Statistical assignment of neutron orbital angular momentum to a resonance

摘要

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 gGamma(n) is an l-wave resonance. The probability is calculated from the Bayes theorem on conditional probability. For each 1, the probability density function (pdf) of gGamma(n) was derived from the X-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 Ag-109 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 Al-27 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.