Recurrence of the excited states of nuclei and time coherency of the de Broglie wave in 16O+n resonances

From the requirement of the time periodicity of a (quasi) stable state, frequencies of the normal modes, which compose the state, are commensurable (integer ratios) with each other, and the excitation energies Ex are written as a sum of inverse integers. We propose an expression: Ex = GΣ1/n, where n = integers and G = 34.5 MeV. Recurrence time is defined as LCM(nj) x τo, where τ0 = 2πℎ/G = 1.20 x 10-22s. LCM vs. Ex are illustrated for all possible nj of 2 and 3 normal modes. In 16O +n resonances, integer ratios are found between the recurrence frequencies of 17O and the de Broglie wave frequencies of incident neutron, meaning time coherency between them. A simple branch pattern is found in 16O +n resonance levels. (author)