 Photon fixed-target production threshold

For a photon of energy $h\nu$ hitting a stationary target of mass $m_2$, the incoming invariant energy satisfies $W^2=m_2^2{c}^4+2m_2{c}^{2}h\nu$. 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