Theoretical basis for the diabatic representation at mode-conversion points

Establish a rigorous theoretical basis for the diabatic representation that permits spin flips at mode-conversion points in semiclassical treatments of spin–orbit coupling, and ascertain the conditions under which this representation is valid when resolving singularities in coupled-channel WKB analyses.

Background

In semiclassical approaches to spin–orbit coupling, the coupled-channel WKB method treats spin as an adiabatic channel but encounters singular dynamics at mode-conversion points where adiabatic Hamiltonians cross. A diabatic representation has been proposed to allow spin flips at these points, removing singularities, and it has shown numerical success.

The paper explicitly notes that despite practical effectiveness, the diabatic treatment remains theoretically ambiguous and lacks a firm foundation. A rigorous framework would clarify its validity and limitations and integrate it consistently into semiclassical periodic-orbit theory.