In such cases, significant breakdown of the BO picture is to be expected. For example, in molecular Rydberg states and in anions, where the outer valence electrons are bound by a fraction of an electron volt, the natural orbit frequencies of these electrons are not much faster (if at all) than vibrational frequencies. Of course, one should expect large corrections to such a model for electronic states in which 'loosely held' electrons exist. This picture is that described by the BO approximation.
Cesium atoms make such quantum jumps by absorbing. These clocks produce electromagnetic radiation, such as microwaves, with a precise frequency that causes atoms in the clock to jump from one energy level to another. This means it should be possible to develop a model in which the electrons 'follow' smoothly as the nuclei vibrate and rotate. We can measure time intervals the duration between two events most accurately with atomic clocks. Along with the thermal and free-fall (aka dynamical) time scales, it is used to estimate the length of time a particular star will remain in a certain phase of its life and its lifespan if hypothetical conditions are met. As a result, the electrons can adjust 'quickly' to the slow motions of the nuclei. In astrophysics, the nuclear timescale is an estimate of the lifetime of a star based solely on its rate of fuel consumption. In most atoms and molecules, the electrons orbit the nuclei at speeds much in excess of even the fastest nuclear motions (the vibrations). Complex laboratory systems measure the second with the highest achievable. The range of accuracy of this separation can be understood by considering the differences in time scales that relate to electronic motions and nuclear motions under ordinary circumstances. The modern world relies on precise timing, based on highly stable atomic clocks. The physical parameters that determine under what circumstances the BO approximation is accurate relate to the motional time scales of the electronic and vibrational/rotational coordinates.
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