Spin interference in the spin density matrix of a compound nucleus in reactions of nuclear fission by cold polarized neutrons

Spin density matrices of neutron resonance states of a compound nucleus formed in the reaction of capture of a polarized neutron by a non-oriented target nucleus for different directions of neutron polarization vector are constructed within the quantum fission theory. The obtained spin matrices are used to calculate T-odd asymmetries in differential cross sections of ternary nuclear fission with the emission of different third particles. It is demonstrated that the expressions for T-odd asymmetries in the cases of neutron polarization direction (p)\vec]_n\vec p_n along the x and y axes in the laboratory reference frame differ by the values of the unified correlator of the form ( (p)\vec]_n , (k)\vec]_LF ,(k)\vec]₃ ] )\left( {\vec p_n ,\left {\vec k_{LF} ,\vec k_3 } \right]} \right) (where (k)\vec]_LF\vec k_{LF} and (k)\vec]₃\vec k_3 are the wave vectors of a light fission fragment and the third particle, respectively), and are transformed into one another if the laboratory reference frame in which (p)\vec]_n\vec p_n is directed along the x axis is rotated to a laboratory reference frame in which (p)\vec]_n\vec p_n is directed along the y axis. It is shown that T-odd TRI and ROT asymmetries are associated, respectively, with the odd and even components of the amplitudes of the angular distribution of third particles perturbed by the collective rotation of a polarized fissile nucleus, and each of these amplitudes can be considerably amplified (or suppressed) relative to one another due to the interference from fission amplitudes of pairs of neutron resonances sJ _s and s′J _s′ .