[continues from 4.7.1]

### 4.7.2 Low energy tail

A monochromatic line gives rise not only to a Gaussian line, but shows also a tail on the low energy side (extending below 1 keV where the Be window is not transparent). The physical reason is that part of the electrons generated by an X-ray may attach to the Be window itself instead of propagating in the drift region (see GSPC operation).

Fig. 4.7.2-I : Example of the spread of a simulated spectrum generated by a 3 keV and 7 keV monochromatic line. The gaussian and tail components (unnormalized) are shown, as well as their (normalized) combination.

The tail is empirically modelled by a complex function (defined only above 1.255 keV) :

```
Ti(Ej) = D4 + D5 exp( (PI-D6)/D7) 			if PI<D6

Ti(Ej) =   D5 exp(-0.5 [3(PI-D6)/(D2-D6)]2) 	 	otherwise

```

where the symbols are as follows :

• PI indicates the i-th output channel
• D2 is the peak of the gaussian component of given energy, given by the gain relation
• D4 is computed indirectly as a function of energy as a quadratic polynomial of the Xenon absorption efficiency (3 coefficients L1,1, L1,2, L1,3 necessary)
• D5 depends on other terms and is given by formula
`     D5 =(C/D7)/(1-exp[(L4-D6)/D7)])`
• where C is a quadratic polynomial of energy up to 8.04 keV, then remains constant (3 coefficients L2,1, L2,2, L2,3 necessary)
• D6 is given by a linear function of energy in two separate stretches (of same slope L5,3, but with two different intercepts L5,1 and L5,2 below and above the Xenon L-edge)
• D7 is computed via the gain relation from a single coefficient L3
• L4 is an independent coefficient giving the start channel above which the tail is defined
The values of the coefficients L are kept in files m{1,2,3}_tail.coeff
The notation Li,j refers to the i-th line and j-th position in line in the file.

Fig. 4.7.2-II : Energy dependency of tail parameters D4 and D5. The values for the different MECS units (colours) are quite similar. Note that coefficients are meaningless (dotted line) below 1.25 keV where the tail is not defined.

Additional representations of simulated spectra can be obtained via the following form. Data is always generated for the three MECS units.

Select energy keV, representation and type of spectral component
Gaussian component (unnormalized)
Tail component (unnormalized)
Their combination (normalized)