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.