXX.

Refer to the [[Fitting]] page for examples of fits to simulated or real yield data.

Once a fit is obtained, the accuracy can be ascertained by comparing the final values of the matrix elements with those used to simulate the data. 

==Estimating the precision of measurements==

The precision of a desired measurement can be predicted by running a [[correlated error]] calculation following the test fit(s) to simulated data.  This provides an estimate of the uncertainties expected in the actual experiment.