# 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 ($$i=1 \text{ to } m$$) energy levels. More highly excited states ($$k=m+1 \text{ to } n$$) 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 ($$k=6 \text{ to } 27$$). 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 $$1 \text{to} m$$ may be written simply as

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

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

• I'm voting to close this question as off-topic because it's a pure physics question – Rory Alsop May 30 '19 at 10:54
• In the paper, the numbered equations go from 1 to 13, can you be more specific which ones you'd like to focus on, and what it is in the text about the equations that isn't clear? Right now you question is pretty broad. Thanks! – uhoh May 30 '19 at 16:03
• @uhoh I am concerned about equation (6) , I want to know how did we approximate this form. Thank you! – Amartya Mondal May 30 '19 at 17:20
• Okay I've added a quote of the beginning of that section, and using MathJax I've added Eq. 6 and labeled it to get you started. I think you can go back to your question and edit further and try make your question more specific. The text of the paper is long and detailed and works hard to explain much of the math, but the Solar corona is a specific, ionized environment where there may be some specialized thermodynamic assumptions that may not be obvious. – uhoh May 30 '19 at 22:34
• The more specific you can be, the better. If you can add a discussion of which parts you do understand in order to contrast with which parts you don't, that's even better! Rather than add more comments, it's better if you edit your question further and make your points clear there. Welcome to Stack Exchange! – uhoh May 30 '19 at 22:35