Conversion TDC to Energy

Calculation

[math]t_n[/math]: Neutron time of flight

[math]t_{\gamma}[/math]: Gamma time of flight

d: Distance between detector and target.

d for polarized case: [math]d_{pol}[/math] = 91.25 inches = 231.775 cm.

d for unpolarized top detector: [math]d_{unpol top}[/math]=96.25 inches = 244.745 cm.

d for unpolarized side detector: [math]d_{unpol side}[/math]=91.39 inches = 232.131 cm.

[math]t_n-t_{\gamma}=\frac{d}{v}-\frac{d}{c}=d(\frac{1}{v}-\frac{1}{c}[/math])

=> [math]v=\frac{1}{\frac{t_n-t_{\gamma}}{d}-\frac{1}{c}}[/math]

[math]\beta_n=\frac{v}{c}[/math]

[math]\gamma_n=\sqrt{\frac{1}{1-\beta^2}}[/math]

[math]E_{tot}=M_n\gamma_nc^2[/math]

[math]E_k=E_{tot}-M_nc^2[/math]

Data

For data go to Link below:

[1]