Angular Correlation Functions for Compound Inelastic Nucleon Scattering

To aid the analysis of nucleon-$\gamma$ angular correlation results for target nuclei having zero and nonzero ground-state spins, the double-differential cross section has been evaluated in explicit form for compound inelastic scattering of spin-½ particles to first or to second excited states of nuclei having g.s. spin $0+,\frac{1}{2}+,1+,\frac{3}{2}+,\frac{3}{2}-,\frac{5}{2}+,\frac{7}{2}-$. In several instances, provision has been made for the coincident $\gamma$ radiation to be of mixed multipolarity or for cascades to include an unobserved intermediate $\gamma$-decay step preceding the $\gamma$ transition under observation. Theoretical results are illustrated quantitatively by correlation curves for inelastic neutron scattering at suitable energies around 3 MeV upon appropriate representative target nuclei (${\mathrm{Ge}}^{70}$, ${\mathrm{Zn}}^{66}$, ${\mathrm{Ni}}^{64}$, ${\mathrm{Fe}}^{56}$; ${\mathrm{Si}}^{29}$, ${\mathrm{P}}^{31}$; ${\mathrm{P}}^{32}$; ${\mathrm{S}}^{33}$; ${\mathrm{Cu}}^{63}$; ${\mathrm{Zr}}^{91}$; ${\mathrm{Co}}^{57}$, respectively).