Particle and Photon Decay of Nuclei Following Electroexcitation

Angular-correlation formulas are derived for a coincidence experiment in which an electron scattered inelastically by a nucleus is detected simultaneously with a heavy particle or photon emitted by the nucleus subsequently to its electroexcitation. The excitation of the nucleus is treated in first Born approximation; i.e., single-photon exchange between electron and nucleus is assumed. The subsequent decay depends on the properties of the emitted particle. Within the framework of the one-level resonance model (i.e., assuming that the level matrix is diagonal), the formulas derived are valid for heavy-particle as well as photon decay. Only slight modifications are necessary, however, to take into account properly the effects of coupled channels for particle decay. The present results differ from those of a previous investigation in that (a) overlapping excited levels are included, as found in most applications (we assume, however, that the level matrix is diagonal), (b) photons as well as spin-½ and spin-0 particles are considered as being emitted in the nuclear decay, and (c) summations over all magnetic quantum numbers were carried out. Examples considered were excitations of isolated $E1\mathrm{}$ and $M1\mathrm{}$ levels of a spinless nucleus, and of the overlapping $E1\mathrm{}$ giant resonance levels of ${}_{}{}^{12}{}_{}{}^{}\mathrm{C}$, evaluated by $R$-matrix theory.