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Gamma Ray Peak (Gaussian + Compton Edge)
a0 = Amplitude (photopeak)
a1 = Center (energy photopeak and edge)
a2 = width (photopeak and edge smearing)
a3 = calibration (MeV/channels)
a4 = edge magnitude (as fraction of a0)
me = mass electron (.511004116)
Built in model:GammaRay
User-defined peaks and view functions: GammaRay(x,a0,a1,a2,a3,a4)
Gaussian Photopeak, Shared Response Fn
The Gamma Ray model combines an amplitude Gaussian with a Gaussian-smeared Compton edge function. This is a five parameter model which assumes the photopeak is Gaussian, and also that the Compton edge is smeared by the same Gaussian response width as the photopeak.
The model requires that channel 0 represent an energy of 0. If this is not so, you must first use a transform to adjust the data, compensating for any non-zero offset.
Evaluation of Integral
We do not have a closed form for the convolution integral representing the Gaussian-smeared edge, and as such this function uses numeric integration, making it PeakLabís slowest function.
This function cannot be automatically placed. Right click the main anchor of the peak automatically positioned at the photopeak and change to the Gamma Ray model. You will then need to adjust the five parameters directly. All values must be positive. The initial estimates assume a 1 MeV midpoint in the graph. You must set the calibration parameter a3 so that the correct edge matches the photopeak. You can lock a3 if you know the calibration accurately. If the edge itself was automatically detected as a separate peak, you will need to either toggle this peak off or delete it.
You must set the Curvature Matrix in Fit Preferences to Full. In the gap between the photopeak and Compton, it is possible that both functions will have decayed to where the sparse matrix procedure will detect a significance limit for the function. This procedure should never be used when fitting a Gamma Ray model.
We thank Dr. Larry Levit for his expertise and assistance in making this function possible in PeakLab. As with earlier versions of the product, this model should be considered experimental.