Integrated yields

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(creation--rough draft from an email)
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Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG)  
Gosia calculates the complete excitation and decay process using OP,INTI (or OP,INTG)  
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including all feeding, internal conversion branches and angular distributions.
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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 p-<math>\gamma</math> angular distribution is integrated over the target thickness and
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the Ge solid angles, but the resulting "YIELD" is quoted in units of <math>mb (mg/cm^2) / sr</math>.   
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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
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angle subtended by the Ge.  This leads to some common misunderstandings.   
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This leads to  a common misunderstanding--that Gosia
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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.
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does almost everything. The reason for the confusion is in the units and two
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factors--the target thickness and the Ge solid angle--that must be applied
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The reason for the confusion is usually the units of the YIELD output and two
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factors&mdash;the target thickness and the Ge solid angle&mdash;that often must be applied
after the integration.
after the integration.
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The "yield" from gosia is in mb(mg/cm^2)/sr, where sr represents the solid
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After an integration, the cross section in mb is obtained by multiplying the yield by
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angle of the Ge.  In the case of a raw detector, it should be the total solid
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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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angle of all crystals in the raw cluster.  So, after an OP,INTG or OP,INTI
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p-gamma counts expected using the equation following equation 6.44b in the manual:
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calculation, the cross section in mb is obtained by multiplying the yield by
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the Ge solid angle in sr and dividing by the target thickness in mg/cm^2.  You can also check the absolute
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p-gamma counts expected using equation after 6.44b in the most recent manual version:
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Detected p-gamma coincident events Ni = 10^(-30)[Q/qe][N_A/A] Y(I-->I_f) epsilon_p epsilon_gamma
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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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DeltaOmega_gamma
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If your absolute efficiency is known well, then you should be able to retrieve
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If the absolute efficiency is known well, then it is possible to retrieve
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the actual counts in the peak, since you are putting the efficiency into the
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the actual counts measured in the photopeak by putting the efficiency into this
equation.
equation.
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In the equation above and your equation (1), the epsilon_gamma 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
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integrated in the "yield").  I think this is properly called the intrinsic
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integrated in the "yield").  Let this be called the absolute photopeak efficiency.
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efficiency, but I always worry that people understand the terms differently.  I
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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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would call it the absolute photopeak efficiency, not efficiency per unit solid
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angle, because the solid angle is in the yield term and Delta_Omega.  The
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DeltaOmega_gamma is the solid angle of the crystal or cluster.  I would expect
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your efficiency epsilon_gamma to be 10--15%.  If you have about 0.1 sr solid
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angle subtended by a crystal, then for one crystal epsilon_gamma *
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DeltaOmega_gamma ~ 0.01, and for a cluster of 4 ~0.04.
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So you can see if the numbers match what you fit in the energy spectrum.
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The answer to your first question, is the factor N_gamma_p only the sum below
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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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the photo-peak, is yes, as long as you are using the photopeak efficiency as I
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mentioned above.
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You definitely don't need any other corrections for the cascade in Gosia's
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<pre>
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"yield."
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N
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<\pre>
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About the "singles," they are the latter: the total number of particles hitting
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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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the detector.  Gosia should reproduce this number using the "integrated
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rutherford cross section," which probably shouldn't be called "Rutherford,"
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because it includes all the inelastic events.  For the scattering kinematics,
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Gosia assumes that the Q-value is the energy of the first excited state--state
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#2 in LEVE.  You can change this using the CONT option NCM, if you think that
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the probability of that state is <<1, for example.  In that case, you might
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pick the ground state. If you put
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OP,STAR
 
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OP,EXIT
 
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in place of OP,YIEL, you can quickly see the probabilities of all states in the
 
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excitation.
 
Maybe the answer to your last question is obvious now, but...  I would not try
Maybe the answer to your last question is obvious now, but...  I would not try

Revision as of 14:02, 1 June 2011

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