Integrated yields

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(creation--rough draft from an email)
(separated p-gamma event calculation into a new subsection)
 
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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>.   
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angle of all crystals in the raw cluster.  So, after an OP,INTG or OP,INTI
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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===
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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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The absolute p-gamma counts expected can be calculated using the equation following equation 6.44b in the manual:
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the actual counts in the peak, since you are putting the efficiency into the
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equation.
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In the equation above and your equation (1), the epsilon_gamma is the absolute
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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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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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efficiency, but I always worry that people understand the terms differently.  I
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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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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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The answer to your first question, is the factor N_gamma_p only the sum below
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If the absolute efficiency is known well, then it is possible to reproduce
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the photo-peak, is yes, as long as you are using the photopeak efficiency as I
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the actual counts measured in the photopeak by putting the efficiency into this
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mentioned above.
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equation.
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You definitely don't need any other corrections for the cascade in Gosia's
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In the equation above the <math>\epsilon_\gamma</math> is the absolute
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"yield."
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efficiency as a fraction between 0 and 1 (not including angular effects already
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integrated in the "yield").  Let this be called the absolute photopeak efficiency.
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About the "singles," they are the latter: the total number of particles hitting
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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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the detector.  Gosia should reproduce this number using the "integrated
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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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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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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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excitation.
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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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