# What/how do we mean/derive statistical equilibrium equation of certain energy levels?

While reading the research paper "Excitation of the Fe XIII Spectrum in the Solar Corona" by D.R. Flower and G. Pineau des Forets in the summary I found the concept of statistical equilibrium equation hard to understand. Please explain me the ways in which I can obtain these equations and what is the physical meaning of these?

1. Solution of the Statistical Equilibrium Equation

In coronal conditions, the full statistical equilibrium equations need be solved for only the first few ($$i=1 ext{ to } m$$) energy levels. More highly excited states ($$k=m+1 ext{ to } n$$) contribute only through the indirect process of electron collisional excitation followed by radiative cascade. In the case of Fe XIII, we solve the statistical equilibrium equations for the states of the ground $$3s^2 3p^2$$ configuration ($$m=5$$) and include the indirect contribution of the states of the excited $$3s 3p^3$$ and $$3s^2 3p 3d$$ configuration ($$k=6 ext{ to } 27$$). The error committed in neglecting all other bound states of the ion and the continuum is considered separately later in this Section. In this approximation, the statistical equilibrium equations of levels $$1 ext{to} m$$ may be written simply as

$$sum_{j=1}^{m} d_{ij} N_j=0 ag{6}$$

with $$d_{ji}$$ defined by… (several long expressions)