I have made also the inverse square law fits. We have data only for 90degre with the 241Am source, but both for the 1. and 2. calibrations. The 1. and 2. calibration data sets treated separate.
2 peaks were investigated, 59.5keV and 26.3keV, at two distances 184.8mm and 217.3mm. These distances are the sum of 4 distances:
a = width of plastic head. uncert.: +/- 0.05mm, measured with caliper.
b = width of the brass collimator. uncert.: +/- 0.05mm, measured with caliper.
c = width of protector plastic ring. uncert.: +/- 0.05mm, measured with caliper.
d= distance of the paper head. uncert: +/- 0.5mm, judged by the eye :)

The Be window and the dead layer of the Ge detector is not taken into account.

The distances calculated as D=a+b+c+d.

The conclusion is that the uncertainty coming from the distance measurements are negligible compared to the other uncertainties. The data obey the inverse square law.


> For all 3 detector the calibration data sets were combined to include the systematics in the fit results directly. Combining means not a weighted average, just simple all data points were included into the fit --> doubled efficiency value for most of the energies.
> The g(x) = a * (1-exp(-(x-c)/b)) * exp(-x/d) function was used to describe the behavior of the Germanium detectors for the whole range of energies (global behavior). From these fits the 80keV outlier point was excluded. This is very strange that it doesn't follow the trend, it would be nice to find out why not.
> Between 40-75keV a linear fit was carried out as well. This can also approximate quite well this local energy range, what we need for the K-REC peaks.
> l(x) = m*x+e
> 
> All the fits were done by gnuplot, but it was also confirmed that ROOT gives us the same parameters + errors + chisquare. One just need to choose well the starting values :)
> 
> 
> 90° fits:
> degrees of freedom    (FIT_NDF)                        : 8
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.419915
> variance of residuals (reduced chisquare) = WSSR/ndf   : 0.176329
> p-value of the Chisq distribution (FIT_P)              : 0.994094
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> a               = 0.00308376       +/- 0.0005144    (16.68%)
> c               = 15.6259          +/- 2.035        (13.03%)
> b               = 9.36888          +/- 3.16         (33.73%)
> d               = 177.141          +/- 84.95        (47.95%)
> 
> degrees of freedom    (FIT_NDF)                        : 4
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.283372
> variance of residuals (reduced chisquare) = WSSR/ndf   : 0.0802998
> p-value of the Chisq distribution (FIT_P)              : 0.988405
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> m               = -6.22672e-06     +/- 1.836e-06    (29.48%)
> e               = 0.00256426       +/- 9.873e-05    (3.85%)
> 
> 
> 
> 145° fits:
> degrees of freedom    (FIT_NDF)                        : 6
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.379472
> variance of residuals (reduced chisquare) = WSSR/ndf   : 0.143999
> p-value of the Chisq distribution (FIT_P)              : 0.990247
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> a               = 0.0012346        +/- 0.0006794    (55.03%)
> c               = 11.3754          +/- 4.075        (35.82%)
> b               = 15.6961          +/- 13.2         (84.1%)
> d               = 116.084          +/- 99.83        (86%)
> 
> degrees of freedom    (FIT_NDF)                        : 2
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.327728
> variance of residuals (reduced chisquare) = WSSR/ndf   : 0.107405
> p-value of the Chisq distribution (FIT_P)              : 0.898161
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> m               = -2.39246e-06     +/- 1.278e-06    (53.42%)
> e               = 0.000848859      +/- 7.329e-05    (8.634%)
> 
> 
> 
> 35° fit:
> degrees of freedom    (FIT_NDF)                        : 7
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 1.40676
> variance of residuals (reduced chisquare) = WSSR/ndf   : 1.97896
> p-value of the Chisq distribution (FIT_P)              : 0.0538635
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> a               = 0.000114396      +/- 0.0002367    (206.9%)
> c               = 14.3178          +/- 8.322        (58.13%)
> b               = 16.7454          +/- 43.21        (258%)
> d               = 79.7991          +/- 173.2        (217.1%)
> 
> degrees of freedom    (FIT_NDF)                        : 3
> rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 1.21233
> variance of residuals (reduced chisquare) = WSSR/ndf   : 1.46975
> p-value of the Chisq distribution (FIT_P)              : 0.220529
> 
> Final set of parameters            Asymptotic Standard Error
> =======================            ==========================
> m               = -3.7879e-07      +/- 3.143e-07    (82.99%)
> e               = 7.31447e-05      +/- 1.788e-05    (24.45%)
> 
> 
> 
> > For the efficiency vs E fit of the 90degree Xray detector I have used the following phenomenological funciton:
> > 
> > f(x) = a * (1-exp(-(x-c)/b)) * exp(-x/d)
> > 
> > Here the first exponent member is a saturation curve. This part describes the passing through of the two Be windows (chamber + before detector) and through the dead layer of Ge crystal. One needs a minimum energy to enter to the detecting Ge crystal = C parameter. b parameter = characteristic absorbtion E of these nondetecting layers.
> > The second exponent is an exponential decrease of the detector efficiency. Photons with higher energy are less detectable by the germaniums. The d parameter is the characteristic E for hard Xray and gamma (>40keV) detectability. 
> > 
> > https://www.amptek.com/internal-products/si-pin-vs-cdte-comparison
> > 
> > //Jan's comment: the tail of this function should more or less follow a linear trend a bit above than 40 keV.
> > 
> > 
> > In the attachment there is an example fit for 90 degree with combined 1. and 2. (before and after beamtime) calibration datasets. 
> > I made the fit with gnuplot:
> > 
> > degrees of freedom    (FIT_NDF)                        : 8
> > rms of residuals      (FIT_STDFIT) = sqrt(WSSR/ndf)    : 0.419915
> > variance of residuals (reduced chisquare) = WSSR/ndf   : 0.176329
> > p-value of the Chisq distribution (FIT_P)              : 0.994094
> > 
> > Final set of parameters            Asymptotic Standard Error
> > =======================            ==========================
> > a               = 0.00308376       +/- 0.0005144    (16.68%)
> > c               = 15.6259          +/- 2.035        (13.03%)
> > b               = 9.36888          +/- 3.16         (33.73%)
> > d               = 177.141          +/- 84.95        (47.95%)
> > 
> > Laszlo's out.