差分
このページの2つのバージョン間の差分を表示します。
| 両方とも前のリビジョン前のリビジョン | |||
| research:memos:kinematics:relativistic_kinematics [2022/01/04 18:25] – [TRIUMF Kinematics Handbook: Sec. V Relativistic Kinematics] kobayash | research:memos:kinematics:relativistic_kinematics [2022/01/09 12:16] (現在) – [TRIUMF Kinematics Handbook: Sec. V Relativistic Kinematics] kobayash | ||
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| \tan\theta_3 &= \frac{\sin\theta_3^*}{\gamma_2^*\left(\delta_{21}^*+\cos\theta_3^*\right)}\\ | \tan\theta_3 &= \frac{\sin\theta_3^*}{\gamma_2^*\left(\delta_{21}^*+\cos\theta_3^*\right)}\\ | ||
| \tan\theta_4 &= \frac{1}{\gamma_2^*}\cot\frac{\theta_3^*}{2} | \tan\theta_4 &= \frac{1}{\gamma_2^*}\cot\frac{\theta_3^*}{2} | ||
| - | \end{align}|\begin{align} | + | \end{align} |
| \tan\theta_3 = \frac{\sin\theta_3^*}{\gamma_2^*\left(1+\cos\theta_3^*\right)}\\ | \tan\theta_3 = \frac{\sin\theta_3^*}{\gamma_2^*\left(1+\cos\theta_3^*\right)}\\ | ||
| - | \end{align}| | + | \end{align} |
| | 8. lab to c.m. angle transformation ($\theta_\mathrm{lab} \rightarrow \theta_\mathrm{cm}$) |\begin{align} | | 8. lab to c.m. angle transformation ($\theta_\mathrm{lab} \rightarrow \theta_\mathrm{cm}$) |\begin{align} | ||
| \cos\theta_3^*=-\frac{\delta_{23}^*(\gamma_2^*\tan\theta_3)^2}{(\gamma_2^*\tan\theta_3)^2+1}\pm\sqrt{\left(\frac{\delta_{23}^*(\gamma_2^*\tan\theta_3)^2}{(\gamma_2^*\tan\theta_3)^2+1}\right)^2-\frac{\delta_{23}^{*2}(\gamma_2^*\tan\theta_3)^2-1}{(\gamma_2^*\tan\theta_3)^2+1}} | \cos\theta_3^*=-\frac{\delta_{23}^*(\gamma_2^*\tan\theta_3)^2}{(\gamma_2^*\tan\theta_3)^2+1}\pm\sqrt{\left(\frac{\delta_{23}^*(\gamma_2^*\tan\theta_3)^2}{(\gamma_2^*\tan\theta_3)^2+1}\right)^2-\frac{\delta_{23}^{*2}(\gamma_2^*\tan\theta_3)^2-1}{(\gamma_2^*\tan\theta_3)^2+1}} | ||
