Determination of nuclear spin states from measurement of the angular correlation function of emitted particles and. gamma. rays

A method of determining the spin states of nuclei is proposed and justified theoretically. It is based on measurement of the angular correlation function of particles and ..gamma.. rays emitted by the final nucleus in an excited state with spin J/sub f/ on transition to the ground state, the ..gamma.. rays being detected in different planes relative to the reaction plane. It is shown that this method gives a unique possibility for recovering the spin density matrix in transitions with J/sub f/ = L (L is the multipolarity of the ..gamma.. transition). The minimal number of planes in which it is necessary to measure the angular correlation function in order to determine the density matrix fully is found. Relationships between the components of the spin tensors of the density matrix and the polarization characteristics of even--even nuclei are derived. The experimental values obtained by this method for the density-matrix spin-tensor components, the substate populations, and the orientations of the tensor operators are compared with the theoretical spin characteristics calculated in the framework of the distorted-wave Born approximation with a finite-range interaction.