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2.3. Solving the system of statistical equilibrium equations

Let us now proceed to set the system of equations to calculate the relative population ratios.

For notation purposes, let us define:

Equation 15 (15)

so that eq. (2) reads (taking into account the possible effect of fluorescence):

Equation 16 (16)

or equivalently in matrix notation:

Equation 17 (17)

After rewriting the system to have the solution expressed in terms of the populations relative to the ground level n1 we are left with:

Equation 18 (18)

Eq. (18) is the linear system of equations that is solved by PopRatio.

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