  Avoided crossings of level pairs with opposite slopes can form potential
energy curves for the external degree of freedom of quantum particles. We
investigate nonadiabatic decay of metastable states on such avoided crossings
(MSACs) using diabatic and adiabatic representations. The system is described
by a single scaled adiabaticity parameter, $V$. The time-independent
two-component Schr\"odinger equation is solved in both representations, and the
nonadiabatic lifetimes of MSACs are determined from a wave-function flux
calculation and from the Breit-Wigner formula, leading to four lifetime values
for each MSAC. We also solve the time-dependent Schr\"odinger equation in both
pictures and derive the MSAC lifetimes from wave-function decay. The sets of
six non-perturbative values for the MSAC lifetimes agree well, validating the
approaches. As the adiabaticity parameter $V$ is increased by about a factor of
ten, the MSAC character transitions from marginally to highly stable, with the
lifetimes increasing by about ten orders of magnitude. The $\nu$-dependence of
the lifetimes in several regimes is discussed. Time-dependent perturbation
theory is found to yield approximate lifetimes that deviate by $\lesssim 30\%$
from the non-perturbative results, while predictions based on the
semi-classical Landau-Zener tunneling equation are found to be up to a factor
of twenty off, over the ranges of $V$ and $\nu$ studied. The results are
relevant to numerous atomic and molecular systems with quantum states on
intersecting, coupled potential energy curves.
