A question regarding the paper The wave function of a Bloch electron in a magnetic field by R.G. Chambers

Question

I was trying to read this paper:

http://iopscience.iop.org/article/10.1088/0370-1328/89/3/325/pdf

got stuck on some derivation just after equation (12), how did he arrive at $\Delta/R_Q = 1/4 n$ and $s_0^2/R_Q^2 = 1/n$ from the Quantization condtion: $\alpha \pi R_Q^2 =2\pi n$ and the previous equations before that condition?

I don't see it, thanks.