Study of beta-delayed neutron with proton-neutron QRPA plus statistical model

β-delayed neutron is known to be important for safety operation of nuclear reactor and prediction of elemental abundance after freeze-out of r-process. A lot of researches on it have been performed. However, the experimental data are far from complete since the lifetime of most of the relevant nuclei is so short that one cannot measure in a high efficiency. In order to estimate half-lives and delayed neutron emission probabilities of unexplored nuclei, we developed a new theoretical method which combines a proton-neutron quasi-particle random-phase-approximation and the Hauser-Feshbach statistical model. The present method reproduces experimentally known β-decay half-lives within a factor of 10 and about 40% of within a factor of 2. However it fails to reproduce delayed neutron emission probabilities. We discuss the problems and remedy for them to be made in future. (author)