= Photon fixed-target production threshold
{title2=$h\nu_{\rm thr}=\frac{(\sum_i\mu_i)^2-m_2^2}{2m_2}c^2$}
For a <photon> of energy $h\nu$ hitting a stationary target of mass $m_2$, the incoming invariant energy satisfies $W^2=m_2^2c^4+2m_2c^2h\nu$. The massive multi-product threshold is the displayed value when $\sum_i\mu_i>m_2$. If the algebraic bound is nonpositive, the lower limit of allowed positive frequencies can be zero. A single final product instead fixes the frequency by invariant-mass equality, and a final massless particle can make a nominal threshold an infimum rather than an attained value.
// Target: classical-mechanics.bigb
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