Neutron energy resolution with start signal from 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 = -\frac{2 \sqrt{2}}{\sqrt{m} d}\ E_n^{3/2} \delta t_n  }[/math]

• [math]\displaystyle{ \delta t_n = 15\ ns }[/math]
• [math]\displaystyle{ mc^2 = 938\ MeV }[/math]

[math]\displaystyle{  d = 0.5\ m: \ \ \   ( \delta E_n/E_n ) = 0.83\ E_n^{1/2}\ MeV  }[/math]
[math]\displaystyle{  d = 0.7\ m: \ \ \   ( \delta E_n/E_n ) = 0.59\ E_n^{1/2}\ MeV  }[/math]
[math]\displaystyle{  d = 1.0\ m: \ \ \   ( \delta E_n/E_n ) = 0.42\ E_n^{1/2}\ MeV  }[/math]
[math]\displaystyle{  d = 1.5\ m: \ \ \   ( \delta E_n/E_n ) = 0.28\ E_n^{1/2}\ MeV  }[/math]
[math]\displaystyle{  d = 2.0\ m: \ \ \   ( \delta E_n/E_n ) = 0.21\ E_n^{1/2}\ MeV  }[/math]