Integrated yields

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(separated p-gamma event calculation into a new subsection)
 
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After an integration, the cross section in mb is obtained by multiplying the yield by
After an integration, the cross section in mb is obtained by multiplying the yield by
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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
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the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>.   
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p-gamma counts expected using the equation following equation 6.44b in the manual:
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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>
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===Detected p-gamma coincident events===
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If the absolute efficiency is known well, then it is possible to retrieve
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The absolute p-gamma counts expected can be calculated using the equation following equation 6.44b in the manual:
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<math>N_i = 10^{-30} [Q / qe] [N_A / A] Y(I_i-->I_f) \epsilon_p \epsilon_\gamma \Delta \Omega_\gamma</math>, (1)
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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,
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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
the actual counts measured in the photopeak by putting the efficiency into this
equation.
equation.
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In the equation above the <math>epsilon_gamma</math> is the absolute
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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
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.
integrated in the "yield").  Let this be called the absolute photopeak efficiency.
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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 10--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>.
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The <math>\Delta\Omega_\gamma</math> term is the solid angle of the Ge detector.  A typical absolute photopeak efficiency  
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<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>.
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If the laboratory setup and the EM matrix are accurately represented in the Gosia input, then the absolute counts can be obtained:
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<pre>
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N
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<\pre>
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Refer to the page on the [particle_singles], which is a cross section given in the same output with the integrated yields.
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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
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Maybe the answer to your last question is obvious now, but...  I would not try
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<math> N_\gamma = 10^{-30} N_p [N_A / A] Y_\gamma \epsilon_p \epsilon_\gamma \Delta\Omega_\gamma </math> (2),
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to think of this as correcting for 4pi, since the gamma-ray angular
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distribution has to be calculated as a function of theta, phi for 4pi in order
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to make that correction.  If you really want Gosia to tell you what the total
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yield would be for a 4pi array, you can change the *.gdt file entries after
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running OP,GDET.  For Gammasphere the *.gdt file would look something like
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<pre>
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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.
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  1
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  25.0
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  5.000E-02
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0.  0.  0.9951
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0.  0.  0.9854
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0.  0.  0.9711
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0.  0.  0.9521
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0.  0.  0.9379
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0.  0.  0.9013
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0.  0.  0.8699
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0.  0.  0.8349
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</pre>
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where the first two columns have been set to 0. to simulate a 4pi array--no
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Refer to the page on the [[particle_singles | particle singles]], which is a cross section given in the same output with the integrated yields.
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angular attenuation.  Then you would have in the YIELD column of the output the
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p-gamma events where the particle hit the detector as you defined it and the
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gamma ray is measured at all angles.  In this case the epsilon_gamma would
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still be the absolute photopeak efficiency, but DeltaOmega_gamma would be 4*pi.
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See pages 48 and 117 in the newest manual version, if you want to do this.  You
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==Representing a <math>4\pi</math> Array in Gosia==
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should be able to figure out that the first two entries in the file above
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should be zero to represent a perfect 4pi array.
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I hope that is all clear.  I can't ever figure out a brief way to explain
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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]].
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things.  Maybe after you figure this out, you can put it on the Wiki.  Your
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questions come up often.
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Latest revision as of 13:40, 15 June 2011

Retrieved from "https://www-user.pas.rochester.edu/~gosia/mediawiki/index.php/Integrated_yields"
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