Four pi arrays

==Representing a summed 4pi array with Gosia==

Gosia can quickly integrate the p-<math>\gamma</math> events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position.  (Doing so would require the user to sum the yields for each detector after the calculation, and this would make the fitting of matrix elements extremely tedious.)  In order to represent a <math>4\pi</math> array, the output file 9 can be modified to make the first two attenuation coefficients 0 for all orders.  (File 9 is the output of OP,GDET, commonly called the *.gdt file.  For Gammasphere the *.gdt file would look something like

<pre>
  1
  25.0
  5.000E-02
0.  0.  0.9951
0.  0.  0.9854
0.  0.  0.9711 
0.  0.  0.9521 
0.  0.  0.9379 
0.  0.  0.9013 
0.  0.  0.8699 
0.  0.  0.8349
</pre>

where the first two columns have been set to 0. to simulate a 4pi array.  In this case the <math>\epsilon_\gamma</math> value would
still be the absolute photopeak efficiency, but <math>\Delta\Omega_\gamma</math> would be 4*pi.

See the manual entries on OP,GDET and "Gamma Detector Solid Angle Attenuation Factors" for more information on these attenuation coefficients.

The accuracy of this calculation depends on the uniformity of the array's acceptance over <math>\theta, \phi</math> polar and azimuthal angles.  For example, the largest gap in coverage in Gammasphere is near <math>\theta=0</math>, <math>\phi=0</math>.  If this non-uniformity does not have a significant influence on the accuracy, then the technique above using the angular attenuation coefficients can be used.  

Approximately uniform gaps in the acceptance of the Ge array can be absorbed into the overall absolute efficiency of the array.  Since Gosia fits to ''relative'' <math>\gamma</math>-ray yield data, the absolute efficiency has no influence on the "typical" calculations.  (See the page on [[normalizing_to_the_rutherford_cross_section | normalizing to the Rutherford cross section]].  This technique requires special considerations.)