Level crossings and branch points studied by the multidimensional partitioning technique

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Abstract
The possibility of level crossings is discussed from a general multidimensional partitioning viewpoint. By extending the traditional motion of a self‐adjoint Hamiltonian to a self‐adjoint analytic family of operators, it is found that level intersections that appear fall into two mutually exclusive categories: the conventional diagonal one corresponding to Jordan blocks of order m = 1, and the nondiagonal one with m ≥ 2. Consequences with respect to some recent examples, such as Longuet‐Higgins “sign‐reversing loop” construction and the 1II near degeneracy in SiO, are discussed and examined.