Neutron energy resolution in NaI detector

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$E_n = \frac{m}{2}\left( \frac{d}{t_n} \right)^2$

$\delta E_n = -2\ E_n \frac{\delta t_n}{t_n} = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n$

• From NaI detector measurements $\delta t_n = 15\ ns$
• $mc^2 = 938\ MeV$

[math] d = 0.5 m: \ \ \   \delta E_n = 0.83\ E_n^{3/2}\ MeV [/math]

[math] d = 1.0 m: \ \ \   \delta E_n = 0.42\ E_n^{3/2}\ MeV [/math]

[math] d = 1.5 m: \ \ \   \delta E_n = 0.28\ E_n^{3/2}\ MeV [/math]

[math] d = 2.0 m: \ \ \   \delta E_n = 0.21\ E_n^{3/2}\ MeV [/math]