= Fixed-target production threshold
{title2=$E_1\geq\frac{(\sum_i\mu_i)^2-m_1^2-m_2^2}{2m_2}c^2$}
For an incident particle of <rest mass> $m_1$ and total energy $E_1$ hitting a stationary target of mass $m_2>0$, <four-momentum conservation> gives $W^2=m_1^2c^4+m_2^2c^4+2m_2c^2E_1$. Applying the <relativistic collision mass threshold> gives the displayed necessary condition. The incoming energy must also satisfy $E_1\geq m_1c^2$; other conserved quantum numbers or reaction dynamics can impose further restrictions.
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