A quasi-static treatment of multiple phase jumps

A quasi-static, WKB-type treatment accounts well for the surprising phase jumps that are odd multiples of pi, (1 + 2n)pi, found as a molecular system journeys adiabatically in a configuration coordinate plane that contains several points of degeneracies. We show that the number n in the phase jump is an integer close to |n '| that appears in the expression for the complex wavefunction amplitude valid (approximately) for times close to when the phase jump occurs: [GRAPHICS] (delta T is a shifted and rescaled trajectory-time parameter and theta is a numerical fraction (< 1) which depends on the adiabaticity of the motion.) The central quantity n ' is local, i.e., depends on the values of the parameters in the Hamiltonian only at the beginning of the trajectory and at the instant of the phase jump.