High Momentum Transfer (quasi-elastic peak)

According to fetter and walecka the width at half maximum of the high momentum transfer (q>>$k_f$) quasielastic peak is related to the Fermi momentum.
This is a question from f&W quantum theory of many body particles text book 5.12 precisely. It basically asks us to show a relationship between the plot and the fermi momentum.

I do not understand the nature of this problem. Therefore I honestly do not know how to ask the question.
Can anyone hear my plea and give me some insight?

Thank You!