Neutron energy resolution in NaI detector

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[math]\displaystyle{ E_n = \frac{m}{2}\left( \frac{d}{t_n} \right)^2 }[/math]

[math]\displaystyle{ \delta E_n = -2\ E_n \frac{\delta t_n}{t_n} = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n }[/math]

• From NaI detector measurements [math]\displaystyle{ \delta t_n = 15\ ns }[/math]
• $mc^2 = 938\ MeV$