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I am searching for electron-collision induced depopulation rates for the atomic states of Helium, while it is embedded in a plasma, but from a higher to a lower level, i.e. I want to be following the electron populations as they cool down from several million Kelvin to a few hundred Kelvin, in a time-dependent manner.

Usually, people give the excitation rates from the ground level to higher levels, as in e.g. this paper, and, but I am looking now for the depopulation levels from any higher level to a lower level.

Specifically, the transition rates from lower level i to higher level j follow the form

$$ q(i\rightarrow j) = p_{ij} \times \frac{1}{\sqrt{k_BT}} \times \exp(-\Delta E_{ij}/k_B T) $$ where $\Delta E_{ij}$ is the energy level difference, $T$ the gas temperature, and $p_{ij}$ is encapsulating a bunch of natural constants and the electron-energy dependent collision strength. Now I'd just be interested in the values of $$ q(i\leftarrow j)$$ or equvalently $p_{ji}$, but my atomic physics is quite a while ago, so I'd appreciate any pointers to literature to compute those numbers.

I presume if I get the steady-state populations from somewhere, I can calculate the transition rates assuming detailed balance, but then I'd further need to assume that free electrons in the plasma are the dominant drivers of population/depopulation.

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