What do you mean by "electron impact width"? - are you referring to the electron cross sections for ionisation/excitation?

Broadening of line by electron impact (electron collision under the impact approximation)

Thank you Cher Manuel. What I want to know is exactly the first part of your answer (a physically interpretation). Mathematically the problem is clear for me.

Thank you again

Dear Lula, there are many approches to evaluate the electron impact widths: semi classical, quantum, semiemipirical... You want to calculate Stark broadening? for ions or neutral? How accurately you want to obtain results? I can provide you the appropriate formula and many useful references if you need.

Lula, you can consult my references (here in Research gate) for the quantum method. The details formalism is presented in the paper " Quantum mechanical calculations of the electron-impact broadening of spectral lines for intermediate coupling" in 2004, and several applications for Be-like ions "Electron impact broadening of spectral lines in Be-like ions: quantum calculations" in 2008 and "Quantum Stark broadening of 3s–3p spectral lines in Li-like ions; Z-scaling and comparison with semi-classical perturbation theory" for Li-like ions. You can see also "Quantum Stark broadening data for the C iv, N v, O vi, F vii and Ne viii resonance doublets" in 2011. May be expressions for Stark broadening depend on ions or lines that you will study also.

Line profiles are the Fourier transform of the dipole-dipole autocorrelation function. This means essentially {U_upper(t) U*_lower(t)} with U the time evolution operator for the bound atomic electron. In the impact approximation this is exp(-Phi t) where Phi is the width and given by

{S_upper S*_lower-1} with S the S-matric (U matrix from t=-infinity to infinity). In perturbation theory this is to first nonvanishing order (i.e. second order) {integral dt_1 V'(t_1) integral dt_2 V'(t2)/hbar**2}. So in perturbation theory it's the action int dt V;(t) which determines the broadening and this in turn is determined by two things : The strength of V' (the interaction in the interaction picture) AND the duration of the interaction. In a nutshell, when you raise T you shorten the time the perturbing electron spends in the vicinity of the emitting electron, hence the collision duration. This is why in perturbation theory and in the impact regime, the width decreases with T. You may wish to look up a recent publication from the Spectral Line shapes workshop Atoms 2014, 2 157-177, doi:10.3390/atoms2020157

BTW "the number of collisions with the target increases" is misleading(I assume you mean per unit time); It is true that iIn the impact approximation the collision FREQUENCY (for a given 'type' of collisions, e.g. velocity and impact parameter/partial wave, ) that matters[since we have an integral over all times of closest approach from -DT to DT divided by 2DT where DT->infinity and this proportional to the root of T[see PRA 37, 1488(1988)] , so that the mean number of collisions in a given time interval is proportional to the interval of course and the root of T; But this is offset by the shrinikng of the collsion duration. You can see all these easily from the standard (e.g. Griem's books) semiclassical electron impact calculations for hydrogen.