Calculation of total ionization cross section

[vrinda mukund]

Hai all,
I need some help in understanding the calculation of total ionization cross section. As per the literatures, for a gas capable of multiple ionization, the total cross section is a charge-weighted sum of partial ionization cross sections. To be more elaborate, consider the case of Xenon. Upon electron impact, Xe can become Xe+ or Xe2+ or Xe3+ ... , cross sections of which are respectively represented as σ1, σ2, σ3 ... etc.
Then total ionization cross section for Xe will be calculated as
σtotal = σ1+ (2*σ2) +(3*σ3)+... .
So my question is, why can't we just add the partial ionization cross section to calculate total ionization cross section instead of adding charge weighted sum ?

 

[mfb]

Do you want to calculate how many xenon atoms get ionized (independent of their state), or how many electrons get set free?
Also, Xe3+ can capture electrons from other xenon atoms afterwards, leading to 3 Xe+ ions for example.