Tail background function

According to the original HYPERMET concept, a slowly decreasing exponential background tailing component may also be used under the low energy side of the peaks, in order to compensate detector surface effects.

Nowadays, however, this phenomenon seems to be less significant with the most common detectors, therefore when you perform a peak evaluation with “Default settings for moderate count rate, regular peaks” configuration, tail will be disabled.

As tail also descends from a convolution of an exponential and a Gaussian, it is very similar to Left skew, but has much less intensity and greater slope.

The picture shows the case of Tail Amplitude=0.01 and Tail Slope=2.5 parameters.

Tail counts may be calculated by the following formula at channel x:

where

	TLAmpl:	Tail Amplitude relative to that of Gaussian (may vary from 0 to 0.01)
	TLSlope:	Tail Slope (2.5 – 50)
	Ampl:	Amplitude of Gaussian
	Pos:	Position of the Gaussian centroid
	Width:	Gaussian width (Width = FWHM/1.66),

and erfc is the standard complementary error function.

Note: If you observe significant scattering of Chi values in the peak fitting residual under the majority of the singlet peaks, and this may not be resolved by adding new peaks, it is possible that the background tail component should be enabled. This may be done either by manually enabling the component in the Peak evaluation algorithm settings window, or selecting another algorithm setting, where tail has been enabled previously.