The absence of certain LS states in atoms leads to the vanishing of several 6-j symbols. One of these vanishing 6-j's explains the absence of a certain jj coupling state in a nucleus, while the other explains the vanishing of a certain state for a system of three bosons. This is part of a continuing study of "companion problems." It is noted that the vanishing 6-j's play an important role for establishing partial dynamical symmetries. Whenever possible we offer alternate explanations that do not involve 6-j symbols. Extensions to vanishing 9-j symbols are also shown. Regge symmetries help to make connections between different topics.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics