Classical sum rules and spin correlations in photoabsorption and photoproduction processes

In this paper we study the possibility of generalizing the classical photoabsorption ($\gamma a \to b c$) sum rules, to processes $b c \to \gamma a$ and crossed helicity amplitudes. In the first case, using detailed balance, the sum rule is written as $\int_{\nu_{th}}^\infty {\frac{{d\nu}}{\nu}} K\Delta \sigma_{Born} (\nu)=0$ where $K$ is a kinematical constant which depends only on the mass of the particles and the center of mass energy. For other crossed helicity amplitudes, we show that there is a range of values of $s$ and $t$ for which the differential cross section for the process $\gamma b \to a c$ or $a c \to \gamma b$ in which the helicities of the photon and particle $a$ have specific values, is equal to the differential cross section for the process in which one of these two helicities is reversed (parallel-antiparallel spin correlation).