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>.  

===Detected p-gamma coincident events===

The absolute p-gamma counts expected can be calculated using the equation following equation 6.44b in the manual:

<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>, (1)

where <math>Q</math> is the integrated beam current incident on the target during the experiment, <math>q</math> is the average charge state of the beam, <math>e</math> is the electron charge, 

If the absolute efficiency is known well, then it is possible to reproduce
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 reproduced.  By appropriately combining the terms in equation (1) above, it can be rewritten

<math> N_\gamma = 10^{-30} N_p [N_A / A] Y_\gamma \epsilon_p \epsilon_\gamma \Delta\Omega_\gamma </math> (2),

where <math>N_p</math> is the total number of ''incident'' particles, <math>N_A</math> is Avogadro's number, <math>A</math> is the mass number of the target species, <math>Y_\gamma</math> the yield given by Gosia (using OP,INTI), <math>\epsilon_p</math> is the particle-detection efficiency, <math>\epsilon_\gamma</math> is the <math>\gamma</math>-detector absolute photopeak efficiency, and <math>\Delta\Omega_\gamma</math> is the solid angle subtended by the Ge detector.

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

==Representing a <math>4\pi</math> Array in Gosia==

A <math>4\pi</math> array can be represented in Gosia in a single calculation without summing the output of a large number of detectors.  See the page on [[four_pi_arrays | 4pi arrays]].