Doorway states and primary neutron capture gamma-rays

Abstract

The Projection Operator formalism of nuclear reactions utilizing the doorway state assumption is applied to neutron capture reactions in the one-photon approximation. The transition matrix divides into three parts, a direct capture term, a semidirect term proceeding through doorway states and a compound nuclear part. The same doorway states contributing to semidirect capture are involved in the resonance term. The partial radiation width amplitude can be written, Γ yij 1 2 = C 1S jkΓ nio 1 2 +C 2jΓ io 1 2 + S jkΓ yiδDk 1 2 +Γ yiδDk 1 2 +Γ yij 1 2 ( random) . Γ nio , S jk 2 are the resonance and final state reduced neutron widths. C 1 and C 2 j are transition matrix elements from the initial single-particle state to the lowlying single-particle state k and the final state j, respectively. The two terms have possible enhancement factors. The third and fourth terms are doorway contributions. The giant dipole resonance is included in the theory. Expressions for the correlation coefficients C( Γ nio , Γ yij ), C( Γ yij , Γ yij′ ), C( S jk 2, Γ yij ) are given. An isolated doorway responsible for radiation to several final states and also connecting entrance channel and compound nucleus results in the first two coefficients being unity. The theory is extended to include the two-group model of the compound nucleus. Application of the theory is made specifically to neutron capture experiments in 93Nb, 165Ho, 166Er, 169Tm, and 183W. Capture ψ-ray results to-date can be understood in terms of the theory.