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I have a question about the derivation of the Fermi golden rule in Kenneth Krane's Introduction to Nuclear Physics. I understand everything up to equation 9.20. However, it is unclear how he goes directly to equation 9.21. Here is equation 9.20,

## d\lambda = \frac{2\pi}{\hbar}g^{2} |M_{fi}|^{2} \frac{(4\pi)^{2}}{h^{6}c^{2}} p^{2} (Q - \sqrt(p^{2}c^{2} + m_{e}^{2}c^{4}) -m_{e}c^{2})dp##

Which is then followed by equation 9.21,

## N(p)dp = Cp^{2}q^{2}dp ##

I under stand that C has the constants not related to p. My question is how did he go from ##d\lambda## to ##N(p)dp##. This says that ##d\lambda = N(p)dp## which is unclear to me. Can someone explain that part to me.

Thank you.