Integrated yields

==The meaning of Gosia's YIELD output==

Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG) 
including all feeding, internal conversion branches and angular distributions. These calculations are referred to as ''integrations'' below.   
The p-<math>\gamma</math> angular distribution is integrated over the target thickness and
the Ge solid angles, but the resulting "YIELD" is quoted in units of <math>mb (mg/cm^2) / sr</math>, where sr represents the solid
angle subtended by the Ge.  This leads to some common misunderstandings.  

The quoted yields represent the absolute cross sections for the chosen particle scattered into the solid angle of the particle detector and the <math>\gamma</math>-ray emitted into the solid angle of the Ge crystal or array, whichever is defined by the user.

The reason for the confusion is usually the units of the YIELD output and two
factors&mdash;the target thickness and the Ge solid angle&mdash;that often must be applied
after the integration.

After an integration, the cross section in mb is obtained by multiplying the yield by
the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>.  You can also calculate the absolute
p-gamma counts expected using the equation following equation 6.44b in the manual:

Detected p-gamma coincident events 

<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>

If the absolute efficiency is known well, then it is possible to retrieve
the actual counts measured in the photopeak by putting the efficiency into this
equation.

In the equation above the <math>\epsilon_\gamma</math> is the absolute
efficiency as a fraction between 0 and 1 (not including angular effects already
integrated in the "yield").  Let this be called the absolute photopeak efficiency.
The <math>\Delta\Omega_\gamma</math> term is the solid angle of the Ge detector.  A typical absolute photopeak efficiency 
<math>\epsilon_\gamma</math> is 0.1 to 0.15.  If the solid angle subtended by the crystal is  ~0.1 sr, then for one crystal <math>\epsilon_\gamma \Delta\Omega_\gamma ~ 0.01</math>.

If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be obtained:

<pre>
N...
</pre>

Refer to the page on the [[particle_singles | particle singles]], which is a cross section given in the same output with the integrated yields.



==Quickly representing a summed 4pi array==

Gosia can quickly integrate the p-gamma events over a <math>4\pi</math> Ge array without adding a detector at every laboratory position.  In order to do this, 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.