Determining the uncertainty of Eγ

To determine the uncertainty in Eγ we pick an angle for the neutron within [[math]\theta_n[/math], [math]\theta_n[/math] + Δ [math]\theta_n[/math]] and a momentum of the neutron between [[math]P_n[/math], [math]P_n[/math] + Δ [math]P_n[/math]].

What are reasonable Δ[math]\theta_n[/math] and Δ [math]P_n[/math]?

[math]P_n[/math] is determined by time of flight.

Knowns:

[math]m_n[/math] = 939.565 ± 0.00028 [math]MeV/c^2[/math]

d = 3 ± 0.005 m

t = 50 ± 1 ns

Fractional Uncertainties

[math]\frac{\delta_m}{m}=\frac{0.00028}{939.565}=0.00003%[/math]

[math]\frac{\delta_d}{d}=\frac{0.005}{3}=0.2%[/math]

[math]\frac{\delta_t}{t}=\frac{1}{50}=2%[/math]

[math]v=\frac{d}{t}=\frac{3 +/- 0.2%}{50 +/- 2%} = 0.2c +/- 2.2%[/math]