Ro-Vibrational Hamiltonian of Three Body Systems Near Collinear Configurations

The paper derives I, h, a, and the reduced Hamiltonian H in Jacobi shape coordinates, then proves H admits a continuous extension to the collinear set by analyzing the potentially singular rotational terms and showing (J1/sinφ)→0 under a body-frame choice that enforces ω2(0)=0; it also computes the explicit collinear value H(0) via a Legendre transform . The model reproduces the same I, I−1, aμ, Aμ, and g, the same explicit H, and uses the same key mechanism (ω2(0)=0 so the 1/sinφ and 1/sin²φ terms vanish). It slightly over-claims J2=O(sinφ), which is stronger than needed; the paper only needs bounded J2 and (J1/sinφ)→0 to conclude continuity . Overall, they agree on the result and method.