Integrated yields
From GOSIA
(more clean-up) |
(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 | ||
| - | the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>. | + | the Ge solid angle in <math>sr</math> and dividing by the target thickness in <math>mg/cm^2</math>. |
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| - | Detected p-gamma coincident events | + | ===Detected p-gamma coincident events=== |
| - | + | The absolute p-gamma counts expected can be calculated using the equation following equation 6.44b in the manual: | |
| - | If the absolute efficiency is known well, then it is possible to | + | <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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<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>. | <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 | + | 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), |
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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. |
Refer to the page on the [[particle_singles | particle singles]], which is a cross section given in the same output with the integrated yields. | 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]]. | |
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| - | See the | + | |
