Statistical Assignment of Neutron Orbital Angular Momentum to a Resonance

We have derived formulas in a general form for suggesting the neutron orbital angular momentum quantum number l to each neutron resonance if it is not identified experimentally. By assuming the (2J + 1) law of level density, these general formulas are reduced to the formulas found in previous works. The suggestion of l is based on the probability that a resonance having a certain value of g_n is an l-wave resonance. The probability is calculated from the Bayes theorem on conditional probability. For each l, the probability density function (pdf) of g_n was derived from the ² distribution proposed by Porter and Thomas. The pdf takes into account two possible channel spins that result in the same total spin for a given l larger than zero. Meanwhile, regardless of the resolution of measurement, we suggest adopting the level density as the prior probability in the Bayesian approach, as Gyulassy et al. did. As a sample problem, we presented the result of l-assignment for ¹⁰⁹Ag resonances. The SUGGEL code, in which the methodology is incorporated, correctly assigned l's for 67 among 70 resonances for which l's had been determined experimentally. The other test for ²⁷Al showed the applicability of the code as a preanalysis tool, even though such applicability is limited to a certain extent for light nuclides. The use of the code SUGGEL is expected to reduce the number of repeated runs of a fitting code such as SAMMY, thus reducing time and effort for the extraction of resonance parameters from measurements.