Neutron Polarimeter

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Relativistic kinematic

energy dependence of outcoming neutron versus energy of incoming photons

[math] E = T + m[/math]
[math] E = p^2 + m^2[/math]

writing four-vectors:

[math] p_{\gamma} = \left( T_{\gamma},\ T_{\gamma},\ 0,\ 0  \right) [/math] 
[math] p_D     = \left( m_D,\ 0,\ 0,\ 0  \right) [/math] 
[math] p_{n} = \left( E_n,\ p_n\cos(\Theta_{n}),\ p_n\sin(\Theta_{n}),\ 0  \right) [/math] 
[math] p_{p} = \left( E_p,\ p_p\cos(\Theta_{p}),\ p_p\sin(\Theta_{p}),\ 0  \right) [/math] 

Doing four-vector algebra:

[math] p^{\mu}_{\gamma} + p^{\mu}_{D} = p^{\mu}_{p} + p^{\mu}_{n} \Rightarrow (p^{\mu}_{p})^2 = (p^{\mu}_{\gamma} + p^{\mu}_{D} - p^{\mu}_{n})^2 [/math]

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