Generalized Reich-Moore R -matrix approximation

A conventional Reich-Moore approximation (RMA) of R-matrix is generalized into a manifestly unitary form by introducing a set of resonant capture channels treated explicitly in a generalized, reduced R-matrix. A dramatic reduction of channel space witnessed in conventional RMA, from N_c × N_c full R-matrix to N_p × N_p reduced R-matrix, where N_c = N_p + N_γ, N_p and N_γ denoting the number of particle and γ-ray channels, respectively, is due to N_p < N_γ. A corresponding reduction of channel space in generalized RMA (GRMA) is from N_c × N_c full R-matrix to N × N, where N = N_p + N, and where N is the number of capture channels defined in GRMA. We show that N = N_λ where N_λ is the number of R-matrix levels. This reduction in channel space, although not as dramatic as in the conventional RMA, could be significant for medium and heavy nuclides where N < N_γ. The resonant capture channels defined by GRMA accommodate level-level interference (via capture channels) neglected in conventional RMA. The expression for total capture cross section in GRMA is formally equal to that of the full N_c × N_cR-matrix. This suggests that GRMA could yield improved nuclear data evaluations in the resolved resonance range at a cost of introducing N(N - 1)/2 resonant capture width parameters relative to conventional RMA. Manifest unitarity of GRMA justifies a method advocated by Fröhner and implemented in the SAMMY nuclear data evaluation code for enforcing unitarity of conventional RMA. Capture widths of GRMA are exactly convertible into alternative R-matrix parameters via Brune tranform. Application of idealized statistical methods to GRMA shows that variance among conventional RMA capture widths in extant RMA evaluations could be used to estimate variance among off-diagonal elements neglected by conventional RMA. Significant departure of capture widths from an idealized distribution may indicate the presence of underlying doorway states.